Finite element implementation of nearly-incompressible rheological models based on multiplicative decompositions

Abstract

International audienc

Linearized behavior of a dissipative rubber with large static preloads

“…The tangent moduli calculation and the finite-element implementation are classical and are not described here (see [16,17] and the references therein). The numerical integration of the evolution equation is discussed in [18,19].…”

Three-dimensional constitutive model for shape memory polymers using multiplicative decomposition of the deformation gradient and shape memory strains

“…Equations (2), (7), and qT    q are substituted into Equation (8), deriving the following inequality (Laiarinandrasana et al, 2003;Lejeunes et al, 2011):…”

“…The subscripts r and g indicate the rubbery and glassy phases, respectively. The original decomposition ( ep  F F F ) of the deformation gradient proposed by Lee (Lee, 1969) or similar decompositions by some studies (Baghani et al, 2012a;Laiarinandrasana et al, 2003;Lejeunes et al, 2011;Qi et al, 2008;Westbrook et al, 2011) were modified to include the contributions of hyperelastic, viscoelas-ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T 11 tic, viscoplastic elements and shape memory strains. Prior to the decomposition of Equation…”

A Finite Strain Thermo-Chemo-Mechanical Coupled Model for Filled Rubber

“…This condition is a constraint for the unknown field p . For more precisions on the variational formulation and the finite element implementation in the context of mixed formulations for incompressible media submitted to large strain, we refer to the work of [23] and references therein.…”

“…where K ′ is the condensed tangent matrix and R ′ is the condensed residue. The local mechanical flow rule (25) is integrated through a Backward Euler scheme (see [23] for more details). This model has been implemented in the object-oriented finite element code FemJava.…”