A self-consistent homogenization framework for dynamic mechanical behavior of fiber reinforced composites

Abstract

This paper proposes a self-consistent homogenization framework for developing finite strain, elastic constitutive models of carbon fiber–epoxy composites for high strain-rate loading. The framework incorporates a concurrent multiscale model, in which an RVE is embedded in a homogenized exterior domain, is developed with self-consistent displacement compatibility and traction reciprocity constraints at the RVE-exterior domain interface. It overcomes limitations of periodic boundary conditions on the RVE for dynamic problems under high strain-rate conditions and allows for the evaluation of material constitutive relations accounting for micro-scale inertia. The proposed self-consistent formulation incorporates the effect of stress waves propagation in the microstructure, along with their interaction with heterogeneities resulting in reflection and transmission at the interfaces. The concurrent model is used to study dynamic composite behavior at strain-rates in the range of 102-105 s−1 for two RVEs, one containing a single fiber and another with 70 randomly distributed fibers. For strain-rates above 104 s−1, the dynamic part of the stress becomes significant and dominates over the static part of the stress. Results of the analysis show that for high strain-rate dynamic loading, constitutive models for the composites must account for micro-inertia, in addition to strain-rates and microstructural morphology.