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

A new three-dimensional temperature-dependent viscoelastic constitutive model for unidirectional fiber reinforced, polymer composite materials subjected to small strains 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: in particular, the matrix deviatoric response is considered viscoelastic, while its volumetric response, as well as the fibres' behavior, are considered elastic. 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 of the composite, 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.