Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

By F. Armero, Christian R. Linder. 2009

146 citations recorded by the source corpus.

This paper presents the extension of some finite elements with embedded strong discontinuities to the fully transient range with the focus on dynamic fracture. Cracks and shear bands are modeled in this setting as discontinuities of the displacement field, the so-called strong discontinuities, propagating through the continuum. These discontinuities are embedded into the finite elements through the proper enhancement of the discrete strain field of the element. General elements, like displacement or assumed strain based elements, can be considered in this framework, capturing sharply the kinematics of the discontinuity for all these cases. The local character of the enhancement (local in the sense of defined at the element level, independently for each element) allows the static condensation of the different local parameters considered in the definition of the displacement jumps. All these features lead to an efficient formulation for the modeling of fracture in solids, very easily incorporated in an existing general finite element code due to its modularity. We investigate in this paper the use of this finite element formulation for the special challenges that the dynamic range leads to. Specifically, we consider the modeling of failure mode transitions in ductile materials and crack branching in brittle solids. To illustrate the performance of the proposed formulation, we present a series of numerical simulations of these cases with detailed comparisons with experimental and other numerical results reported in the literature. We conclude that these finite element methods handle well these dynamic problems, still maintaining the aforementioned features of computational efficiency and modularity.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/74508de81e88648b96875be03ab17ee3d9ef8ca6

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In Mechanics of Materials

Citations in the corpus

Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation (2012, methodology): “Defects of the classical Griffith-type theory such as its non-ability to initiate cracks can be overcome by variational methods based on energy minimization as suggested in the pioneering works of Francfort and Marigo (1998) and Bourdin et al.”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, background): “An alternative strategy usually referred to as the strong discontinuity approach (SDA) [10, 33– 36] is based on the multiscale treatment of different components involved in material failure, identifying an individual finite element as a local neighborhood of a failed material point.”
A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, Cohesive Element Method (2011, methodology): “a=1 N a (ξ)Xa± , (28) where Xa± , a ∈ [1, 6] are the nodal coordinates of the surface elements in the reference configuration.”
New finite elements with embedded strong discontinuities for the modeling of failure in electromechanical coupled solids (2011, background): “[25] within a regularized approach and in Armero and Linder [8] without the need for an additional regularization parameter.”
A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns (2013, background): “Finite elements with embedded discontinuities, which allow branching based on a velocity-based branching criterion, were recently outlined in [40,41].”