Week 10 Challenge: Hyper-Elastic Material Models Challenge

Course: LS-DYNA for Structural Mechanics/ FEA

Submitted by: Amanpreet Singh Whan

Supervisor: Tholkappiyan D

September 08, 2021

Table of Contents

1 Introduction.

2 Aims.

3 Methodology.

4 Results.

5 Conclusion.

1 Introduction

LS-DYNA is an advanced general-purpose multiphysics simulation software package developed by the former Livermore Software Technology Corporation (LSTC), which was acquired by Ansys in 2019. While the package continues to contain more and more possibilities for the calculation of many complex real-world problems, its origins and core competency lie in highly nonlinear transient dynamic finite element analysis (FEA) using explicit time integration. LS-DYNA is used by the automobile, aerospace, construction and civil engineering, military, manufacturing, and bioengineering industries.

Material modeling is a common process in industries. This process involves testing new material or alloy through experiments to extract the behavior of the new material and then modeling this material using the extracted test data to generate a mathematical equation representing the stress-strain behavior of the material and finally validating this approximate equation with the test data which later can be used while performing any type of simulation.

Material modeling is carried out in most of the industries mainly in Research and development sectors because new materials are preferred by the industries to eliminate certain parameters and impart new ones that could be beneficial for the application like improved fatigue, life cycle, thermal and wear-resistant, eliminating manufacturing costs, etc. This newly modeled material can later be used in any type of engineering analysis (Buckling, linear static, thermal) using FEA tools thus preventing testing upon a physical model over and over again until our result reaches fidelity and thus eliminating the high cost and possible error outcomes.

The purpose of the Week 10 challenge is to create a MAT 077 H-Hyper Elastic Rubber or MAT 077 O-Ogden Rubber material card from the given engineering stress/ strain raw data and use it to perform a uniaxial tension test of the given dog-bone specimen with 100 percent strain.

2 Aims

1. Create a MAT 077 H-Hyper Elastic Rubber or MAT 077 O-Ogden Rubber material card.
2. Calculate the Mooney Rivlin and Ogden material constants.
3. Use constants in the material card to perform the uniaxial test of dog bone specimen and validate the post-processing engineering stress-strain results with the given raw data.

3 Methodology

To model a new material whose data either as 'Force vs Displacement' or 'Engineering Stress vs Strain' is collected through different physical testing processes. This data must be represented in terms of a mathematical equation that replicates the behavior of the material which then can be successfully used for future engineering analysis. In LS-DYNA, this data is modeled using a MAT 077_H-HYPERELASTIC_RUBBER or MAT_077-O-OGDE-RUBBER material card by defining the Load-Curve parameter and where the new data is fed.

The section also describes different stages that were performed to set up simulation file using an engineering tool LS-DYNA for the completion of the Week 10 Challenge task. These stages can be broadly categorized into creating an input deck containing different cards such as contact, control, database, element, hourglass, Boundary condition, keyword, MAT, node, part, section, and title.

Given Engineering Stress Strain raw data

Table 1- Given Engineering Stress Strain Data.

Eng strain	Eng Stress
0	0
2.50E-02	4.46E-02
5.00E-02	8.67E-02
7.50E-02	1.27E-01
1.00E-01	1.64E-01
1.25E-01	2.00E-01
1.50E-01	2.34E-01
1.75E-01	2.67E-01
2.00E-01	2.98E-01
2.25E-01	3.28E-01
2.50E-01	3.56E-01
2.75E-01	3.83E-01
3.00E-01	4.09E-01
3.25E-01	4.34E-01
3.50E-01	4.58E-01
3.75E-01	4.81E-01
4.00E-01	5.03E-01
4.25E-01	5.24E-01
4.50E-01	5.45E-01
4.75E-01	5.65E-01
5.00E-01	5.84E-01
5.25E-01	6.03E-01
5.50E-01	6.20E-01
5.75E-01	6.38E-01
6.00E-01	6.55E-01
6.25E-01	6.71E-01
6.50E-01	6.87E-01
6.75E-01	7.02E-01
7.00E-01	7.17E-01
7.25E-01	7.32E-01
7.50E-01	7.46E-01
7.75E-01	7.60E-01
8.00E-01	7.73E-01
8.25E-01	7.86E-01
8.50E-01	7.99E-01
8.75E-01	8.11E-01
9.00E-01	8.23E-01
9.25E-01	8.35E-01
9.50E-01	8.47E-01
9.75E-01	8.58E-01
1.00E+00	8.69E-01

This curve will be fed to the Load Curve parameter for the challenge purposes. What follows hereafter is the set of images representing the process followed to create different cards and values assigned to their key parameters.

