TY - JOUR

T1 - Approximation-based implicit integration algorithm for the Simo-Miehe model of finite-strain inelasticity

AU - Shutov, A. V.

AU - Ufimtsev, K. P.

PY - 2024/7/16

Y1 - 2024/7/16

N2 - We propose a simple, efficient, and reliable procedure for implicit time stepping, regarding a special case of the viscoplasticity model proposed by Simo and Miehe (1992). The kinematics of this popular model is based on the multiplicative decomposition of the deformation gradient tensor, allowing for a combination of Newtonian viscosity and arbitrary isotropic hyperelasticity. The algorithm is based on approximation of precomputed solutions. Both Lagrangian and Eulerian versions of the algorithm with equivalent properties are available. The proposed numerical scheme is non-iterative, unconditionally stable, and first order accurate. Moreover, the integration algorithm strictly preserves the inelastic incompressibility constraint, symmetry, positive definiteness, and w-invariance. The accuracy of stress calculations is verified in a series of numerical tests, including non-proportional loading and large strain increments. In terms of stress calculation accuracy, the proposed algorithm is equivalent to the implicit Euler method with strict inelastic incompressibility. The algorithm is implemented into MSC.MARC and a demonstration initial-boundary value problem is solved.

AB - We propose a simple, efficient, and reliable procedure for implicit time stepping, regarding a special case of the viscoplasticity model proposed by Simo and Miehe (1992). The kinematics of this popular model is based on the multiplicative decomposition of the deformation gradient tensor, allowing for a combination of Newtonian viscosity and arbitrary isotropic hyperelasticity. The algorithm is based on approximation of precomputed solutions. Both Lagrangian and Eulerian versions of the algorithm with equivalent properties are available. The proposed numerical scheme is non-iterative, unconditionally stable, and first order accurate. Moreover, the integration algorithm strictly preserves the inelastic incompressibility constraint, symmetry, positive definiteness, and w-invariance. The accuracy of stress calculations is verified in a series of numerical tests, including non-proportional loading and large strain increments. In terms of stress calculation accuracy, the proposed algorithm is equivalent to the implicit Euler method with strict inelastic incompressibility. The algorithm is implemented into MSC.MARC and a demonstration initial-boundary value problem is solved.

KW - Simo-Miehe model

KW - efficient numerics

KW - large strain Maxwell model

KW - non-iterational time-stepping

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85198714782&origin=inward&txGid=00536e9eb862eb737e65d7ec0ddc8c29

UR - https://www.mendeley.com/catalogue/81511595-8b93-3116-8b7a-17c30c3d035d/

U2 - 10.1002/nme.7566

DO - 10.1002/nme.7566

M3 - Article

VL - 125

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 21

M1 - e7566

ER -