Estimation of representative length-scales for heterogeneous brittle materials subjected to high-strain-rate loading

Abstract

Continuum-scale modeling of dynamic compressive failure of brittle materials has several important applications such as the design of protective structures under impact loading. These materials can often be highly heterogeneous due to the presence of several cracks or other crack-nucleating defects. Since cracking is a dominant failure mechanism in such problems, material heterogeneity (‘microstructure’) also evolves dynamically as a large number of cracks grow in the material. This necessitates a dynamic damage modeling approach since modeling individual cracks explicitly is cost-prohibitive. When mesh-based computational techniques are utilized for such problems, often a need for fine mesh resolution arises to generate high-fidelity results. Most often mesh sensitivity studies focus on optimizing the mesh size for computational cost, and assume that the constitutive formulation itself remains scale-free. In this work, we propose a procedure to establish a ‘representative length-scale’ for dynamically loaded heterogeneous materials, above which the material can be described by an appropriate local constitutive formulation for the purpose of predicting the response during dynamic failure. Microstructural evolution due to cracking is modeled using synthetic microstructures representing the cracking process assuming a Poisson Point process of pre-existing defect centers. A modulus-increment-based criterion is proposed for representative length-scale determination where the change of material modulus as damage progresses is compared across non-local and local constitutive response. The effect of rate of loading on the predicted RL is also quantified. A demonstration of the defect point process determination procedure in the case of a specific advanced engineering ceramic, boron carbide, is also provided.