The study and prediction of failure is one of the most challenging issues of mechanical ans¡d structural engineering. In this context, an accurate analysis of strain localization, which typically triggers failure in many softening materials such as steel or concrete, is of great interest. The classical limit-state methods used to study localization phenomena are insufficient, and the finite element method appears as a proper analysis tool.
Unfortunately, the numerical simulation of strain localisation in continuum mechanics has to face two important difficulties: the need of a mathematically consistent constitutive model on one side, and of a cost-effective computational strategy capable of capturing the multi-scale nature of localisation problems on the other side. Several formulations have appeared to overcome the fisrt challenge, usually known as regularization techniques or localisation limiters. On the order hand, adaptivity appears as the natural solution to the computational difficulty.
In the present work, an adaptive remeshing procedure based on a residual type error estimator is presented in the context of quasi-static localisation problems with softening materials. Two well-known localisation limiters have been used: rate dependence has been used to regularize J2 softening plasticity (via Perzyna viscoplasticity) presenting shear band localisation, and the Mazars damage model with nonlocal regularization has been applied to simulate fracture localisation. These constitutive models simulate steel and concrete respectively.
Numerical examples show the good performance of the presented procedure, that captures accurately and cost-effectively the micro-scale of strain localisation problems.Furthermore, this error estimator driven adaptive procedure constitutives an objective alternative to the usual approaches that are based on error indicators.
Several topics of interest are also dealt with throughout the work, such as the analysis of the shear band width in quasi-static two-dimensional problems with Perzyna viscoplasticity, the influence of pollution errors in the adaptive process, or the use of error estimation analysis to deduce or test indicators.