An efficient augmented finite element method for arbitrary cracking and crack interaction in solids

Abstract

SUMMARYThis paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra‐elemental discontinuities in 2D solids. The augmented finite element method (A‐FEM) employs four internal nodes to account for the crack displacements due to an intra‐elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece‐wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A‐FEM's high‐fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A‐FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust. Copyright © 2014 John Wiley & Sons, Ltd.

Augmented finite-element method for arbitrary cracking and crack interaction in solids under thermo-mechanical loadings

“…Equation ( However, for the piece-wise linear cohesive laws in figure 2, a consistency-check-based solution algorithm has been established in [29,30]. It is directly applicable to solve equation (3.7) and we shall not repeat the solving procedure here.…”

“…More recently, a new version of the A-FEM, which allows for explicit inclusion of descriptions of cohesive cracks, without the need to change mesh adaptively or to add extra d.f. dynamically as the cracks propagate, has been developed and demonstrated with much improved numerical performance for a variety of fracture problems [2,[29][30][31]. It has been shown repeatedly that the new A-FEM is able to account for multiple, arbitrary cracks and crack interactions in solids with much improved numerical efficiency [29,30] (2-3 orders of magnitude in many cases).…”

“…Following the discretization scheme detailed in [29,30], the following thermal-mechanical equilibrium equations for the two subdomains can be derived: …”

Stochastic Virtual Tests for High-Temperature Ceramic Matrix Composites

“…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.…”

“…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.…”