Strain-rate based arclength model for nonlinear microscale analysis of unidirectional composites under off-axis loading

In this paper, a micromechanical framework for modeling the rate-dependent response of unidirectional composites subjected to off-axis loading is introduced. The model is intended for a thin slice representative volume element that is oriented perpendicular to the reinforcement of the composite material. The testing conditions from a uniaxial off-axis test are achieved by a dedicated strain-rate based arclength formulation. The constraint equation of the arclength model is constructed such that the deformation state of the micromodel, as imposed in its local coordinate system, corresponds to the strain-rate applied on the material in global frame of reference. The kinematic description allows for finite strains in the material, meaning that the micromodel changes orientation during the deformation process. This geometric nonlinear effect is also included in the evaluation of external loading, ensuring that the external forces are equivalent to the applied off-axis stress in global coordinate system. Several examples are considered in order to show that the model resolves rate-dependency of the material, accounts for different off-axis loading, and captures finite strains exactly. Additionally, a small strain version of the model is derived from the general nonlinear framework. Results obtained with this simplified approach are compared to results of the large deformation framework.