Strain Injection Techniques in Numerical Modeling of Propagating Material Failure

I. DIAS; J. OLIVER; A E. HUESPE

Barcelona

Congreso; Computational Plasticity XII ? Fundamentals and Applications; 2013

The methodology proposed in this work explores the use of the strain injection concept in acombination of classical strain localization methods [1][2] and embedded strong discontinuities [3],to remove the flaws (stress locking and mesh bias dependence) of the former, and simultaneouslyabdicate of the global tracking algorithms usually required by the later. The basic idea is to use, afterthe bifurcation instant, i.e. after the time that elements are amenable to develop discontinuities, amixed continuous displacements - discontinuous constant strains condensable finite elementformulation (Q1/ e0 ) for quadrilaterals in 2D. This formulation provides improved behavior results,specially, in avoiding mesh bias dependence. In a first, very short, stage after the bifurcation theconcept of strong discontinuity is then left aside, and the apparent displacement jump is capturedacross the finite element length (smeared) like in classical strain localization settings. Immediatelyafter, in a second stage, the kinematics of those finite elements that have developed deep enoughstrain localization is enriched with the injection of a weak/strong discontinuity mode that minimizesthe stress locking defects. The necessary data to inject the discontinuity (the discontinuity directionand its position inside the finite element) is obtained by a post process of the strain-like internalvariable field obtained in the first stage, this giving rise to an elemental based tracking algorithm (thecrack propagation problem) that can be locally and straightforwardly implemented in a finite elementcode in a non-invasive manner. The obtained approach enjoys the benefits of embedded strongdiscontinuity methods (stress locking free, mesh bias independence and low computational cost), at acomplexity similar to the classical, and simpler, though less accurate, strain localization methods.Moreover, the methodology is applicable to any constitutive model (damage, elasto-plasticity, etc.)without apparent limitations. Representative numerical simulations validate the proposed approach.