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© 2011 ANSYS, Inc. January 15, 2015 2
Nonlinear Modeling for Health Care Applications
Ashutosh Srivastava
Marc Horner, Ph.D.
ANSYS, Inc.
© 2011 ANSYS, Inc. January 15, 2015 12
Motivation
© 2011 ANSYS, Inc. January 15, 2015 13
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
© 2011 ANSYS, Inc. January 15, 2015 14
Overview of Nonlinearity
© 2011 ANSYS, Inc. January 15, 2015 15
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.
© 2011 ANSYS, Inc. January 15, 2015 17
… 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).
© 2011 ANSYS, Inc. January 15, 2015 18
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!
© 2011 ANSYS, Inc. January 15, 2015 53
Changing Status Nonlinearities
© 2011 ANSYS, Inc. January 15, 2015 54
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.
© 2011 ANSYS, Inc. January 15, 2015 55
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
© 2011 ANSYS, Inc. January 15, 2015 59
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
© 2011 ANSYS, Inc. January 15, 2015 62
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
© 2011 ANSYS, Inc. January 15, 2015 63
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
© 2011 ANSYS, Inc. January 15, 2015 64
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
© 2011 ANSYS, Inc. January 15, 2015 69
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.
© 2011 ANSYS, Inc. January 15, 2015 70
Thank You