Homogenized finite elastoplasticity and damage: Theory and computations: Fid-Bau Portal

Homogenized finite elastoplasticity and damage: Theory and computations

Clayton, J.D. / McDowell, D.L.

Explicit volume averaging procedures are employed to construct a multi-scale framework describing finite elastoplasticity and damage processes in a polycrystalline aggregate. A hybrid additive-multiplicative decomposition for the macroscopic deformation gradient captures precisely the kinematics of anisotropic damage and offers insight into mesoscopic distributions of residual elastic lattice strain attributed to heterogeneity of local deformation occurring at both intergranular and intragranular scales. The proposed multi-scale framework also provides a convenient setting from which to evaluate new continuum-type failure criteria in terms of homogenized variables constructed from mesoscopic (i.e., locally varying) incompatibility fields. The new failure parameters supplement traditional criteria such as porosity or crack density, offering additional information regarding accommodation of deformation and related length scale effects. Finite element calculations performed on aggregates of multiple grains, with each grain discretized into several hundred elements, are conducted to evaluate the model's capabilities. Crystal plasticity theory describes the elastoplastic behavior of the grains at the mesoscale. Cohesive zone finite elements are included to model intergranular fracture, with a formulation tailored to represent the failure of polycrystalline copper with trace antimony segregated at grain boundaries. The computational results illustrate that the build-up of elastic strain energy density due to incompatibility, and subsequent crack initiation and growth, depend heavily upon the initial grain boundary misorientation distribution and grain morphology.