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/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 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
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.
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, [...]