Piecewise-uniform homogenization of heterogeneous composites using a spatial decomposition based on inelastic micromechanics

Abstract

The homogenized mechanical response of heterogeneous, elasto-plastic composite materials is investigated by the use of the transformation field analysis (TFA), a two-scale algorithm relying on microscopically piece-wise uniform fields of internal variables. Not optimized spatial subdomain decompositions of the microscopic domain cause over-stiff composite material responses modeled by the TFA since the main characteristics of the inelastic field interactions are not well-represented. To improve mechanical predictions using the TFA approach, emerging inelastic fields were used to achieve enhanced spatial decompositions. The numerical estimation of the interaction functions between the subdomains allows the use of this TFA approach for the numerical modeling of a wide variety of composite materials without the need of any pre-determined reference stiffnesses. The new TFA approach was tested for materials with isotropic and anisotropic microstructures and various material systems, with a particular emphasis on the complex case of perfectly plastic material phases. Comparisons are drawn between the TFA modeling using elasticity-based and inelasticity-based spatial divisions and to reference full-field computations. The achieved results prove that more accurate predictions for the mechanical responses of composite materials can be found when inelastic fields are considered as the foundation of the spatial division into subdomains.