Boundary:

The keyword BOUNDARY provides a way of defining imposed motions on boundary nodes. The Prescribed Motion Set Displacement boundary condition was defined for the challenge purposes. Also, the SPC Set (single Point Constraint) boundary condition was used to restrict the motion of the nodes.

Control:

The keyword control cards can be used to change defaults. The control energy, hourglass, implicit auto, implicit general, implicit solution, implicit solver, and control termination cards were created for the challenge purposes.

Database:

The database definitions are necessary to obtain output files containing results information. The binary D3Plot, Extent Binary and ASCII options were selected for the challenge purposes.

Define:

The keyword DEFINE provides a way of defining boxes, coordinate systems, load curves, functions, tables, transformations, and orientation vectors. The curve option was selected, and the assigned value of load-displacement is presented in the following card.

Hourglass:

Hourglass (HG) modes are nonphysical, zero-energy modes of deformation that produce zero strain and no stress. Hourglass modes occur only in under-integrated (single integration point) solid, shell, and thick shell elements.

Mat:

The keyword MAT helps in defining and assigning different types of materials to a part as per requirements. For this challenge MAT 077_H-HYPERELASTIC_RUBBER was selected, and the values assigned to material card parameters are presented in the following card.

Section:

Under section, the element formulation, integration rule, nodal thicknesses, and cross-sectional properties are defined. A shell section was created as per challenge requirements and assigned values for their parameters are presented in the following picture.

Part:

Here define combine material information, section properties, hourglass type, thermal properties, and a flag for part adaptivity.

4 Results

Since the challenge requires the calculation of Mooney Rivlin and Ogden constants for the creation of MAT 077 H-Hyper elastic rubber and MAT 0770-Ogden rubber material cards, the uniaxial tensile test simulations were run for three different orders i.e., N=1, 2, 3 to calculate constants along with developing an understanding of how these constants can affect engineering stress-strain values.

After feeding the information of stress-strain behavior to the LCID parameter of the material card, the simulations were run for three different orders to calculate values of different Mooney Rivlin and Ogden constants. Usually, these values can be obtained from the D3HSP file once the normal termination is achieved. What follows hereafter is the set of images presenting the process followed to calculate Mooney Rivlin and Ogden constants along with their effect on engineering stress versus strain plots.

The following table presented the results of both Mooney and Rivlin constants calculated for three different orders.

D3HSP Engineering Stress-Strain Simulation Results of MAT 077 Hyper-Elastic Rubber card

Simulated Engineering Stress-Strain Results of MAT 077 Hyper-Elastic Rubber card

Simulated Engineering Stress-Strain Results of MAT 077 Ogden Rubber card

5 Conclusion

The main aim of the Week 10 challenge was to model MAT 077 Hyper-Elastic or Ogden Rubber material card from the given Engineering stress-strain raw data and use it to not only calculate Mooney Rivlin and Ogden constants but also perform a uniaxial tension test of the given dog-bone specimen to validate the post-processing stress-strain results with the given raw data. It was observed that the engineering stress-strain curves for MAT 077 Hyper-Elastic card obtained from the D3HSP file closely fit with the given experimental stress-strain data.

However, the engineering stress-strain curves obtained from the post-processing of the performed simulation indicate a slight variation in the values of engineering stresses and strains in comparison with the given experimental data. Similarly, the engineering stress-strain data obtained from uniaxial tensile test simulation of a dog bone specimen with MAT 077 Ogden rubber card indicates a slight variation in the values of engineering stresses and strains in comparison with the given experimental data. This could have happened either due to improper modeling of material card parameters such as density & poisons ratio or due to the high non-linearity of the material itself.