Parametrically Homogenized Continuum Damage Mechanics (PHCDM) Models for Composites from Micromechanical Analysis

Abstract

This paper develops a parametrically homogenized continuum damage mechanics (PHCDM) model for unidirectional fiber-reinforced composites undergoing progressive damage. The PHCDM models are designed to overcome limitations of prohibitive computational overhead associated with many homogenization methods. They are thermodynamically consistent, reduced-order continuum models with explicit representation of microstructural morphology. The PHCDM model is derived from detailed micromechanics of representative volume element (RVE) using energy equivalence principles. Micromechanical failure is due to fiber–matrix interface debonding and matrix cracking. The macroscopic PHCDM models represent damage anisotropy through a second-order damage tensor that contributes to the evolution of a damage surface in the space of damage work conjugate. The damage surface characterizes the initiation and evolution of damage. The constitutive relation between damage and its work conjugate is represented by an anisotropic fourth-order damage surface tensor $P_{ijkl}$, whose components are expressed as functions of current damage state and composite morphology. These are calibrated and validated from homogenized micromechanical (HMM) responses. The PHCDM model is incorporated in a commercial finite element code, and analysis of macroscopic composite components is executed for understanding concurrent damage at multiple material length scales.