Engineering Structures 29 (2007) 1889–1902www.elsevier.com/locate/engstruct

Built in dampers for family homes via SMA: An ANSYS computationscheme based on mesoscopic and microscopic experimental analyses

V. Torraa,∗, A. Isalguea, F. Martorella, P. Terriaultb, F.C. Loveyc

a CIRG-DFA-ETSECCPB, Univ. Pol. de Catalunya, E-08034 Barcelona, Catalonia, Spainb LAMSI, Ecole de technologie superieure, H3C 1K3, Montreal, Quebec, Canadac Centro Atomico Bariloche, Instituto Balseiro, 8400 S.C. de Bariloche, Argentina

Received 14 November 2005; received in revised form 16 August 2006; accepted 17 August 2006Available online 28 November 2006

Abstract

Shape memory alloys (SMA) are good candidates for solid state dampers because of their large recoverable strain and hysteresis. In this work,experimental analysis and modeling of the thermomechanical behavior for two SMAs is done. The SMA models are developed and included ina finite element simulation environment (ANSYS). Using these developing tools, a complete damping solution for a family house is outlined.The paper presents the design and optimization methodology for the dampers, analyzes their performance, and quantifies the relevant physicaleffects from the experimental measurements. The simulation results show that the SMA dampers are capable of reducing the maximum oscillationamplitude induced by “El Centro” accelerations by a factor 2 and that they dissipate 50% of the energy transmitted to the structure. Furthermore,SMA dampers constitute a passive, unsupervised damping solution appropriate for family houses.c© 2006 Elsevier Ltd. All rights reserved.

Keywords: Earthquake damping; Passive control; Shape memory alloys (SMA); Martensitic phase transformation; Diffusion; Self-heating; Finite element analysis

1. Introduction

Increasing the quality of life is one of the main goals ofsmart materials and systems. In houses, one of the practicalproblems is the suppression/reduction of external perturbationphenomena (vibrations/oscillations) via the integration ofactuators and sensors in the structure [1]. In Civil Engineering,two different kinds of oscillation phenomena can be considered:first, repeated or “continuous” oscillations with differentamplitude scales, such as those induced by wind and rainin large structures (sky-scrapers, high towers, and stayedcables in bridges); second, the particular situation inducedby earthquakes: the action of scarce groups of large wavesafter several years of complete inactivity. This situation isdifferent from those considered in other technical areas, suchas Mechanical Engineering, where other time scales may beconsidered. One example of such phenomena includes groups

∗ Corresponding address: Polytechnical University of Catalonia, CIRG-DFA-ETSECCPB, C/. Gran Capita s/n, Campus Nord B-4, 08034 Barcelona,Spain. Tel.: +34 934016859; fax: +34 934015972.

E-mail address: vtorra@etseccp6.upc.es (V. Torra).

0141-0296/$ - see front matter c© 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2006.08.028

of oscillations occurring in relatively short time interval (i.e.,one or two weeks), such as satellite launching or the continuouseffects in wheels, for instance in car driving.

The use of classical dampers, for instance, in reinforcedisolated buildings (e.g. rubber–lead bearings) after an eventrequires the recentering of devices and, also, appropriatestructure displacements are required to renew the bearingsafter a few years. The actual development of smart systemsfor use in damping of sky-scrapers, high towers, and stayedcables in bridges uses dampers based in magneto-rheologicalfluids [2] with semi-active control systems. Eventually, usingtuned masses when appropriate. These, and similar devices,need supervision and maintenance. For instance, the problemsintroduced by the eventual long time intrinsic instability ofthe damping fluid or the changes in control hardware andsoftware modifying/affecting the proprietary programs need tobe carefully solved. In fact, all active devices are inappropriateand expensive for relatively small constructions: at extremelylong times (several decades), a well guaranteed passive methodis a better approach.

In the recent literature, Shape memory alloys (SMA) [3,4] are suggested for damping in civil structures [5–12].

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Fig. 1. Left: External view of the sample family house. Right: Structural sketch of the house.

The singular properties of the SMA i.e., the shape memoryeffect, the pseudoelasticity, or the hysteresis cycle are dueto a martensitic thermoelastic phase transformation betweenmetastable phases. SMA can be used as sensors and/oractuators and, also, their hysteresis cycle, which convertswork (oscillation energy) into heat, allows the use of SMA(initially, in the parent phase) as dampers with recenteringcapabilities (as opposed to working in the martensite phasewithout recentering). In the passive application domain, withoutexternal power, the practical SMA can be classified into twogroups, the Cu-based and the NiTi alloys. There are alwayssome possible tunable actions (or use of semi-active controlmethods) for SMA, but the main interest for use on the CivilEngineering time scales focuses on their use as passive deviceswithout continuous technical supervision or, eventually, via thedevelopment of passive self-adjusting methods.

The use of SMAs for earthquake damping requires adeep knowledge of static and dynamic SMA and structureproperties. Also, an evaluation of the long time diffusivecontributions related to atomic order evolution is required [4,12–15]. For instance, the devices need to be guaranteed afterseveral decades under the action of summer–winter temperatureeffects. Any evolution (macroscopic or microscopic) should besuppressed or, at least, controlled or, at least, acknowledged.The applicability of each alloy must be assured for eachapplication. The particular applicability of NiTi in the healthdomain (i.e., orthodontic and surgical devices) [3] does notimply automatically an excellent behavior in other domains.The correct response of SMA dampers requires avoiding theplastic deformation associated with cycling, at high stress andtemperature, which progressively increases the damper length.The accumulated deformation may be practically suppressedby keeping the damper inside the recoverable limits defined bythe pseudoelastic window (PEW). The PEW is determined bythe material composition and its thermomechanical treatment,which ensures an appropriate material behavior. Some recentapplications fail to ensure a guaranteed behavior by, apparently,not considering the effects associated with temperature changes(summer–winter or self-heating) [16,17].

