Non-uniform Hardening Constitutive Model for Compressible Orthotropic Materials with Application to Sandwich Plate Cores

A constitutive model for the elastic-plastic behavior of plastically compressible orthotropic materials is proposed based on an ellipsoidal yield surface with evolving ellipticity to accommodate non-uniform hardening or softening associated with stressing in different directions. The model incorporates rate-dependence arising from material rate-dependence and micro-inertial effects. The basic inputs are the stress-strain responses under the six fundamental stress histories in the orthotropic axes. Special limits of the model include classical isotropic hardening theory, the Hill model for incompressible orthotropic solids, and the Deshpande-Fleck model for highly porous isotropic foam metals. A primary motivation is application to metal core structure in sandwich plates wherein the core is modeled by a continuum constitutive model. The constitutive model is implemented within a finite element framework to represent the behavior of square honeycomb metal cores of sandwich plates subject to quasi-static and dynamic loads. Input identification is illustrated for numerical formulations that employ one element through the core thickness. Representations of the core with one element through the thickness are shown to be able to capture most of the important influences of nonlinear core behavior on overall response of sandwich plates under both quasi-static and