A large deformation gradient theory for glassy polymers by means of micromorphic regularization - Hamdoun, Ayoub; Mahnken, Rolf (Archive of Applied Mechanics)
Abstract Cold forming of polycarbonate films results in the formation of shear bands in the necking zone. The numerical results obtained from standard viscoplastic material models exhibit mesh size dependency, requiring mathematical regularization. For this purpose, we present in this work a large deformation gradient theory for a viscoplastic isotropic material model published before. We extend our model to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom along with its first gradient. This variable represents a microequivalent plastic strain. The relation between the macroequivalent plastic strain and the micromorphic variable is accomplished by a micromorphic coupling modulus. This coupling forces proximity between the macro- and microvariables, leading to the targeted regularization effect. The micromorphic model is implemented as a three-dimensional initial boundary value problem in an in-house finite element tool. The analysis is performed for both uniaxial and biaxial specimens. The provided numerical examples show the ability of our model to regularize shear bands within the specimens and address the issue of localization.

Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters - Mahnken, Rolf (Archive of Applied Mechanics)
Abstract Optimized material parameters obtained from parameter identification for verification wrt a certain loading scenario are amenable to two deficiencies: Firstly, they may lack a general validity for different loading scenarios. Secondly, they may be prone to instability, such that a small perturbation of experimental data may ensue a large perturbation for the material parameters. This paper presents a framework for extension of hyperelastic models for rubber-like materials accounting for both deficiencies. To this end, an additive decomposition of the strain energy function is assumed into a sum of weighted strain mode related quantities. We propose a practical guide for model development accounting for the criteria of verification, validation and stability by means of the strain mode-dependent weighting functions and techniques of model reduction. The approach is successfully applied for 13 hyperelastic models with regard to the classical experimental data on vulcanized rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944), showing both excellent fitting capabilties and stable material parameters.
Keywords: Mechanical Engineering

A statistically based strain energy function for polymer chains in rubber elasticity - Mahnken, Rolf; Mirzapour, Jamil (Archive of Applied Mechanics)
Keywords: Mechanical Engineering

A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations - Cheng, C.; Mahnken, Rolf (Archive of Applied Mechanics)

"A least squares approach for effective shear properties in an n-layered sphere model" - Mahnken, Rolf; Lenz, Peter; Dammann, Christian (Archive of Applied Mechanics)

A least squares approach for effective shear properties in an $${{\varvec{n}}}$$ n -layered sphere model - Mahnken, Rolf; Lenz, Peter; Dammann, Christian (Archive of Applied Mechanics)

A thermodynamic framework for coupled multiphase Ginzburg-Landau/Cahn-Hilliard systems for simulation of lower bainitic transformation - Düsing, Martin; Mahnken, Rolf (Archive of Applied Mechanics)

Simulation of strain-induced anisotropy for polymers with weighting functions - Mahnken, Rolf; Dammann, Christian (Archive of Applied Mechanics)

A stochastic model for parameter identification of adhesive materials - Nörenberg, Nicole; Mahnken, Rolf (Archive of Applied Mechanics)

Finite elasto-viscoplastic modeling of polymers including asymmetric effects - Mahnken, Rolf; Shaban, A. (Archive of Applied Mechanics)