Contributions to the Stability Analysis of Explicit Enriched Meshfree Methods

Esteban Samaniego, Hossein Talebi, Cristóbal Samaniego, Timon Rabczuk


Meshfree methods have certain advantages with respect to other more classical numerical methods. The Element Free Galerkin Method (EFGM), in particular, seems to offer a good performance when dealing with problems that include the treatment of large deformations together with the presence of strong or weak discontinuities to model cracks or material interfaces. A possible approach is to introduce the discontinuity to the discretization by adding special enrichment functions to the standard shape functions. The cracking particles method, based on EFGM, is an example of such approaches. When dealing with dynamic applications by means of explicit time integration schemes, a lumped mass matrix is necessary for an efficient numerical simulation. However, when the shape functions include discontinuous enrichment, studying the behavior of the critical time step becomes problematic. Moreover, it may tend to very small values, thus leading to computationally expensive simulations. In this work, we present some contributions to the study of these stability issues for an explicit enriched EFGM for oneand two-dimensional problems.

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