Light buildings, such as single or double floor family houses,under the effects of an earthquake (i.e. “El Centro” [18]),

suffer oscillation amplitudes close to 10 cm and reaction forcesunder 800 kN. These buildings are usually unprotected againstearthquakes due to the cost of actual damping systems and theirmaintenance. To illustrate the damping capabilities of SMA, wehave designed a building [19] according to structural Spanishstandards [20]. Fig. 1 left shows a general view of the house(ground area 11.5 × 16.6 m2). It is a two story building withapproximately 200 m2 on the ground floor and 100 m2 onthe first floor. The structure has two main sections divided bya ground garden. The front section has a single floor with asecond garden on the roof establishing an excellent view fromthe main living area (the second floor in the back section). Thestructure of the building has been designed with steel beamsto increase its robustness. Fig. 1 right depicts the completebeam structure according to the structural requirements inBarcelona. The possible emplacement for the dampers in theportico diagonals is also indicated. In this paper, we focus ourefforts on the damping of the single floor section which has thehigher load due to the elevated garden.

The goal of this work is to reduce the oscillation amplitudesby at least a factor 2, thereby avoiding structural damagein the building (oscillation amplitudes under the steel plasticdeformation) and providing a self-recentering capacity. Thesystem is passive and must not require supervision. Thedampers are designed to work optimally for a given earthquakemagnitude (6.0–7.0 degrees in the Richter scale as, forinstance, the earthquake “El Centro” used in simulation). Forevents below the nominal level, neither the dampers nor thestructure suffer any damage. Earthquakes in the nominal rangemay produce damage in the dampers as they dissipate themechanical energy. After the event, it is necessary to revisethe dampers. For larger earthquakes, both the dampers and thebuilding structure may suffer structural damage and must bechecked afterwards. In this worst situation, the dampers are stillable to reduce the oscillation amplitudes by a factor of nearlyone half and recenter the structure due to the material’s largerecoverable strain.

The main target of this work is to provide a passive andunsupervised damping solution with recentering capabilitiesfor family houses (light civil structures) via appropriatelyguaranteed SMAs. The paper furnishes a complete damping

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Fig. 2. Schematic behavior of the hysteresis cycles in σ , ε, T representation.

solution. In this work, the SMA damper characteristicsrequired for this application are described. Once the relevantSMA properties for Civil Engineering are outlined and thehysteresis cycle and temperature effects modeled, the housestructure is established and the damping capabilities of thissolution are shown by simulating the house response underseveral earthquake events extracted from the literature usingANSYS [21]. The paper is divided into three parts. The firstpart contains an outline of the SMA properties especiallyconsidering all necessary conditions for this application(Sections 2 and 3). The second part is devoted to aphenomenological model adapted to ANSYS requirements(Section 4). The third part centers on the dynamical simulation(Section 5). Remarks and improvements are presented in theconclusions.

2. Basic SMA behavior

The origin of the peculiar properties of SMA is afirst-order solid–solid phase transformation between twometastable phases with hysteresis cycle. In single crystals,this thermoelastic martensitic transformation produces ashape change (shear type) inducing length change of up to10% in the appropriate crystallographic direction (Fig. 2).Martensitic transformations may be induced by stress (σ )

and temperature (T ). In the phase coexistence betweenparent and martensite, the macroscopic coupling between thestress and temperature is related by the Clausius–Clapeyroncoefficient (CCC) (defined by the slope α = dσ/dT ) [3,22].Classically, in temperature induced transformations withoutexternal stresses, the hysteresis cycle may be described by fourtemperatures. Starting from austenite (high temperature phase),Ms (martensite start) establishes the initial appearance ofmartensite, and Mf (martensite finish) the complete conversionto martensite. The backwards process starts with As (austenitestart). The end of the retransformation process is characterizedby Af (austenite finish) with the complete recovery of the parentphase.

The Fig. 2 depicts the hysteresis cycle for different workingtemperatures. As the temperature increases, the critical stress(σcs) necessary to initiate the phase transformation also in-creases (σcs,T 1 < σcs,T 2 < σcs,T 3) according to thermody-namic formalism (i.e., Clausius–Clapeyron equation [23]). Thecycle is not modified by this shift, but it is necessary to con-sider that the working temperatures near the spontaneous trans-formation temperature (martensite start or Ms) may prevent the

return to parent phase in the unloading process due to the hys-teresis width (1σh) (see, point a in Fig. 2). Temperatures whichare too high (>T3) may produce a stress which overcomes theplastic deformation level (σpd) for a given strain, producing apermanent deformation in the alloy or, eventually, its fracture.The macroscopic pseudoelasticity or the slope (dσ/dε) in thetransformation zone, the hysteresis in coordinates of stress (σ ),strain (ε) and temperature (T ), and the Clausius–Clapeyronequation are the more relevant thermomechanic macroscopicproperties in damping applications. These properties dependon the material characteristics, the sample preparation, and theevolution of the sample while cycling (see Figs. 3 and 4).

