Nonlinear Modeling for Health Care Applications Ashutosh Srivastava Marc Horner, Ph.D. ANSYS, Inc.

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1 Nonlinear Modeling for Health Care Applications Ashutosh Srivastava Marc Horner, Ph.D. ANSYS, Inc. 2

2 Motivation 12

3 Motivation 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. 13

4 Overview of Nonlinearity 14

5 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 K T (tangent stiffness) represents the tangent to the force deflection curve 15 u

6 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. 16

7 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). 17

8 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! 18

9 Changing Status Nonlinearities 53

10 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. 54

11 Example 4: Two-Way FSI Simulation of a 55

12 Example 4: Two-Way FSI Simulation of a Nonlinearity considered Large Deformation effects Contact Nonlinearity 56

13 6 cm Geometry Details Example 4: Two-Way FSI Simulation of a Casing (Rigid) Elastic Tube (0.5 mm thick) Roller(Rigid) Clamp 1.5 cm dia Clamp Outlet 1 cm dia Inlet Bottom Support (Rigid) 57 Dimensions and Components of a P-Pump The roller is modeled with an interference of 0.45 cm which is resolved and then other boundary conditions are applied.

14 Example 4: Two-Way FSI Simulation of a Workflow 58

15 Mechanical Setup Material Properties Example 4: Two-Way FSI Simulation of a Casing (Rigid) Elastic Tube Elastic Tube (0.5 mm thick) Roller(Rigid) All other structural components are modeled as rigid. Bottom Support (Rigid) 59

16 Mechanical Setup Contact Details Example 4: Two-Way FSI Simulation of a Contact between Elastic tube and roller Contact between Elastic tube and casing 60

17 Mechanical Setup Example 4: Two-Way FSI Simulation of a Boundary and Loading Conditions Clamps are fixed for all dofs Casing and Bottom surface is fixed for all dofs 61 Roller rotates 360 degrees about the center of the casing

18 Mechanical Setup Example 4: Two-Way FSI Simulation of a Boundary and Loading Conditions The surface of the tube is defined as an FSI interface Elastic foundation is defined for the elastic tube 62

19 CFD Setup Example 4: Two-Way FSI Simulation of a Zone and Interfaces Deforming Wall System Coupling Deforming Zone Inlet and Outlet face Rigid Zone 63

20 CFD Setup Example 4: Two-Way FSI Simulation of a Boundary Conditions Outlet Inlet Momentum settings: Gauge pressure = 0 Pa Backflow Direction Specification method: Normal to Boundary Operating Conditions: Operating Pressure: Pa 64

21 CFD Setup Example 4: Two-Way FSI Simulation of a Material Properties Filled Liquid 65

22 Example 4: Two-Way FSI Simulation of a System Coupling Setup Two Data Transfers are setup for the single FSI interface: 1. Force transfer from Fluent to Mechanical 2. Deformation transfer from Mechanical to Fluent 66

23 Example 4: Two-Way FSI Simulation of a 67 Total Deformations

24 Example 4: Two-Way FSI Simulation of a 68 Velocity vectors

25 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. 69

26 Thank You 70