Finite elements with embedded strong discontinuities for the modeling of failure in solids

By Christian R. Linder, F. Armero. 2007

277 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d0bdf7ac260d194a3c7e15d5faeb0a70c07cd93a

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Mixed stabilized finite element methods in nonlinear solid mechanics: Part II: Strain localization (2010, background): “The test is far more demanding that the previously presented case (pure stretching), because the simulation of linear displacement jumps occurring across bands formed by low order triangular and quadrilateral finite elements requires some attention ([41,43]).”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “Furthermore, the initial approach did not ensure a continuous crack surface, which was subsequently corrected by incorporating linear interpolation between adjacent elements (Linder and Armero 2007).”
Numerical simulation of dynamic fracture using finite elements with embedded discontinuities (2009, background): “…formulation is fully objective with respect to mesh size (that is, it does not exhibit the pathological mesh dependence typical of continuum elements due to the incorrect resolution of the localized dissipativemechanismassociatedwithfracture)as illustrated in detail in Linder and Armero (2007).”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, background): “A derivation of 2-D analytical solutions in a similar problem setup can be found in [37], which assumes linearly varying loading and linear cohesive law.”
On three-dimensional modelling of crack growth using partition of unity methods (2010, background): “possible to incorporate linear crack opening into EFEM [71].”
Revisiting the problem of a crack impinging on an interface: A modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model (2017, background): “; (ii) extended FE strategies with nodal kinematic enrichment (extended-FEM, X-FEM) that rely on Partition of Unity Methods (PUM) [25, 26, 27] and element enrichment formulations (enhancedFEM, E-FEM) [28, 29, 30, 31]; (iii) adaptive insertion of cohesive interface elements during the computation or ”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, methodology): “The load scenario consists of two stages [31, 36, 75]: (i) the block is first stretched uniformly in direction x, until a discontinuity forms along the height; (ii) the stretch continues by imposing displacements with the rate of pulling at the bottom of the block being double that at the top, i.”
New finite elements with embedded strong discontinuities in the finite deformation range (2008, methodology): “These observations identify an alternative strategy for the definition of the enhanced deformation gradient, as originally discussed in [7] for plates and [30] for infinitesimal continuum elements.”
Towards a generalization of a discrete strong discontinuity approach (2009, methodology): “More recently, Linder and Armero [25] and Oliver et al.”
Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids (2015, methodology): “where a fine scale equilibrium projection matrix [39,24] P(x) :=  Pk(x)  is introduced to project the stresses σ , generally known only at quadrature points, to the discontinuity Se, i.”