bond failure, is the basis for the continuum damage evolution within MCM [17]. Matrix or fiber material properties are degraded as submicrocracks accumulate, where submicrocracks are consecutive failures of interatomic bonds in the polymer matrix [17]. Material property degradation is applied to constituents and the continuum, and apparently leads to a macroscopic response that resembles experimentally observed inelastic material behavior [17]. Composite strains are determined using a given finite element formulation. Composite strains are decomposed into constituent strains. Constituent stresses are determined from constituent strains based on a constituent volume-fractionweighted linear elasticity with anisotropic (transversely isotropic) stiffness material properties determined from composite and constituent material properties using micromechanics and including thermal effects [17]. The micromechanics model for plain weave architecture is shown in Fig. 14.1, which is adapted from work by Barbero et al. [24]. Failure is determined from modified Hashin criteria [20], which uses constituent stresses rather than homogenized composite stresses, allowing distinct failure modes to be predicted for constituents [18]. Assuming transverse isotropy, the failure state of a given constituent is expressed in terms of transversely isotropic stress invariants [25]. Simplifying assumptions are made to ensure matrix dominated failure in the transverse direction and fiber dominated failure in the longitudinal direction of a unidirectional composite. The failure criterion expression coefficients, which are functions of known ultimate tensile, compressive, and shear strengths of constituents, are determined from pure tension, compression, and in-plane shear load cases for each constituent [17]. For plain weave architecture, two constituent theory is extended to three constituents: fiber bundles are themselves unidirectional composites, as shown in Fig. 14.2, but the warp and fill bundles are treated as individual Fig. 14.1 3D model of plain weave architecture upon which micromechanics calculation of constituent material properties are calculated. From left to right: composite, warp fiber bundle constituent, fill fiber bundle constituent, and matrix constituent. Geometry adapted from Barbero et al. [24] Fig. 14.2 View of macro to meso length scales of plain weave composite architecture 14 Initial Experimental Validation of an Eulerian Method for Modeling Composites 105
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