Frameworks for finite strain viscoelastic-plasticity based on multiplicative decompositions. Part II: Computational aspects Original Research Article

Computational aspects of the two formulations of viscoelastic-plasticity at finite strains proposed in Part I of this work are examined in detail. These formulations are based upon distinct kinematic assumptions resulting from different multiplicative decompositions of the deformation gradient. However, the corresponding sets of local evolution equations consistent with continuum thermodynamics and adopted in this work have globally the same structures and, therefore, lead to similar algorithmic treatments. The key idea in the design of the integration algorithms is the systematic use of the nowadays well-known exponential mapping algorithms in conjunction with the notion of operator split methodology. These numerical approximations are then applied to the model examples proposed in Part I together with their extensions to incorporate rate-dependent plasticity. The implementation within the framework of the finite element method is described in detail and, finally, we present a set of representative numerical simulations to illustrate the features of the proposed models.