Regularization of material instabilities by meshfree approximations with intrinsic length scales

By Jiun-Shyan Chen, Cheng‐Tang Wu, Ted Belytschko. 2000

168 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/37dbb949c76aa6dfd5a47140089bc415981d7f11

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

A Smoothed Finite Element Method for Mechanics Problems (2007, methodology): “In this section, we formulate SFEM based on the conventional FEM incorporating the idea of strain smoothing operation used in the mesh-free nodal integration method [6].”
Limit analysis of plates and slabs using a meshless equilibrium formulation (2010, methodology): “A strain smoothing method was firstly presented in [26] for the regularization of material instabilities.”
A cell‐based smoothed finite element method for kinematic limit analysis (2010, unknown): “A strain smoothing formulation is given by [45] 2̃(xC) = ∫ ΩC 2h(x)φ(x,x− xC) dΩ = ∫ ΩC ∇uh(x)φ(x,x− xC) dΩ (11) where 2̃ is the smoothed value of strains 2 for smoothing cell ΩC , and φ is a distribution function or a smoothing function that has to satisfy the following properties [45,46] φ ≥ 0 and”
A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS (2008, methodology): “Edelen (1972)], the smoothed particle hydrodynamics (SPH) [Lucy (1977); Monaghan (1982); Liu and Liu (2003)], in resolving the material instabilities [Chen and Belytschko (2000)] and spatial instability in nodal integrated meshfree methods and restoring conformability [Chen et al. (2001)], and obtai”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “RKPM has been shown to be particularly effective for large deformation problems (Chen and Wu 1997; Chen et al. 1996, 1998a, 2000a, e; Yoon and Chen 2002; Yoon et al. 2001), smooth contact (Chen and Wang 2000a; Wang 2000; Wang et al. 2014), multibody contact, and fragment-impact problems (Chen et…”
Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity (2012, background): “The consequence of such an anomalous stress–strain relationship is that the traditional finite element solutions based upon classical continuum description typically suffer from numerical instabilities, severe mesh-size and mesh-alignment sensitivities as well as zero-energy dissipation (Pietruszcza”
Stabilized conforming nodal integration in the natural‐element method (2004, methodology): “In one stabilization procedure (originally developed for strain localization problems), the strain measure is replaced by a non-local approximation [17, 23].”
Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures (2011, methodology): “The gradient and dilatational stabilization methods with stress point integration were also discussed by DuanandBelytschko[32].Startingfromthelinearexactness condition and the gradient smoothing technique [ 33 ], Chen et al. [34–36] introduced a stabilized conforming nodal integration (SCNI) method ”
An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics (2007, methodology): “[7,8] to stabilize the nodal integration in the context of mesh-free method.”
A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method (2015, methodology): “where ε̃ (X) is the standard expression of non-local strain in the regularization of strain localization problem [7] and it is defined by”
An implicit gradient model by a reproducing kernel strain regularization in strain localization problems (2004, methodology): “In [ 9 ], we introduced the following kernel regularization of the strain:”
Gradient plasticity theory with a variable length scale parameter (2005, background): “…many others in solving the localization problem (see for example de Borst and Mühlhaus, 1992; de Borst et al., 1993; de Borst and Pamin, 1996; Claudia and Perego, 1996; Chen et al., 2000; Zervos et al., 2001; Voyiadjis et al., 2001, 2003, 2004; Engelen et al., 2003; and references quoted therein).”