Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach

By Javier Oliver, Alfredo Huespe, S. Blanco, Dorian L. Linero. 2006

135 citations recorded by the source corpus.

Abstract Robustness and stability of the Continuum Strong Discontinuity Approach (CSDA) to material failure are addressed. After identification of lack of symmetry of the finite element formulation and material softening in the constitutive model as possible causes of loss of robustness, two remedies are proposed: (1) the use of an specific symmetric version of the elementary enriched (E-FEM) finite element with embedded discontinuities and (2) a new implicit–explicit integration of the internal variable, in the constitutive model, which renders the tangent constitutive algorithmic operator positive definite and constant. The combination of both developments leads to finite element formulations with constant, in the time step, and non-singular tangent structural stiffness, allowing dramatic improvements in terms of robustness and computational costs. After assessing the convergence and stability properties of the new strategies, three-dimensional numerical simulations of failure problems illustrate the performance of the proposed procedures.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a293f6bf7a39ec4e3c76fa477a290b4ce8199637

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

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 ”
New finite elements with embedded strong discontinuities in the finite deformation range (2008, background): “Following [44,38], the slope is assumed elastic perfectly plastic with Young modulus E = 10 MPa, Poisson ratio m 1⁄4 0:4 and yield limit of sY 1⁄4 0:1 MPa.”
Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations (2015, methodology): “As regards the SKON formulation, Petrov–Galerkin method shall be used in order to improve the numerical stability [35,36].”
Effective 3D failure simulations by combining the advantages of embedded Strong Discontinuity Approaches and classical interface elements (2011, unknown): “[34].”
A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM (2006, methodology): “In this sense, the implicit– explicit procedure, presented elsewhere [24] [25] [26], has been used to integrate the constitutive model.”
Crack patterns in clayey soils: Experiments and modeling (2012, background): “The jump is activated when a failure criterion is met [75].”