Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems

By Michael Hillman, Jiun-Shyan Chen, Sheng-Wei Chi. Annual Symposium on Combinatorial Pattern Matching, 2014

65 citations recorded by the source corpus.

Galerkin meshfree methods can suffer from instability and suboptimal convergence if the issue of quadrature is not properly addressed. The instability due to quadrature is further magnified in high strain rate events when nodal integration is used. In this paper, several stable and convergent nodal integration methods are presented and applied to transient and large deformation impact problems, and an eigenvalue analysis of the methods is also provided. Optimal convergence is attained using variationally consistent integration, and stability is achieved by employing strain smoothing and strain energy stabilization. The proposed integration methods show superior performance over standard nodal integration in the wave propagation and Taylor bar impact problems tested.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1f1d95ee1e15140b66fd857f0ce1fc78940c7bf7

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Meshfree Methods: Progress Made after 20 Years (2017, unknown): “More recently, several other meshfree formulations for non-linear mechanics have been introduced (Yreux and Chen 2016; Chi et al. 2015; Hillman and Chen 2015; Hillman et al. 2014; Wu et al. 2016, 2016, 2014).”
An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics (2016, background): “Several nodal integration methods have been developed that are convergent and stable [13, 25, 28, 29], but in the end sacrifice efficiency because of the approaches taken to ensure accuracy and stability.”
A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method (2015, methodology): “Moreover, their method has been shown [18] to remarkably alleviate the unstable deformation mode in the simulation of impact problems.”