An Accurate and Efficient Augmented Finite Element Method for Arbitrary Crack Interactions

Abstract

This paper presents a new augmented finite element method (A-EEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method {X-EEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoEs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-EEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.

Stochastic Virtual Tests for High-Temperature Ceramic Matrix Composites

“…The A-FEM correctly tracks the discontinuities in displacement fields that are introduced by cracks within elements, as well as the discontinuity in the cohesive tractions acting along one crack when it is impinged upon by a second crack (25).…”

“…A recent reformulation of the A-FEM improved its ability to treat general crack configurations and its speed (25,196). In the new formulation, there is no need for external virtual nodes to account for the discontinuous displacement fields; internal nodes are used with degrees of freedom that can be condensed out from the elemental equilibrium equation.…”

“…In the heterogeneity of an advanced composite, failure occurs by a complex combination of interacting cracks and local damage events, which are governed by nonlinear material behavior. Key advances in theory have enabled a realistic depiction of the nonlinear mechanics of crack initiation, growth, bifurcation, and coalescence; critically, the location and path of each crack are determined by local stress conditions during a simulation, rather than being prescribed in advance (17)(18)(19)(20)(21)(22)(23)(24)(25)(26). Fidelity in simulations was impossible before such generality was achieved.…”

“…This development allows local convergence to be achieved in one or at most a few steps. The combination of the new iteration algorithm, the compact definition of a multi-ply cracked element, and the use of advanced quadrature algorithms that permit an element to be somewhat larger than the length of the fracture process zone leads to high computational speed (25,196). For a single crack in a bending beam or a delamination crack, a solution to failure, including accurate analysis of snapback in the case of the bending beam, takes several seconds on a standard workstation of 2012 vintage.…”

Stochastic analysis of inter- and intra-laminar damage in notched PEEK laminates

“…While some computational methods, i.e. phantom-node method [16], extended-finite element method (X-FEM) [17] and augmented-finite element method (A-FEM) [18,19] to simulate progressive arbitrary failure in composite materials can yield more accurate results than numerical methods considering reducing the material properties to zero at the time of failure and turning the element's load carrying capacity off, the objective of the present work is to investigate the progressive degradation, delamination behavior, and strength of an open-hole AS4/PEEK laminate with the stochastic distribution of material properties using a three-dimensional numerical simulation. The cohesive elements technique proposed by Camanho and Dávila [20] are considered between two adjacent layers to model the failure due to delamination.…”