Local and non-local thermomechanical modeling

What is it about?

This paper deals with the numerical analysis of instabilities in elastic-plastic materials undergoing large deformations in non-isothermal conditions. The considered isotropic model is fully thermomechanically coupled and includes temperature induced softening which is another source of strain localization next to geometrical effects. Due to complexity of the model a symbolic-numerical tool Ace is used for the preparation of user supplied subroutines for the finite element method. The computational verification is performed using two benchmark tests: necking of circular bar in tension and shear banding of elongated rectangular plate in plain strain conditions. The attention is focused on mesh dependence of the numerical results and the regularizing effect of heat conduction. The research reveals that the conductivity influences the shear band width and ductility of the material response, however, for the adiabatic case the results are discretization-sensitive and another regularization is needed. A new gradient-enhanced thermomechanical model is developed which introduces an internal length parameter governing the size of the shear band caused by thermal softening. The numerical verification of the non-local model is performed for the adiabatic case. Subsequently, the simultaneous application of the gradient enhancement and heat conduction in the model is analyzed, which reproduces an evolving shear band.

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Why is it important?

A thermoplastic material description is proposed in which an averaged temperature governs thermal softening. In such model an internal length scale is introduced which limits strain localization in the adiabatic conditions. In the case of non-adiabatic problem an evolution of the instability can be simulated. Special algorithms are developed using the symbolic-numerical tools Ace in the Mathematica environment.