TY - GEN

T1 - Efficient integration for the SIMO-Miehe model with mooney-rivlin potential

AU - Shutov, Alexey V.

N1 - Funding Information: The research was partially supported by RFBR (grant number 17-08-01020) and by the integration project of SB RAS (project number 0308-2018-0018). Publisher Copyright: copyright © Crown copyright (2018).All right reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Efficient Numerics

KW - Finite Strain

KW - Mooney-Rivlin Potential

KW - Simo-Miehe Model

KW - Stress-Dependent Viscosity

KW - Zener Model

UR - http://www.scopus.com/inward/record.url?scp=85081065432&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85081065432

T3 - Proceedings 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

SP - 1927

EP - 1937

BT - Proceedings of the 6th European Conference on Computational Mechanics

A2 - Owen, Roger

A2 - de Borst, Rene

A2 - Reese, Jason

A2 - Pearce, Chris

PB - International Centre for Numerical Methods in Engineering, CIMNE

T2 - 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018

Y2 - 11 June 2018 through 15 June 2018

ER -