# Viscoelastic-plastic constitutive model for thermoplastics

Dear Dr. Bergstrom,

I would like to simulate a thermoforming process with a commercial finite element software with available material models.

I have uniaxial tensile cyclic measurements at different temperatures.

A typical cyclic measurement is depicted in the attached figure.

One cycle is consist of an uploading, strain-holding , unloading, zero force-holding parts.

The material shows viscoelastic behaviour with yielding. I have permanent deformation after every cycles.

So I thought that a visco-hyperelastic model combined with a hardening plastic part may be a good candidate to simulate the measurements in FEA.

I am able to obtain the steady state response which is illustrated with red curve in the figure. The cyclic measurement allows me to separate the total stretch into the product of an elastic and a plastic ( permanent ) parts. Using the elastic part, I am able to fit a hyperelastic model for every cycle. Using the plastic part, I can obtain the logarithmic strain - yield stress data, which shows hardening.

Furthermore, every holding period after the uploading can be considered (as an approximation) as a relaxation test. Thus, the Prony series representation of the relaxation can be easily obtained.

So I obtained every material parameters. The next step is to construct/combine the constitutive model, which would be a visco-hyperelastic model in series with a plastic sliding frictional element representing the hardening yield curve.

Before I am trying to formulate the constitutive model, I ask you, as an expert in this field, is there an available material model in ABAQUS or in ANSYS or in MSC MARC or in COMSOL MP, which can be used for this simulation?

Could you help me, which available material model should I use for this simulation? Maybe the TNM would be a good candidate?

Thank You Very Much!

Kind Regards,

Attila

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