Based on the general macroscopic potential theory, a method to find macroscopic plastic potential and the corresponding constitutive relation is developed for visco-plastic materials containing cylindrical voids. The constitutive relation of the matrix has a generalized overstress form. A comparison of the exact macroscopic potential with its upper bound is made. The numerical results show little difference between the upper bound potential and the exact one. The macroscopic constitutive relation is investigated under triaxial loading conditions. When the strain rate sensitive parameter tends to zero, Gurson's model (1977) is retrieved. When the loading condition is axisymmetric, the present result reverts to Licht and Suquet's result (1988). When the matrix becomes infinite, the result of Budiansky et al. (1982) is obtained. Finally, the macroscopic constitutive relation and the corresponding dynamic loading surface are investigated for the case of axisymmetric load. An approximate analytical expression of the dynamic loading surface is suggested through analysis and numerical fitting.KEY WORDS: plastic potential, visco-plastic material, cylindrical void growth, dynamic loading surface.

We analyze progressive damage and failure of composite laminates by using a micromechanical bridging model and compare numerical and experimental results for three fracture problems, namely, the four-point bending, the simple tension, and the simple tension of a laminate with an open hole at its centroid. These problems involve fiber–matrix interface debonding, constituents’ damage, interlayer delamination, and localized damage due to stress concentration. Macroscopic constitutive equations of unidirectional lamina, derived from those of the fiber and the matrix by using the bridging model with the fiber material assumed to be linearly elastic and the matrix to be elasto-plastic obeying the Drucker–Prager yield criterion, are employed. Strains in each constituent of the composite are assumed to be infinitesimal for the additive decomposition of strains into elastic and plastic parts to be valid, and the incremental plasticity theory is used. Stresses in the two constituents are found from their values in the homogenized material by using a dehomogenization technique. The intra-layer damage is assumed to initiate at a material point when the failure criterion for either the fiber or the matrix is satisfied. Young’s modulus of a constituent is degraded by following a Weibull distribution. A finite element is deleted when an energy-based failure criterion is satisfied in it, and the analysis is continued till the structure fails. The delamination between adjacent plies is simulated by including a thin resin layer at the interface and studying failure initiation and propagation in it. The computed reaction force versus the displacement curves and the failure patterns in the three problems are found to agree with the corresponding experimental data.

No abstract