Application of three-dimensional (3D) woven composites is growing as an alternative to the use of ply-based composite materials. However, the design, analysis, modeling, and optimization of these materials is more challenging due to their complex and inherently multiscale geometries. Herein, a multiscale modeling procedure, based on efficient, semi-analytical micromechanical theories rather than the traditional finite element approach, is presented and applied to a 3D woven carbon–epoxy composite. A crack-band progressive damage model was employed for the matrix constituent to capture the globally observed nonlinear response. Realistic microstructural dimensions and tow-fiber volume fractions were determined from detailed X-ray computed tomography (CT) and scanning electron microscopy data. Pre-existing binder-tow disbonds and weft-tow waviness, observed in X-ray CT scans of the composite, were also included in the model. The results were compared with experimental data for the in-plane tensile and shear behavior of the composite. The tensile predictions exhibited good correlations with the test data. While the model was able to capture the less brittle nature of the in-plane shear response, quantitative measures were underpredicted to some degree.

A thermodynamically-based work potential theory for modelling progressive damage and failure in fibre-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory, utilises separate ISVs for modelling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed, matrix microdamage is the dominant damage mechanism in continuous, fibre-reinforced, polymer matrix laminates, and its evolution is captured with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. Typically, failure evolution (i.e. post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method numerical setting. Therefore, consistent characteristic element lengths are introduced into the formulation of of the three failure potentials. The theory is implemented into commercial FEM software. The model is verified against experimental results from a laminated, quasi-isotropic, T800/3900-2 panel containing a central notch. Global load versus displacement, global load versus local strain gauge data, and macroscopic failure paths obtained from the models are compared to the experiments. Finally, a sensitivity study is performed on the failure parameters used in the model.