A coupled incremental damage and plasticity theory for rate-independent and rate-dependent composite materials is introduced here. This allows damage to be path-dependent either on the stress history or thermodynamic force conjugate to damage. This is achieved through the use of an incremental damage tensor. Damage and inelastic deformations are incorporated in the proposed model that is used for the analysis of ®ber-reinforced metal±matrix composite materials. The damage is described kinematically in both the elastic and inelastic domains using the fourth-order damage eect tensor which is a function of the second-order damage tensor. A physical interpretation of the second-order damage tensor is given in this work which relates to the microcrack porosity within the unit cell. The inelastic deformation behavior with damage is viewed here within the framework of thermodynamics with internal state variables.
Computational aspects of both the rate-independent and rate-dependent models are discussed in this work. The Newton±Rapson iterative scheme is used for the overall laminate system. The constitute equations of both the rate-independent and the rate-dependent plasticity coupled with damage models are additively decomposed into the elastic, inelastic and damage deformations by using the three-step split operator algorithm [J.W. Ju, Internat. J. Solids Struc. 25 (1989) 803±833]. The main framework return maping algorithm [M. Ortiz, C. Simo, Internat. J. Numer. Meth. Eng. 23 (1986) 353±366] is used for the correction of the elasto-plastic and viscoplastic states. However, for the case of the damage model these algorithms are rede®ned according to the governed damage constitutive relations.
In order to test the validity of the model, a series of laminated systems 0 8s Y 90 8s Y 0a90 4s Y À45a45 2s are investigated at both room and elevated temperatures of 538°C and 649°C. The results obtained from the special purpose developed computer program, DVP-CALSET (Damage and Viscoplastic Coupled Analysis of Laminate Systems at Elevated Temperatures), are then compared with the available experimental results and other existing theoretical material models obtained from the work of B.