3. Experimental analysis of SMA

In this work, the applicability of two different SMA arestudied. The first is CuAlBe, a Cu-based polycrystalline alloy.Wires of CuAlBe of several diameters were produced andfurnished by Trefimetaux, France in the years 2003 and 2004.For the cast AH140, the reference data are: Ms = 255 K; Mf =

226 K; As = 253 K; Af = 275 K. The chemical compositionin weight per cent is: Al = 11.8%; Be = 0.5%; Cu = 87.7%.The samples were cut, when necessary, by a low speed diamondsaw (ISOMET), mechanically polished with fine grinding paperand, eventually, electropolished. The standard heat treatmentfor Cu-based alloys consists of an appropriate homogenizationor betatization via a short time at high temperature (1123 K),followed by a fast quench in water at room temperature (293 K)and a long aging at temperatures between room temperature and373 K.

The second alloy is NiTi. The analysis carried out in NiTiuses mostly wires with diameters of 0.5 mm, surface as “hardblack oxide” (Fig. 3(a)), and 2.46 mm with surface “lightoxide” (Fig. 3(b)) of a superelastic Ni–Ti alloy from SpecialMetals [11], which is used “as furnished” (55.8 wt% of Ni). Inthis situation, from TEM analysis, the grain size is determinedto be around 50 nm. In addition, some samples prepared froman alloy with 44.1 wt% Ti and 55.9 wt% Ni with wire length80 mm and diameter 0.5 mm are also studied (Fig. 3(c)).The preparation process consists of a further heat treatmentof the “as received” wire followed by mechanical cycling.That is, aging at 673 K for 30 min followed by 15 stabilizingmechanical cycles at room temperature at a strain rate of0.1 mm/s with a maximal deformation of 4%.

3.1. Experimental setup

As SMA are relatively new materials and their applicationto Civil Engineering is innovative, there are no establishedmeasurement and characterization standard procedures (asingle ASME criteria related to SMA is available, whichonly specifies the determination – qualitative information –of characteristic temperatures [24]), and ad hoc proceduresneed to be used. To characterize the behavior of these alloys,we have used four types of complementary experimentalmeasurements. (1) For thermomechanical and transient analysis(force or stress, deformation or strain, temperature and time),

1892 V. Torra et al. / Engineering Structures 29 (2007) 1889–1902

Fig. 3. Shapes of the hysteresis cycle and bilinear models in NiTi. (a) Thin wire (diameter: 0.5 mm). (b) Thick wire (diameter 2.46 mm after 130 fast cycles).(c) Thin wire general hysteresis shape after heat treatment.

Fig. 4. Hysteretic behavior for CuAlBe and NiTi alloy. Progressive creep on cycling for samples with standard heat treatments.

an INSTRON 5567 with cooler–heater chamber 3119-005 anda Materials Test System MTS 810 were used. For thinnerNiTi wires, an ENDURATEC Bose ELF 3200 testing machinehas been used. Also, for long time analysis, equivalent low-cost home-made devices are used. (2) For temperature inducedtransformations, calorimetric equipment (such as the Q1000DSC of TA Instruments), and resistance measurements provideinformation about the transformation temperatures at zerostress. (3) The long time analysis is mostly measured usingdata with more than 4 figures (resolution near 1 in 10,000) forresistance measurements R(t, T ). (4) Also, when necessary, X-rays and TEM or HRTEM are used to characterize the samples’

structure and optical microscopy is used to characterize graingrowth.

3.2. Relevant SMA behavior for Civil Engineering

Our dampers are based on the physical properties of theSMA. So, the relationship between stress–strain–temperature isthe determinant for the correct response of these dampers. Allthe phenomena that affect this relationship must be evaluatedto ensure a long time guaranteed system. In this section, wereview and quantify the effects that must be considered for thisapplication.

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Fig. 5. Permanent deformation (or creep) with cycling in CuAlBe alloy. (a) Standard heat treatment. (b) Enhanced thermomechanical treatment that reduces remnantdeformation in samples.

Table 1Experimental CCC values for the studied CuAlBe and NiTi alloys (SM = Special Metals)

Samples CuAlBe (Nimesis) CuAlBe (Trefimetaux) NiTi (SM) NiTi (SM)

CCC (MPa/K) 2.12 2.26 6.23; 6.59 6.38; 5.94Diameter (mm) 1.6 3.4 0.5 2.46Cycles realized 1–3 1–3 1 and 130 1 and 130

3.2.1. Permanent deformation and heat treatmentThe permanent deformation of the alloy (i.e., a cumulative

“SMA creep”) is probably the most important problem in thisapplication. If the SMA length increases permanently withcycling, the practical strain is reduced along with the amountof mechanical energy which is converted into heat. If the SMAcreep is large enough, the lower oscillation amplitudes maynot even start the transformation in the alloy, and the energydissipation is zero. Furthermore, the reaction force produced bythe dampers is zero or greatly reduced. The preparation of SMAis crucial for keeping permanent deformation under acceptablevalues and avoiding the modification of the hysteresis cycle.Fig. 4 shows the behavior of CuAlBe and NiTi samples with astandard heat treatment. The cumulative SMA creep and thecycle deformation with a great loss of hysteresis width areclearly observed. Our group has developed a heat treatment forCuAlBe (extruded wires) that permits us to eliminate the creepfor deformation under 4.5% (Fig. 5) [14]. At the moment, thereis no similar treatment furnishing similar results for NiTi [25].

