A new mechanism-based thermo-viscoelastic model for unidirectional polymer matrix composites based on Cartan decomposition

A new three-dimensional thermo-viscoelastic constitutive model for unidirectional fiber reinforced, polymer composite materials is developed in this work. The key point is to introduce the viscoelastic behavior only where appropriate, based on the constitutive behavior of the underlying constituents, elastic fibers and viscoelastic (in shear) matrix. In order to achieve this, an irreducible Cartan decomposition for the stress and strain tensors under the hypothesis of transverse isotropy is derived. The integrity basis for the decomposition is used to formulate the energy functional, which enables us to define uncoupled constitutive laws in which the contributions of the underlying constituents are easily identified. In order to describe the viscoelastic behavior in shear of the matrix, a generalized Maxwell model is applied to the appropriate terms of the stress and strain decomposition, in agreement with the underlying physical mechanism. Thermal strains and temperature effects on the viscoelastic behavior are introduced through the time-temperature superposition principle. Various numerical simulations are performed to show the key features of the presented constitutive model and an Abaqus UMAT is implemented in order to perform structural simulations.