PI: Prof. Nicholas Zabaras Participating student: Swagato Acharjee
Materials Process Design and Control Laboratory, Cornell University
Robust design and analysis of deformation processes
Research Objectives:
To develop a mathematically and computationally rigorous methodology for virtual materials process design that is based on quantified product quality and accounts for process targets and constraints with explicit consideration of uncertainty in the process.
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20
Iterations
Final iteration – Flash reduced , no underfill
First iteration Underfill
Reference problem Large Flash
Object oriented, parallel MPI based software for Lagrangian finite element analysis and design of 3D hyperelastic-viscoplastic metal forming processes.
Implementation of 3D continuum sensitivity analysis algorithm. Mathematically rigorous computation of gradients - good convergence observed within few optimization iterations
Advanced unstructured hexahedral remeshing using the meshing software CUBIT (Sandia).
Thermomechanical deformation process design in the presence of ductile damage and dynamic recrystallization
Multi-stage deformation process design
I - Deterministic Design of Deformation Processes
Equilibrium equation
Design derivative of equilibrium
equation
Material constitutive laws
Time & space discretized weak form
Sensitivity weak form
Contact & frictionconstraints
Incremental sensitivity contact
sub-problem
Conservation of energy
Schematic of the continuum sensitivity method (CSM)
Continuum problemDesign
differentiateDiscretize
Incrementalthermal sensitivity
sub-problemIncremental
sensitivity constitutive sub-problem
II – Uncertainty modeling in inelastic deformation processes
III– Ongoing work - Robust design with explicit consideration of uncertainty
MOTIVATION - All physical systems have an inherent associated randomness
•Uncertainties in process conditions
•Input data
•Model formulation
•Material heterogeneity
•Errors in simulation software
PROBLEM STATEMENT
Compute the predefined random process design parameters which lead to a desired objectives with acceptable (or specified) levels of uncertainty in the final product and satisfying all constraints.
• Robustness limits on the desired properties in the product – acceptable range of uncertainty.
• Design in the presence of uncertainty/ not to reduce uncertainty.
• Design variables are stochastic processes or random variables.
• Design problem is a multi-objective and multi-constraint optimization problem.
SOURCES OF UNCERTAINTIES
Engineering component
Random Meso-Scale
featuresDesign variables
Fail Safe
http://mpdc.mae.cornell.edu
Objective Function
0 0.2 0.4 0.6 0.80
2
4
6
8
10
12
14
Displacement (mm)
Lo
ad
(N
)
Mean
Preform Optimization of a Steering LInk
Uncertainty modeling in a tension test using Generalized Polynomial Chaos Expansions (GPCE). The input uncertainty is assumed in the state variable (deformation resistance) – a random heterogeneous parameter
UNCERTAINTY DUE TO MATERIAL HETEROGENEITY
NON INTRUSIVE STOCHASTIC GALERKIN (NISG) MODELING OF PROCESS UNCERTAINTY IN UPSETTING
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Displacement (mm)
SD
Lo
ad
(N
)
Similar homogeneos material
Heterogeneous material
Effect of heterogeneities at linear-nonlinear transition
SELECTED PUBLICATIONS•S. Acharjee and N. Zabaras "The continuum sensitivity method for the computational design of three-dimensional deformation processes", Computer Methods in Applied Mechanics and Engineering, in press.
•S. Acharjee and N. Zabaras, "Uncertainty propagation in finite deformation plasticity -- A spectral stochastic Lagrangian approach", Computer Methods in Applied Mechanics and Engineering, in press.
•S. Acharjee and N. Zabaras, "A support-based stochastic Galerkin approach for modeling uncertainty propagation in deformation processes", Computers and Structures, submitted.
•S. Acharjee and N. Zabaras, "A gradient optimization method for efficient design of three-dimensional deformation processes", NUMIFORM, Columbus, Ohio, 2004.
•N. Zabaras and S. Acharjee, "An efficient sensitivity analysis for optimal 3D deformation process design", 2005 NSF Design, Service and Manufacturing Grantees Conference, Scottsdale, Arizona, 2005.
•S. Acharjee and N. Zabaras "Modeling uncertainty propagation in large deformations", 8th US National Congress in Computational Mechanics, Austin, TX, 2005.
•S. Acharjee and N. Zabaras, "On the analysis of finite deformations and continuum damage in materials with random properties", 3nd M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, 2005.
Financial support from NSF, AFOSR and ARO. Computing facilities provided by Cornell Theory Center
Input support space
SD
E
PDF of design Objective
Adaptive discretization of the PDF of the design objective based on Smooth (S) Extreme (E) and Discontinuous (D) regions
Void fraction: 0.002 0.004 0.007 0.009 0.011 0.013 0.016
0 0.2 0.4 0.6 0.8 1500
1000
1500
2000
2500
Me
an
Fo
rce
(N)
Stroke (mm)0 0.2 0.4 0.6 0.8 1
50
100
150
200
250
300
350
400
Stroke (mm)
Std
. D
ev.
Fo
rce
(N)
Uncertainty in die/workpiece friction and initial shape
Random realizations