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## Introduction

Recent versions of LS-DYNA support the ability to add inelasticity to almost any existing material model (like a hyperelastic model). This is quite a unique idea that does not, as far as I know, exist in any other FE software. Using this approach you can, for example, take any of the LS-DYNA hyperelastic models and then convert it to a multi-network model with flow elements. In some cases this may be useful for FE simulations of polymers. In this article I will show how you can explore and calibrate this type of model framework using MCalibration! Figure: Rheological representaion of the *MAT_ADD_INELASTIC model from the LS-DYNA User’s Manual.

## Example 1: Two Network Model

As a first example I will create a two-network model consisting of one network with a Neo-Hookean spring, and a second network with a Neo-Hookean spring in series with a Norton-Bailey creep flow component. This creep model has the following equation:

$$\dot{\varepsilon}_C = \displaystyle\left[ A \left( \frac{\sigma}{\sigma_0}\right)^n \left( \frac{T}{T_0} \right)^p \left( (1+m)(\varepsilon_0+\varepsilon_c) \right)^m \right]^{1/(1+m)}$$

This material model can be used in MCalibration using the following LS-DYNA template:

				
$$Units: [length]=mm, [force]=N, [time]=sec, [temperature]=K$$ For LS-DYNA R13
*MAT_HYPERELASTIC_RUBBER
$$Neo-Hookean$$     mid,       ro,      pr
1,    1.0e-9,  %PR=0.4995%
$$c10 %C10=1.0% *MAT_ADD_INELASTICITY$$ Norton-Bailey Creep
$$mid, nielinks 1, 1$$ nielaws,   weight
1, %w=0.8%
$$law, model 5, 3$$       A,     sig0,       n,      T0,    p,    m, eps0
%A=1.0%, %sig0=3.0%, %n=4.0%, %T0=293.0%, %p=0.0%, %m=0.0%, %eps0=0.0%



The details of the *MAT_HYPERELASTIC_RUBBER and *MAT_ADD_INELASTICITY commands are provided in the LS-DYNA User’s Manual. Note 1: I converted some of the floating point values to MCalibration variables using the %variable=[value]% syntax. Note 2: LS-DYNA comments need to have two dollar signs in MCalibration. When using this material model in MCalibration it is necessary to specify that LS-DYNA is the solver that should be used, see the following Load Case Dialog image. MCalibration can quickly perform stress-strain calculations once the material model and load case have been specified. Here’s an example in which I applied monotonic uniaxial tension with at constant strain rate of 0.01/s to an engineering strain of 0.5, and then unloaded back to zero strain using the same rate. ## Example 2: Four Network Model

It is easy to work with and calibrate models with more parallel networks. The following example shows one case in which I defined a 4 network model consisting of Neo-Hookean springs and Norton-Bailey creep.

				
$$Units: [length]=mm, [force]=N, [time]=sec, [temperature]=K$$ For LS-DYNA R13
*MAT_HYPERELASTIC_RUBBER
$$Neo-Hookean$$     mid,       ro,      pr
1,    1.0e-9,  %PR=0.4995%
$$c10 %C10=1.0% *MAT_ADD_INELASTICITY$$ Norton-Bailey Creep
$$mid, nielinks 1, 3$$ - Net 1 -
$$nielaws, weight 1, %w1=0.3%$$     law,    model
5,        3
$$A, sig0, n, T0, p, m, eps0 %A=1.0%, %sig1=3.0%, %n=4.0%, %T0=293.0%, %p=0.0%, %m=0.0%, %eps0=0.0%$$ - Net 2 -
$$nielaws, weight 1, %w2=0.3%$$     law,    model
5,        3
$$A, sig0, n, T0, p, m, eps0 %A=1.0%, %sig2=3.0%, %n=4.0%, %T0=293.0%, %p=0.0%, %m=0.0%, %eps0=0.0%$$ - Net 3 -
$$nielaws, weight 1, %w3=0.3%$$     law,    model
5,        3
       A,     sig0,       n,      T0,    p,    m, eps0
%A=1.0%, %sig3=3.0%, %n=4.0%, %T0=293.0%, %p=0.0%, %m=0.0%, %eps0=0.0% • MCalibration makes it is easy to both examine and calibrate the new LS-DYNA *MAT_ADD_INELASTICITY framework models.