For CuAlBe samples with a 3.4 mm diameter, the standardbetatization of the alloy (i.e., two minutes at 1123 K withimmediate quenching in water and, later, 1 h at 373 K), providesa wire with a satisfactory level of working stresses (fractureabove 350 MPa) and deformation (6% or more) for a seriesof cycles. The material with standard heat treatment showsa relevant and accumulative permanent deformation (creep)while cycling (see Fig. 5(a), the deformation against time forseveral fast hundreds of cycles at frequencies of 0.5 or 0.25 Hz).The available working deformation is nearly constant at 3%as an increasing creep tracks the progressive deformation. Theenhanced heat treatment, by increasing the betatization time,increases the grain diameter (i.e., the mean grain radius roughlychanges from 0.14 to 0.75 mm), causing it to approach the

behavior of a single crystal. The extended homogenization timein the furnace at 1123 K, in addition to the aging at 373 K,reduces the accumulated deformation (see Fig. 5(b)) withminor degradation of the mechanical properties (the fracturelevel reduces to near 300 MPa). The observations recommendusing a deformation under 4.5% (sample fracture over 6%)with a remnant deformation below 0.25% at room temperature(293 K). At this level, the material works in an intermediateposition inside the PEW.

3.2.2. Clausius–Clapeyron coefficient in parent–martensitephase coexistence

The effects induced by external temperature changesor by self-heating during damping dissipation produce adisplacement in the stress axis of the hysteresis cycle. Areasonable simulation requires a well known experimentalvalue of the CCC [(d f/dT )coex or (dσ/dT )coex] with anuncertainty below 10%. The CCC can be well establishedfor single crystals – in particular, when parasitic effects(such as minor local composition changes and the intrinsicpseudoelasticity) are minimized – from a thermodynamicanalysis in the frame of the First and Second ThermodynamicLaws [22,23]. However, in polycrystalline materials, theprogressive interaction among martensite variants, in differentgrains, provides a cycle with relevant pseudoelasticity (seeFig. 3(b) and (c)), and it is necessary to experimentally evaluatethe CCC for each wire type (Table 1). In the CuAlBe alloys,the initial part of the transformation (deformation under 2% or3%) is used in order to avoid the accumulative creep. In NiTi,it is convenient to do some preliminary cycles. The inflexionpoint in the transformation path (∂2 f/∂x2

= ∂2σ/∂ε2= 0) is

used to evaluate the CCC in hysteresis cycles such as those inFig. 3(b) and (c). After several sets of measurements, the CCC

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Fig. 6. Self-heating effects in SMA wires. (a) CuAlBe wire (diameter 3.4 mm). (b) NiTi wire (diameter 2.46 mm).

Table 2Diffusion phenomena and asymptotic temperature effects on Ms for the studied alloys

Alloy CuAlZn [4] CuAlBe NiTi

τ1 at T 1390 s at 373 K 1.95 days at 373 K 1.9 days at 410 Kτ1 at T 11 020 s at 353 K 4.63 days at 353 K 55 days at 363 KActivation energy 13 630 K 5790 K 10 700 Kτ2 at T 47 200 s at 373 K – –τ2 at T 226 700 s at 353 K – –Activation energy 10 330 K – –100 ∗ 1Ms/1TRT −(10.5(1) + 6.7(2)) 14(1)

a 15(1)b

a Only one time constant from Ms measurements.b Rough approach, time constants are from resistance measurements against time; Ms changes are determined from changes in peak positions in DSC

measurements.

is evaluated. For CuAlBe, it is close to 2.2 MPa/K and, forNiTi, the value approaches 6.3 MPa/K. The overall uncertaintyis below 10%.

3.2.3. Self-heatingSelf-heating effects are highly dependent on the frequency

rate, deformation percentage, and sample cross section. At thepresent state of the art, each alloy wire requires an independentevaluation. In fact, the transformation mechanism is different:CuAlBe transforms in distributed domains along the materialand in NiTi is more like the progress of transformation front.In the experiments, oscillations with amplitudes of up to 3.5%can produce average temperature fluctuations up to 10 K inCuAlBe wires with a 3.4 mm diameter. Fig. 6(a) shows itstemperature increase for several cycling rates (0.02–1 Hz) andstrains (1%–4%). In the study of the dynamic behavior ofNiTi, it seems that the experimental temperature increase isapproximately twice that observed in the equivalent CuAlBesamples. Fig. 6(b) depicts NiTi temperature increase for cyclingat 0.5 Hz and deformation of 5%.

3.2.4. Summer–winter temperature effectsSummer–winter temperature changes induce two actions.

First, the direct stress changes through the CCC. Second, thediffusion contributions induced by time and temperature. Thediffusive effects act at different levels. Initially, they act inthe parent phase, immediately after quenching. Later, whenthe quench effects are homogenized, appear in the parent

and in the martensite phase and, also, in phase coexistence.The martensite stabilization in CuAlZn [3,4] and in otherCu-based alloys increases, for instance, the transformationtemperature. In particular, when the material is transformedin martensite immediately after quenching, the stabilization isvery relevant [26,27]. This effect is one of the drawbacks for theapplication of these alloys. In particular, the practical interestsusually demand long time in martensite or in phase coexistencewith no relevant change of behavior. After stabilization, thematerial requires a higher temperature (an increase of 100 K orhigher) or an equivalent stress reduction to recover the parentstate.

A phenomenological approach suggests that the temperatureand the stress in the parent phase produce a similar effecton the subsequent martensitic transformation [13,28]. Theinternal state of the sample under the external thermodynamicforces (i.e., stress and temperature) is progressively modified.The analysis via external temperature actions in the parentphase shows that the transformation temperature tracks theexternal temperature via an exponential behavior [4]. Each timeconstant, highly temperature dependent, is related to a differentactivation energy and asymptotic change in Ms. Table 2 showsthe transformation temperature changes associated with a stepat room temperature (close to 10% for one time constant),the time constant and the activation energy for CuZnAl andfor CuAlBe (only one activation energy is evaluated). Also, apreliminary evaluation for the values for NiTi is included.

