| Linear viscoelastic constitutive relationships incorporating the effects of distributed damage are developed for fiber reinforced composite materials. Micromechanics based analysis is presented to obtain the overall linear viscoelastic response of a matrix cracked cross-ply laminate. A 2-D lower bound solution and an approximate 3-D solution to the overall properties are obtained using the Laplace transform based elastic-viscoelastic correspondence principle.; Since the micromechanics-based constitutive equations are specific to the considered laminate geometry and damage modes, they are not suitable for general purpose finite element based structural analysis codes. Further, micromechanics-based constitutive equations may be difficult to obtain when damage is such that no periodic representative volume element can be identified. Thus a more general internal variables based continuum damage model is developed. Using the Laplace transformed based elastic-viscoelastic correspondence principle, a pseudo strain energy function is defined in terms of Laplace transformed strain and damage internal variables. For the case of non-evolving damage, this pseudo strain energy function is expanded as a polynomial in its arguments in accordance with the orthotropic symmetry restriction imposed by the material. The time domain relationships are obtained by inverse Laplace transform. The approach is illustrated for the specific case of matrix cracked symmetric cross-ply laminates. The generality of the approach is illustrated by showing how transient temperature, moisture and physical aging effects can be incorporated.; Evolution of damage in viscoelastic laminates is studied using a cohesive finite element approach. A two dimensional, four noded finite element is developed incorporating a rate-independent traction-displacement cohesive law. This element is used in conjunction with plane strain bulk elements behaving in a linear viscoelastic manner to simulate crack evolution between two existing transverse cracks in symmetric cross-ply laminates. The effects of loading strain-rate, ply constraints and initial crack density are studied. |
