Micromechanical modeling of viscoelastic behavior of polymer matrix composites undergoing large deformations

In the present investigation, a comprehensive finite strain micromechanical analysis is offered for the prediction of the viscoelastic behavior of polymer matrix composites undergoing large deformations. The finite viscoelasticity of the matrix governs the rate-dependent response of the composite, its hysteresis in cyclic loading-unloading, as well as its creep and relaxation behavior. The finite viscoelasticity of the polymeric constituent of the composite allows, in particular, large deviations away from the thermodynamic equilibrium. Finite linear viscoelasticity (where the deviations are small) and linear viscoelasticity are obtained as special cases. In addition, perfectly elastic behavior of the polymeric matrix (hyperelasticity) forms another special case of the present theory. Furthermore, the possibility of evolving damage in the polymeric finite viscoelastic matrix is accounted for. This is expressed by an evolution law according to which the damage accumulates depending on the maximum strain history. As a result, the Mullins damage effects can be modeled and observed. The micromechanical modeling is based on the homogenization technique for periodic microstructure, which establishes, in conjunction with its instantaneous tangent and viscoelastic-damage tensors, the macroscopic (global) constitutive equations of the viscoelastic composite undergoing large deformations. Results are given which exhibit the response of the composite to cyclic loading as well as its creep and relaxation behavior in various circumstances.