Multiscale Analysis of Multiple Damage Mechanisms Coupled with Inelastic Behavior of Composite Materials

Thermodynamically consistent constitutive equations are derived here in order to investigate size effects on the strength of composite, strain, and damage localization effects on the macroscopic response of the composite, and statistical inhomogeneity of the evolution-related damage variables associated with the representative volume element. This approach is based on a gradient-dependent theory of plasticity and damage over multiple scales that incorporates mesoscale interstate variables and their higher order gradients at both the macro- and mesoscales. This theory provides the bridging of length scales. The interaction of the length scales is a paramount factor in understanding and controlling material defects such as dislocation, voids, and cracks at the mesoscale and interpreting them at the macroscale. The behavior of these defects is captured not only individually, but also the interaction between them and their ability to create spatiotemporal patterns under different loading conditions. The proposed work introduces gradients at both the meso- and macroscales. The combined coupled concept of introducing gradients at the mesoscale and the macroscale enables one to address two issues simultaneously. The mesoscale gradients allow one to address issues such as lack of statistical homogeneous state variables at the macroscale level such as debonding of fibers in composite materials, cracks, voids, and so forth. On the other hand, the macroscale gradients allow one to address nonlocal behavior of materials and interpret the collective behavior of defects such as dislocations and cracks. The capability of the proposed model is to properly simulate the size-dependent behavior of the materials together with the localization problem. Consequently, the boundary-value problem of a standard continuum model remains well-posed even in the softening regime. The enhanced gradient continuum results in additional partial differential equations that are satisfied in a weak form. Additional nodal degrees of freedom are introduced that leads to a modified finite-element formulation. The governing equations can be linearized consistently and solved within the incremental iterative Newton-Raphson solution procedure.