Efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach

• Published in: International journal for numerical methods in engineering Vol. 88; no. 10; pp. 1008 - 1041
• Main Authors: Mosler, J., Stanković, L., Radulović, R.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 09.12.2011; Wiley
• Subjects: Calculus of variations and optimal control; Discontinuity; embedded strong discontinuities; Exact sciences and technology; Failure; finite elements; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); homogenization; Inelasticity (thermoplasticity, viscoplasticity...); material failure; Mathematical analysis; Mathematical models; Mathematics; Minimization; Optimization; Parametrization; Physics; Sciences and techniques of general use; SDA; Solid mechanics; Static elasticity (thermoelasticity...); Strain; Structural and continuum mechanics; variational constitutive updates; Deformation band; Constitutive equation; Performance evaluation; High strain; Evolution equation; variational constitutive updates; Parameterization; Flexibility; Modeling; Finite element method; SDA; Inelasticity; Conservation law; Model matching; Elastoplasticity; Strain gradient; Kinematics; Slip band; Variational calculus; Localization; Discontinuity; Rupture; Homogenization; Minimization; Maximum principle; Non associated plasticity; embedded strong discontinuities; material failure; finite elements; Structural analysis
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3210

This paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains. Focus is on localized plastic deformation particularly relevant for slip bands. In contrast to already existing models, the proposed implementation allows to consider several interacting discontinuities in each finite element. Based on a proper re‐formulation of the kinematics, an efficient parameterization of the deformation gradient is derived. It permits to compute the strains explicitly that improves the performance significantly. However, the most important novel contribution of the present paper is the advocated variational constitutive update. Within this framework, every aspect is naturally driven by energy minimization, i.e. all unknown variables are jointly computed by minimizing the stress power. The proposed update relies strongly on an extended principle of maximum dissipation. This framework provides enough flexibility for different failure types and for a broad class of non‐associative evolution equations. By discretizing the aforementioned continuous variational principle, an efficient numerical implementation is obtained. It shows, in addition to its physical and mathematical elegance, several practical advantages. For instance, the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities. Copyright © 2011 John Wiley & Sons, Ltd.