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%
The following figure shows the load-unload predictions from this model.
Summary
- MCalibration makes it is easy to both examine and calibrate the new LS-DYNA
*MAT_ADD_INELASTICITYframework models. - My typically recommendation is to use 2 networks for rubber-like materials, and 3 networks for thermoplastics.
