Abstract

The methodology proposed in this research work explores the use of the strain injection concept in a combination of classical strain localization methods and embedded strong discontinuities, to remove the flaws (stress locking and mesh bias dependence) of the former, and simultaneously abdicate of the global tracking algorithms usually required by the later. The basic idea is to use, after the bifurcation instant, i.e. after the time that elements are amenable to develop discontinuities, a mixed continuous displacements - discontinuous constant strains condensable finite element formulation (Q1/ε0 ) 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 the concept of strong discontinuity is then left aside, and the apparent displacement jump is captured across the finite element length (smeared) like in classical strain localization settings. Immediately after, in a second stage, the kinematics of those finite elements that have developed deep enough strain localization is enriched with the injection of a weak/strong discontinuity mode that minimizes the stress locking defects. The necessary data to inject the discontinuity (the discontinuity direction and its position inside the finite element) is obtained by a post process of the strain-like internal variable field obtained in the first stage, this giving rise to a local (elemental based) tracking algorithm (the crack propagation problem) that can be locally and straightforwardly implemented in a finite element code in a non invasive manner. The obtained approach enjoys the benefits of embedded strong discontinuity methods (stress locking free, mesh bias independence and low computational cost), at a complexity similar to the classical, and simpler, though less maccurate, strain localization methods. Moreover, the methodology is applicable to many constitutive model (damage, elasto-plasticity, etc.) without apparent limitations. mRepresentative numerical simulations validate the proposed approach.

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