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Nonlinear Modeling for Health Care Applications

Ashutosh Srivastava

Marc Horner, Ph.D.

ANSYS, Inc.

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Motivation

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Linear analysis works well for only small number of applications. The majority of today’s applications require the inclusion of nonlinearities such as material, large deformations and contacts.

Motivation

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Overview of Nonlinearity

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What is nonlinear behavior? A linear structure obeys this linear relationship given by Hooke’s law:

F = KU Linear structures are well‐suited to finite element analysis, which is based on linear matrix algebra.

Significant classes of structures do not have a linear relationship between force and displacement.

Because a plot of F versus U for such structures is not a straight line, such structures are said to be nonlinear.

The stiffness is no longer a constant and KT (tangent stiffness) represents the tangent to the force deflection curve

u

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Types of Nonlinearity There are three main sources of nonlinearities:

• Geometric nonlinearities: If a structure experiences large deformations, its’ changing geometric configuration can cause nonlinear behavior.

• Material nonlinearities: A nonlinear stress‐strain relationship, such as metal plasticity shown on the right, is another source of nonlinearities.

• Contact: A “changing status” nonlinearity, where an abrupt change in stiffness may occur when bodies come into or out of contact with each other.

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… Types of Nonlinearity

Of course, all three types of nonlinearities are commonly encountered in combination.

ANSYS can readily handle combined nonlinear effects.

Rubber Boot Seal

An example of

nonlinear geometry

(large strain and large

deformation), nonlinear

material (rubber), and

changing status

nonlinearities (contact).

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Nonlinear FEA Issues

Three main issues arise whenever you do a nonlinear finite element analysis:

• Obtaining convergence

• Balancing expense versus accuracy

• Verification

It takes care and skill to

juggle these three

issues successfully!

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Changing Status Nonlinearities

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Changing Status Nonlinearities A change of status that causes an abrupt change in stiffness is another common cause of nonlinear behavior. For example:

– A cable can change status from slack to taut

– Two parts in an assembly can come into contact

In this example, the

contact status changes

from “open” to “closed” as

load increases, causing a

stiffness change.

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Peristaltic Pump

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Example 4: Two-Way FSI Simulation of a Peristaltic Pump

Nonlinearity considered • Large Deformation effects • Contact Nonlinearity

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Dimensions and Components of a P-Pump

1 cm dia 6

cm

1.5 cm dia

Elastic Tube (0.5 mm thick)

Clamp Clamp

Roller(Rigid)

Casing (Rigid)

Bottom Support (Rigid)

Outlet

Inlet

The roller is modeled with an interference of 0.45 cm which is resolved and then other boundary conditions are applied.

Geometry Details

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Workflow

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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All other structural components are

modeled as rigid.

Elastic Tube

Elastic Tube (0.5 mm thick)

Roller(Rigid)

Casing (Rigid)

Bottom Support (Rigid)

Material Properties

Mechanical Setup…

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Contact between Elastic tube and roller Contact between Elastic tube and casing

Contact Details

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

Mechanical Setup…

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Clamps are fixed for all dofs

Roller rotates 360 degrees about

the center of the casing

Casing and Bottom surface

is fixed for all dofs

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

Mechanical Setup…

Boundary and Loading Conditions

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The surface of the tube is

defined as an “FSI”

interface

Elastic foundation is defined for

the elastic tube

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

Mechanical Setup…

… Boundary and Loading Conditions

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Deforming Wall System Coupling Deforming Zone

Inlet and Outlet face Rigid Zone

CFD Setup…

Zone and Interfaces

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Momentum settings:

Gauge pressure = 0 Pa

Backflow Direction Specification method: Normal to Boundary

Operating Conditions:

Operating Pressure: 101325Pa

Inlet

Outlet

CFD Setup…

Boundary Conditions

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Filled Liquid

CFD Setup…

Material Properties

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Two “Data Transfers” are setup for the single FSI interface:

1. Force transfer from Fluent to Mechanical 2. Deformation transfer from Mechanical to Fluent

System Coupling Setup…

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Example 4: Two-Way FSI Simulation of a Peristaltic Pump

Total Deformations

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Velocity vectors

Example 4: Two-Way FSI Simulation of a Peristaltic Pump

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Summary

Nonlinear analysis is essential for accurate simulations for various health care applications since most of the process involved do not follow linear behavior.

A wide variety of options are available to perform nonlinear analysis in ANSYS Mechanical which can be used to analyze these problems.

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Thank You