A strain-morphed nonlocal meshfree method for the regularized particle simulation of elastic-damage induced strain localization problems

• Published in: Computational mechanics Vol. 56; no. 6; pp. 1039 - 1054
• Main Authors: Wu, C. T., Wu, Youcai, Koishi, M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015; Springer
• Subjects: Classical and Continuum Physics; Computational Science and Engineering; Computer simulation; Engineering; Galerkin methods; Joining; Mathematical models; Meshless methods; Original Paper; Regularization; Strain; Strain localization; Theoretical and Applied Mechanics; Nonlocal; Nodal integration; Stabilization; Regularization; Meshfree
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-015-1217-3

In this work, a strain-morphed nonlocal meshfree method is developed to overcome the computational challenges for the simulation of elastic-damage induced strain localization problem when the spatial domain integration is performed based on the background cells and Gaussian quadrature rule. The new method is established by introducing the decomposed strain fields from a meshfree strain smoothing to the penalized variational formulation. While the stabilization strain field circumvents the onerous zero-energy modes inherent in the direct nodal integration scheme, the regularization strain field aims to avoid the pathological localization of deformation in Galerkin meshfree solution using the weak-discontinuity approach. A strain morphing algorithm is introduced to couple the locality and non-locality of the decomposed strain approximations such that the continuity condition in the coupled strain field is met under the Galerkin meshfree framework using the direct nodal integration scheme. Three numerical benchmarks are examined to demonstrate the effectiveness and accuracy of the proposed method for the regularization of elastic-damage induced strain localization problems.