Adaptive space and time discretizations of updated Lagrangian formulations: Application to shaped elastoplastic fiber pullout using a hybrid interface model

The fiber pullout test has long served as a surrogate for estimating fracture toughness of fiber-matrix systems. A quasi-static analysis of the elastoplastic fiber pullout process is simulated by the hp-adaptive finite element method based on an updated Lagrangian formulation. To approximate the nonlinear behavior of the fiber-matrix interface, we propose a mixed cohesion-friction model. The use of such a model enables us to simulate the entire pullout process. A combination of von Mises yield criterion and associated flow rule is utilized as the constitutive model to describe the plasticity in the annealed copper fiber. Through comparison with the experimental results from straight fiber pullout, key parameters for describing the interface model are determined and the model is validated. The model is then applied to simulate the pullout of the "nail-head" shaped fiber family. Simulation results are used to design an optimal shape of the head to maximize the pullout work. An explicit a posteriori estimator based on the patch-recovery gradient technique and element residual method is developed to obtain the optimal mesh for fiber pullout problem. Finally, we implement an adaptive time discretization scheme that can adjust the load step automatically during fiber pullout, so computational cost can be reduced while preserving the solution accuracy.