Parametrically Homogenized Damage Models from Micromechanical Analyses of Statistically Equivalent RVE’s

ABSTRACT

Pure micromechanical analysis of a structural component is computationally prohibitive due to the large number of heterogeneities in the underlying microstructure.  This calls for hierarchical multi-scale models, entailing bottom-up coupling for unidirectional transfer of information from lower to higher scales. The information transferred is usually in the form of effective material properties. A number of hierarchical models have incorporated the asymptotic homogenization theory in conjunction with computational micromechanics models. A subset of the hierarchical models has been branded as the FE² multi-scale methods, where micro-mechanical RVE models are solved to obtain homogenized properties for macroscopic analysis. However, this method can incur prohibitively large computational costs as it entails solving the micromechanical RVE problem for every element integration point in the computational domain. Parametric homogenization can overcome these limitations through homogenized constitutive-damage models from micromechanical analyses of heterogeneous RVEs.

             This talk will discuss the rigorous development of parametrically homogenized constitutive-damage models (PHCDMs) that are thermodynamically consistent with the micromechanical response of the RVE or SERVE under identical conditions of overall loading. A departure from phenomenological models is in the design of constitutive parameters and their dependencies in these models. Calibrated from thermodynamic consistency conditions, e.g. equivalence of strain energy or its increment, the constitutive parameters are designed to have direct dependence on the microstructural morphological variables through functions that represent their distributions.  In addition, these parameters also evolve with macroscopic state variables that represent aggregate effects of the microstructural deformation mechanisms. The parametrically homogenized constitutive models are effectively reduced-order models that have significantly reduced variables in their representation in comparison with detailed micromechanical models. This talk will focus on the development of PHCDMs representing damage in composite structures.

             A second aspect that will be discussed in this talk is the development of exterior statistics-based boundary conditions (ESBCs) accounting for the presence of fibers and their interactions in the domain exterior to the statistically equivalent RVE. ESBCs are derived for statistically inhomogeneous microstructures using the two-point correlation functions used in the statistically informed Green’s functions. Comparisons will be made with the statistical volume element (SVE) approach. Simulations with ESBCs have a definite advantage over other methods in defining optimal sized SERVEs for clustered and matrix-rich microstructures.