An Elastoplastic Augmented Finite Element Method And Numerical Stabilizing Analysis

Advanced composite materials are playing an increasingly important role in engineering and industrial applications,especially in the fields of civil engineering,mechanical manufacturing industry,aerospace systems,offshore platforms,and so on.They are designed and manufactured by the combination of two or more distinct materials with excellent mechanical properties,fitted to the engineering requirements,where conventional materials may not work.Despite the many advantages,heterogeneous and anisotropic characteristics of laminated or textile composites may lead to the occurrence of arbitrary crack coalescence and bifurcation under complex loading conditions,which directly affect the effective mechanical properties and reliability of structural systems.Therefore,high-fidelity material failure simulation has become a significant challenge for the community of engineering science.In recent years,a novel numerical method named augmented finite element method(A-FEM)has been proved to be able to deal with quasi-static nonlinear fracture problems accurately and efficiently.Nevertheless,the current A-FEM mainly focuses on linear elastic materials and stable crack propagation,and both the behavior of elastoplastic materials and unstable crack propagation has not been addressed.In this paper,we shall present a novel elastoplastic augmented finite element method(EP A-FEM)for arbitrary crack initiation and propagation in elastoplastic solids.Meanwhile,a novel inertia-based numerical stabilizing method is proposed for the quasi-static simulation of problems with local or global unstable processes.Based on the elastoplasticity theory,we present one-dimensional and two-dimensional EP A-FEMs,which can deal with the nonlinear fracture in solids with significant plastic deformation and has been implemented into the commercial software package ABAQUS as a user-defined element.The EP A-FE employs linear isotropic hardening model and von Mises yield criterion for the pre-cracking elastoplastic deformation,and a piece-wise linear cohesive law to account for the ensuing crack initiation and propagation.Internal nodes are introduced to ensure smooth transition from a continuous state to a discontinuous state due to cohesive fracture,but their degrees of freedom(DoFs)are fully condensed in each element via a consistency-check based algorithm.The numerical performance of the proposed EP A-FEM has been assessed through several benchmark numerical tests and in all cases the numerical results have been demonstrated that the method is rather insensitive to mesh sizes and mesh structures.Besides,it is shown that the proposed EP A-FEM is numerically very efficient,accurate,and robust.In response to quasi-static simulations of fracture problems with unstable(fast or dynamic)crack propagation,the novel inertia-based stabilizing method is proposed to overcome the loss of numerical convergence.The method guarantees unconditional convergence as the time increment step progressively decreases and it does not need any numerical damping or other solution enhancement parameters.It has been demonstrated,through direct simulations of several numerical examples with severe local or global instabilities,that the proposed method can effectively and efficiently overcome severe instability points unconditionally and regain stability if there exist mechanisms for stable crack propagation after passing through such instability points.In all the numerical tests,the new method outperforms other solution enhancement techniques,such as numerical damping,arc-length method,and implicit dynamic simulation method,in the solution accuracy and numerical robustness.