A hysteretic model for fiber-reinforced composites at finite strains: fractional derivatives, computational aspects and analysis

Abstract Deep drawing complex composite parts including strong geometrical non-linearities are currently of major interest. Such forming process induces non-monotonous variations in bending and in-plane shear deformation modes. Moreover, it is experimentally shown that these specific variations lead to an hysteretic behavior of the material. Hence, non dissipative models are no longer appropriate to accurately describe the behaviour since these variations of load cannot longer be neglected. The objective of this paper is therefore to propose an anisotropic model under large strains capable of describing the hysteretic trajectories of the material’s behavior. For this purpose, a fractional derivative approach was applied and identified. Through this hysteretic approach, it is now possible to predict the shape, shear and bending strain more accurately when the fabric undergoes heavy transformation. This model also gives the possibility to predict the residual stress and plastic strain. These predictions lead to quantify the spring back of the material when the punches are removed, which is very important since new deep drawing strategies are emerging. Discretization procedures for fractional derivatives models are described and Matlab source codes are also provided.