Analysis and Numerical Simulation of the Behavior of Composite Materials with Natural Fibers Under Quasi-Static Frictional Contact

This paper analyzed the behavior of polymer composite materials reinforced with randomly oriented short natural fibers (hemp, flax, etc.) subjected to external stresses under quasistatic contact conditions with dry Coulomb friction. We presumed the composite body, a 2D flat rectangular plate, being in frictional contact with a rigid foundation for the quasistatic case. The manuscript proposes the finite element method approximation in space and the finite difference approximation in time. The problem of quasistatic frictional contact is described with a special finite element, which can analyze the state of the nodes in the contact area, and their modification, between open, sliding, and fixed contact states, in the analyzed time interval. This finite element also models the Coulomb friction law and controls the penetrability according to a power law. Moreover, the quasi-static case analyzed allows for the description of the load history using an incremental and iterative algorithm. The discrete problem will be a static and nonlinear one for each time increment, and in the case of sliding contact, the stiffness matrix becomes non-symmetric. The regularization of the non-differentiable term comes from the modulus of the normal contact stress, with a convex function and with the gradient in the sub-unit modulus. The non-penetration condition was achieved with the penalty method, and the linearization was conducted with the Newton–Raphson method.