Multiscale analysis of multiple damage mechanisms coupled with inelastic behavior of composite materials

Thermodynamically consistent constitutive equations are derived here in ord er to investigate size effects on the strength of composite, strain, and da mage localization effects on the macroscopic response of the composite, and statistical inhomogeneity of the evolution-related damage variables associ ated with the representative volume element. This approach is based on a gr adient-dependent theory of plasticity and damage over multiple scales that incorporates mesoscale interstate variables and their higher order gradient s at both the macro- and mesoscales. This theory provides the bridging of l ength 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 b ehavior of these defects is captured not only individually, but also the in teraction 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 introduc ing gradients at the mesoscale and the macroscale enables one to address tw o issues simultaneously. The mesoscale gradients allow one to address issue s such as lack of statistical homogeneous state variables at the macroscale level such as debonding of fibers in composite materials, cracks, voids, a nd so forth. On the other hand, the macroscale gradients allow one to addre ss nonlocal behavior of materials and interpret the collective behavior of defects such as dislocations and cracks. The capability of the proposed mod el is to properly simulate the size-dependent behavior of the materials tog ether with the localization problem. Consequently, the boundary-value probl em of a standard continuum model remains well-posed even in the softening r egime. The enhanced gradient continuum results in additional partial differ ential equations that are satisfied in a weak form. Additional nodal degree s of freedom are introduced that leads to a modified finite-element formula tion. The governing equations can be linearized consistently and solved wit hin the incremental iterative Newton-Raphson solution procedure.