Prediction of shape distortions Part I. FE-implementation of a path dependent constitutive model

There is a great interest, especially from the aircraft industry, to increase the ability to understand and predict development of shape distortions and residual stresses during manufacture of polymer composite components. An increased ability to predict shape distortions will result in more cost efficient development, improved performance and optimised manufacturing of composites. To be able to predict residual stresses and shape distortions a model is needed that accounts for all important mechanisms involved. In a previous work by the authors, it was demonstrated that such—models must account for thermal expansion (different in glassy and rubbery state), chemical shrinkage due to the crosslinking reaction and finally frozen-in deformations. The present paper presents a simple mechanical constitutive model that accounts for the mechanisms mentioned above. The model is a limiting case of linear visco-elasticity that permits us to replace the rate dependence by a path dependence on the state variables: strain, degree of cure and temperature. This means significant savings in computational time, memory requirements and costs for material characterisation as compared to conventional visco-elastic models. This is the first of two papers, the second paper deals with experimental validation and analysis of mechanical boundary conditions during prediction of shape distortion.