Efficient integration for the SIMO-Miehe model with mooney-rivlin potential

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Abstract

A model of finite-strain visco-plasticity proposed by Simo and Miehe (1992) is considered. The model is based on the multiplicative split of the deformation gradient, combined with hyperelastic relations between elastic strains and stresses. This setup is a backbone of many advanced models of visco-elasticity and visco-plasticity. Therefore, its efficient numerical treatment is of practical interest. Since the underlying evolution equation is stiff, implicit time integration is required. A discretization of Euler backward type yields a system of nonlinear algebraic equations. The system is usually solved numerically by Newton-Raphson iteration or its modifications. In the current study, a practically important case of the Mooney-Rivlin potential is analyzed. The solution of the discretized evolution equation can be obtained in a closed form in case of a constant viscosity. In a more general case of stress-dependent viscosity, the problem is reduced to the solution of a single scalar equation or, in some situations, even can be solved explicitly. Simulation results for demonstration problems pertaining to large-strain deformation of different types of viscoelastic materials are presented.

Original languageEnglish
Title of host publicationProceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publicationSolids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
EditorsRoger Owen, Rene de Borst, Jason Reese, Chris Pearce
PublisherInternational Centre for Numerical Methods in Engineering, CIMNE
Pages1927-1937
Number of pages11
ISBN (Electronic)9788494731167
Publication statusPublished - 1 Jan 2020
Event6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 - Glasgow, United Kingdom
Duration: 11 Jun 201815 Jun 2018

Publication series

NameProceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018

Conference

Conference6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
CountryUnited Kingdom
CityGlasgow
Period11.06.201815.06.2018

Keywords

  • Efficient Numerics
  • Finite Strain
  • Mooney-Rivlin Potential
  • Simo-Miehe Model
  • Stress-Dependent Viscosity
  • Zener Model

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