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Fig. 7. Static coexistence effects in CuAlBe. The deformation increase after 3 days at constant stress in CuAlBe alloy is shown.

Table 3Expected changes in CuAlBe (σp < 300 MPa) and in NiTi alloy (σp < 700 MPa)

Parameters 1T (K) (CuAlBe) 1T (K) (NiTi)

Hysteresis width 30–50 15–35Summer–winter 40 40Self-heating (3.5% in used wires) 10 20Quenched sample 5 –Phase coexistence (dynamic) −10 −4.5a

Summer–winter tracking and asymptotic 3; 5.5 1; 6a

Security level 10–20 10–20Global effect 110 or near 240 MPa 100 or near 630 MPa

The CCC approaches, respectively, 2.2 MPa/K and 6.3 MPa/K. The manufacturer establishes that the yield strength of NiTi is close to 700 MPa.a Indicative values.

3.2.5. Coexistence effectsThe parent and martensite phases coexist along the whole

transformation curve [4]. The dynamic coexistence, whencycling, produces changes related to diffusion (enhanced bythe presence and displacement of interfaces) and to self-heatingproduced by latent heat and frictional contributions associatedwith the hysteresis cycle. In Cu-based alloys and “quasi-static”conditions, a progressive increase in the quantity of martensiteis observed at constant stress and temperature (see Fig. 7).Alternatively, at constant strain, a decrease of stress wouldexist. Preliminary analysis of NiTi shows particular effects inparent phase and coexistence coherent with CuAlBe. In fact,these effects indicate that set-ups with pre-strained SMA seemsinappropriate for long time applications.

3.3. Pseudo-elastic window usage

All of these physical properties of SMA can be summarizedin the evaluation of the PEW usage [12]. The contributionof each effect is evaluated as a temperature increase throughwhich the CC coefficient is converted to a stress change. ThePEW must consider all relevant effects plus a certain securitylevel. Table 3 shows the evaluation of the PEW for the studiedalloys. From these evaluations, the importance of CCC is shown(translates temperature changes into stress and vice versa). For

higher temperature fluctuations (room temperature and/or self-heating), the NiTi alloy may overcome the plastic deformationlimit.

4. SMA model for structural simulations

Modeling the SMA behavior is a complex topic ofpermanent interest. See [4] and related references and, forseveral recent approaches, [29–36]. The inherent complexity ofthe martensitic transformation of SMA requires a formulationat various depth levels. The importance of each level dependson the requirements which are to be satisfied by the material inthe working situations. Each material presents several differenttime scales. There are fast effects related to thermomechanicaloscillations governing the damping actions under earthquakeeffects, and slow effects governed by atomic diffusion thatdetermine the material lifetime and usefulness. All these effectsmust be considered when designing damping applicationsfor Civil Engineering. We have developed one dimensional(1D) models especially considering traction, temperature, anddiffusion effects, which are the most relevant effects for ourapplication.

4.1. The 5 levels of the complete model

The first 1D model that considers most relevant physicaleffects was developed for a CuAlZn single crystal [4,33,37].

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Fig. 8. Mechanical hysteresis cycle defines a single transformation domain.Total (1-2-3-4-5-6-7-8-9-1), partial (1-2-3-b-c-8-9-1), or internal (a-b-c-d)cycles are depicted. The CSRT position (A) depends on thermal and atomicdiffusion phenomena.

The model is built from observations on SMA single crystalswhich transform from the beta to martensite phase with smalltransformation domains along the sample. The model mimicsthe physical transformation structure of a single crystal (androughly of polycrystal material). For this reason, it is built bya large number, L (500–1000 elements), of similar elementsor domains. Each transformation domain is described by thecoordinates stress σ (or force f ), deformation ε (or lengtheningx), temperature (T ), and time (t) [37], and supposes five levelsof analysis:Level 0: Classical thermomechanical representation: Thislevel describes the classical dilatation coefficient and theYoung modulus (in the parent and martensite phase). Theseeffects are superimposed onto the phase transformation, atomicevolutions, and thermal effects.Level 1: Mechanical representation of phase transition:The detailed physical analysis describes the martensitictransformation from the phenomenological data in the intrinsicparameters. This level considers classical nucleation andgrowth of the phase transformation for each element of thewire (or bar) under the action of the external thermodynamicforces (stress and temperature) as shown in Fig. 8. The plotillustrates the different paths a domain describes when cyclingby the effect of an external force. For example, the path (1-2-3-4-5-6-7-8-9-1) corresponds to a complete cycle. This pathhas a maximum hysteresis width h2. The trajectory a-b-c-d-arepresents an internal loop with a minimum hysteresis widthh1. The hysteresis cycle is characterized by the Critical Stressof Reversible Transformation (CSRT) – point A in the plot –that places the whole cycle in the force axis. CSRT is affectedby the temperature (level 2) and atomic state of the material(level 3) thus linking the mechanical actions with the thermaland diffusive phenomena.Level 2: Thermal effects: External temperature and dynamicalthermal effects: The sample temperature (external temperatureplus self-heating) modifies the mechanical properties of thematerial as shown in the experimental description. Self-heating

is not uniform along the sample. Thus, it is necessary toevaluate frictional and latent heat phenomena and use theheat transfer Fourier formalism to compute the local sampletemperature (Tdom).Level 3: Atomic diffusion effects: As can be seen fromthe experimental data, the material state evolves, therebymodifying its transformation temperature (for instance, Ms).Experimental analysis furnishes the time constants for eachdiffusion phenomena (parent phase evolution – after quencheffects, summer–winter tracking – and coexistence).Level 4: Statistical representation of the material: EachSMA has its own characteristics that define the resultingthermomechanical behavior. For example, single crystalCuZnAl has a different hysteresis cycle than polycrystalCuAlBe or NiTi [4,12]. To be able to represent the differentcycles, it is necessary to add statistical information to themodel. This is done by using slightly different parameters foreach transformation domain. The identification process adjustsall of these parameters.

This model is a 1D distributed model. The global hysteresiscycle is the result of the behavior of the set of elementarytransformation domains; one for each martensite plate [4,37],with a statistical scatter in its defining parameters. Using thisapproach, the calculation of the model is relatively simple.It only involves the addition of L simple element responsesinstead of a complex global function.

4.2. Model implementation for dynamic structural simulations

A detailed model built from a serial array of transformationdomains is able to accurately predict the long time evolutionand dynamic effects of including SMA [4,37]. However,the computational load is too large for complex structuralsimulations which include several dampers. We use thepredictions of this model to calculate the initial state ofthe sample for a given simulation. In fact, three initialstates are calculated: standard, low and high temperature.Using this information the material response in all workingconditions can be modeled by a simplified model speciallydeveloped for structural simulations. This model is developedfor polycrystalline CuAlBe and NiTi alloys. It is composedof a set of parallel transformation domains. The parallelconfiguration is suitable for simulation environments, like inANSYS, where elongation is the element input parameter.Besides, this structure is particularly valid for polycrystallinealloys, as has been reported for similar materials [38]. Inthe present examples (see Fig. 9), the model is composed ofonly 9 parallel elements (Fig. 9(a)). Fig. 9 shows the modelpredictions and the experimental data for CuAlBe (b) andNiTi (c). Temperature changes are calculated using the CCC.The model accuracy for global, partial, and internal cyclesis very good and has a reduced computation time. Also, asimpler model (Fig. 3(a) and (c)) for NiTi slow cycling isdeveloped based on the bilinear theory (which is widely usedfor NiTi [32]). However, the error is important, especially wheninternal loops are present. Furthermore, the computational timefor the proposed parallel model is similar to the bilinear model.

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Fig. 9. Model with 9 parallel elements. (a) Sketch of the model construction.(b) Experimental and simulated behavior of a CuAlBe sample. (c) Experimentaland simulated behavior of a NiTi sample.

5. Simulations of earthquake actions

A SMA damper may be simply a wire or rod of materialthat, due to its hysteresis cycle, is able to convert mechanicalenergy into heat. In principle, we may use a single SMArod with an appropriate thickness to endure the stress in thestructure. However, there are several reasons that suggest theuse of a set of thinner SMA wires instead. First, to be ableto use the material, it is necessary to prepare the sample witha thermomechanical treatment (Section 3.2.1). This samplepreparation loses its efficiency when the thickness of the sampleincreases (the sample thickness imposes a temperature gradientin the betatization process that prevents Ms homogenization).Second, the grain complexity grows with the sample thickness.This produces the increase of undesired material behavior in,

Fig. 10. SMA damper built from 12 CuAlBe wires of diameter 3.4 mm.

for instance, quenching which modifies the hysteresis shape(see, Fig. 3). For these reasons, we propose a damper structurewith N thin wires (diameter less than 5 mm) as Fig. 10shows. Obviously, this configuration only allows the dampersto work in traction. No compression work is achievable. Toovercome this limitation, the dampers always work in pairs ona counteracted geometry.

The design and optimization of the dampers consist ofdetermining the best length and number of wires that composethe damper. We are using CuAlBe wires with a diameter of3.4 mm able to undergo a stress of 2.5 kN with an ultimate strainabove 6% (4.5% without SMA creep), and NiTi wires with adiameter of 2.46 mm with similar stress and strain maximumlevels. To ensure an appropriate response of the dampers, weconsider only strains up to 3.5%–4%. This limitation has tworeasons: to reduce the accumulated creep and to provide asafety margin. The calculation of the maximum strain andstress for each damper requires the analysis of the structureunder the simulated effects of an earthquake. By studying thefree oscillation of the building, we obtain the free oscillationamplitude, the stresses induced in the structure, and from thesteel properties the maximum deformation the structure canundergo without plastic deformation. From the free oscillationamplitude, we determine the length of the SMA wires in orderto not overcome the maximum expected strain in SMA withstresses under plastic deformation. We calculate the number ofwires required to produce a total stress of around 10%–30%of the stresses induced in the structure by the event. Usually,starting from these data, a trial and error iterative process isrequired to fully optimize the dampers.

5.1. Structure description

Here, we focus on the single floor section with the gardenon the roof (Fig. 11 left depicts the beam structure and damperplacement). This structure is composed of three triple porticos.The damper optimization process is done in two steps. First, weanalyze the triple portico with the highest load simplifying thedesign process. Second, at the end this section, we check theresponse of the whole garden with the dampers designed in theprevious step. The central portico of the garden structure hasthe highest load. Fig. 11 right sketches the three-arch porticowith its load and characteristics. The portico height is 3 m. Thewidth of the arches is 2.35 m (lateral) and 6.80 m (central).The pillars are built by HEB200 beams (central) and HEB140(external). The horizontal girders are HEB240 for the centralarch and IPN160 for the lateral ones. In simulation, we useA570 grade 50 steel with Young modulus 206 GPa, density7850 kg/m3, yield stress of 344 MPa and damping coefficientsα = 0.01 and β = 0.001 according to ANSYS steel model. The

1898 V. Torra et al. / Engineering Structures 29 (2007) 1889–1902

Fig. 11. Left: Beam structure for the garden section with the placement of SMA dampers. Right: Schematic description of the garden central triple portico with H(vertical) and I (horizontal) steel elements, the distributed loads and the SMA damper situation.

Fig. 12. (a) Acceleration pattern for ‘El Centro’ earthquake (magnitude 7.1 in the Richter scale) and (b) oscillations induced in the portico (linear steel model)without dampers.

total portico load is 46.5 Tm. The pairs of dampers are installedin the diagonals of the lateral arches. Steel cables (with higherstiffness than the dampers) are used to link the dampers withthe structure.

5.2. Analysis of the triple portico structure and damper design

Using the structural software ANSYS, in which our modelshas been included via usermat routine, we analyze theresponse of the portico to the action of an earthquake. Severalearthquakes have been used, but the most detailed analysis andthe optimization of the dampers has been performed using thedata from ‘El Centro’ seism (1940) [18] with a magnitude of7.1 in the Richter scale. In this simulation we use the first 10 splus 3 s of no acceleration at the end. Fig. 12(a) shows theacceleration pattern for this seism. It produces a maximum freehorizontal oscillation on the upper section of the portico withamplitude of 7.3 cm (Fig. 12(b)). The reaction forces involvedare close to 650 kN, with a total input energy of 23.4 kJ.

The working temperature and the Ms parameter determinethe SMA response. It is possible to modify the Ms value

by changing the alloy composition. In these simulations weconsider the optimal working temperature for each alloy.We have designed the dampers using CuAlBe wires with adiameter of 3.4 mm. After some iterative analysis for theused alloy, the best results are obtained using a set of 25wires with a length of 0.6 m. The SMA mass per damperis about 1.2 kg (100–200 e/kg for extruded material) thatreduces the maximum oscillation amplitude to 3.1 cm (at278 K). The damper supports a total force of 44.2 kN, andthe maximum stress and strain for each wire is 195 MPaand 3.1%, respectively. They dissipate 66% of the energytransmitted to the structure by the earthquake. Fig. 13 top,shows the oscillation amplitudes (a1), the energies present inthe system (b1) (we depict the kinetic energy (Ek), the energydissipated by the SMA dampers (WSMA), and the earthquakeinput energy (Wquake) calculated according to [39,40]), andthe dampers’ hysteresis cycle (c1). Using NiTi wires with adiameter of 2.46 mm, the optimum dampers are also built from25 wires, each with a length of 60 cm (both wires producesimilar stresses). NiTi dampers reduce the maximum oscillation

V. Torra et al. / Engineering Structures 29 (2007) 1889–1902 1899

Fig. 13. Detailed response of the portico to ‘El Centro’ using SMA dampers. Top: CuAlBe damper. Bottom: NiTi damper. The figure shows the oscillation amplitude(a), the energy values involved in the event (b), and the dampers’ working cycles (c).

Fig. 14. Portico response with SMA dampers at different temperatures. Optimal temperature (Topt = 5 and 20 ◦C) and worst case simulation (Topt + 40 ◦C) forCuAlBe (a) and NiTi (b).

amplitude to 3.7 cm (at 293 K) and undergo a maximumforce of 49.4 kN. The wires composing the dampers support amaximum stress and strain of 330 MPa and 3.4%. The dampingsystem dissipates 48% of the transmitted energy. Fig. 13 (a2, b2and c2) shows the system response with NiTi dampers. Withoutany further consideration, both systems perform similarly.

Finally, it is important to evaluate the material behaviorunder the worst conditions. To perform this simulation,we increase the working temperature. The analysis of thetemperature increase must consider the external temperaturefluctuations (summer–winter), the material self-heating, theatomic diffusion effects, and a certain security margin(according to Section 3.3). In fact, the dampers are placed in theinterior of the building, therefore the room temperature changesremain clearly under 20 K. A rough approximation for the self-heating temperature increase is 20 K. Therefore, we estimate

the total temperature increase in worst conditions to be 40 K.Fig. 14 compares the damper response in optimal conditions(Topt) and under worst case conditions (Topt+40 K). The resultsdemonstrate that the dampers are robust and able to work evenin this extreme situation. The maximum oscillation is higher,but the damping is still important (3.1 cm in optimal conditionsin front of 4.2 cm in the worst conditions for CuAlBe (a) and3.7 and 4.5 cm for NiTi (b) against 7.3 cm without dampers).In these simulations, it is also possible to observe that NiTi ismore sensitive to room temperature changes due to its higherCCC. CuAlBe may undergo nearly 20 K more of a temperaturechange than NiTi without difficulties. This difference indicatesthat, in the actual state of the art, CuAlBe dampers are a bettersolution for light Civil Engineering structures.

Once the dampers are optimized for a particular earthquake,it is necessary to check that they are valid for other events,

1900 V. Torra et al. / Engineering Structures 29 (2007) 1889–1902

Fig. 15. Simulations for three Japanese earthquakes with magnitudes 8.0 (2003), 6.2 (1997) and 6.0 (2005) on the Richter scale 1, 2 and 3 respectively. From top tobottom: earthquake acceleration patterns (a1, a2, a3), portico free oscillation response (b1, b2, b3), portico response with CuAlBe dampers (c1, c2, c3) and porticoresponse with NiTi dampers (d1, d2, d3).

as each earthquake seismogram contains its own frequenciesthat, combined with the building resonant frequencies, canproduce very different effects. For this reason, the responseto a single earthquake is not a conclusive probe of thedamping capabilities of SMAs. To probe whether the dampersare useful in a wide range of situations, we have simulatedthe triple portico response for three different recent Japaneseearthquakes registered in the stations KSRH03 (2003), KGS005(1997) and KNGH10 (2005) of magnitudes 8.0, 6.2 and 6.0respectively [41]. Fig. 15 presents the accelerograms for eachevent, the free oscillation, and the damped oscillation with

the designed SMA dampers with CuAlBe and NiTi wires. Inall of the cases, the damped oscillations reduce the maximumoscillation amplitude by a factor close to 2 even considering aworking temperature of 293 K for both alloys.

5.2.1. NiTi remarkIn the present state of the art, one of the biggest drawbacks

of NiTi is associated to its high CCC value (over 6 MPa/K): theroom temperature plus self-heating (latent heat oscillations plushysteresis dissipation) near 1 Hz may overcome the maximumplastic deformation inducing progressive SMA creep with loss

V. Torra et al. / Engineering Structures 29 (2007) 1889–1902 1901

Fig. 16. Garden response to ‘El Centro’ with and without CuAlBe dampers. (a) Oscillation amplitude (x-axis) of the garden structure to ‘El Centro’ earthquake.Free oscillation and response with the designed CuAlBe dampers. (b) Energies involved in the event with dampers installed. (c) Damper response during the event.

of damping capabilities. For wires with diameter near or largerthan 2.5 mm this limitation is highly relevant. Until thislimitation is fully solved by appropriate improvements, theNiTi in pseudoelastic state (with recentering capabilities) doesnot seem to be a satisfactory alloy for earthquake dampingapplications in Civil Engineering. Other diffusion effects aredescribed in [15].

5.3. Garden response to ‘El Centro’

Finally, we simulate a preliminary response of the wholegarden structure with the CuAlBe dampers to the first 15 sof ‘El Centro’ accelerogram. The complete garden structure iscomposed by the beam structure depicted in Fig. 11 (left) witha reinforced concrete slab on top which increases the systemrigidity. The total structure’s load is 98.3 Tm. The concreteslab distributes the loads among all three porticos reducingthe maximum displacement to 4.3 cm which differs from thetriple portico. Therefore, when considering the whole structureit is necessary to refine the damper design to adapt them atthe structure. The final design considers 12 dampers built from22 CuAlBe wires and length 38 cm with a mass per damperof 0.75 kg. Using these devices the maximum oscillation isreduced to 2.4 cm (at 293 K). Fig. 16 presents the structureoscillation on the x-axis with and without SMA dampers (a),the energies acting in the system when the dampers are present(b) indicating an energy dissipation of 56% and the stress–straincycle for the dampers (c) showing the working domain for thesedampers (stress 240 MPa and strain 3.7%).

The present house structure is designed according toBarcelona seismic requirements which do not consider largeearthquakes. Using these dampers, the structure is able to resistthe actions of ‘El Centro’ north–south component. However,the structure is too weak in the z-axis to apply these devicesappropriately. In this case it is necessary to reinforce the beamstructure before considering the SMA dampers.

6. Conclusions

SMA alloys in pseudoelastic state are suitable materialsfor the development of passive solid state dampers in CivilEngineering. Several years of observations of CuZnAl, CuAlBeand, to some extent, NiTi suggest that the studied alloysshow similar behavior with different time scales. These

observations provide the required knowledge to guarantee thematerial behavior for long time applications (several years).The relevant physical phenomena for damping applications arethe summer–winter temperature actions, the atomic diffusioneffects (parent phase and coexistence) and the self-heating.The evaluation of these phenomena provides the upper andlower limits of the alloy changes. Using this information anda thermomechanical model introduced in standard structuralsimulation software (ANSYS), we can simulate SMA damperbehavior at any point of its lifetime.

Dampers with forces near 50 kN are built from several wiresof SMA (20–25) with global cross sections around 300 mm2

of CuAlBe or NiTi. The paper describes the designing processfor these dampers using ANSYS structural simulations. Toillustrate this process a damping system for a family houseis described. The system is able to reduce the maximumoscillation amplitudes induced by high magnitude earthquakesby approximately a factor 2 and dissipate around 50% of theenergy absorbed by the structure. In fact, similar results areobtained with both materials. CuAlBe with an appropriatethermomechanical treatment undergoes deformations near4.5% without permanent deformation. However, at the presentstate of the art, similar NiTi wires cannot avoid the SMAcreep. Unless appropriate improvements solve this limitation,the NiTi in pseudoelastic state does not seem a reliable alloyfor earthquake damping applications in Civil Engineering.

This paper analyzes one of the applications of SMA: thedamping effects using the hysteresis cycle. The SMA propertiesare studied according to the user needs in earthquake damping:several years without any action and, later, near one or twominutes with relevant accelerations and 100–200 oscillationsof the structure.

Acknowledgements

Work realized in the frame of Spanish projects: MAT2002-10423E, PCI2005-A7-0254 (MEC) and FPA2000-2635-E(M.F.). Cooperation between CIRG (UPC) and ETS (Montreal,Quebec, CA) and with CAB-IB (University of Cuyo,Argentina) is supported by Quebec government and CNEA and,in the past, by DURSI (Gen. Catalonia). V.T. acknowledgessupport in NiTi analysis from Dr. A. Yawny and Eng. H. Soul.Experimental support from Mr. Pablo Riquelme and creativeideas in the development of hand controlled devices from Mr.

1902 V. Torra et al. / Engineering Structures 29 (2007) 1889–1902

Raul Stuke is also acknowledged. The collaboration of Mr. S.Ruiz from TA Instruments for the calorimetric measurements inNiTi is gratefully cknowledged.

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