Journal ArticleDOI
Two gradient plasticity theories discretized with the element-free Galerkin method
TLDR
The element-free Galerkin method is exploited to analyze gradient plasticity theories and it is shown that the regularization properties of the higher-order gradients are necessary, since, similar to finite element methods, a severe discretization sensitivity is encountered otherwise.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2003-05-23. It has received 88 citations till now. The article focuses on the topics: Discretization & Finite element method.read more
Citations
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Incorrect initiation and propagation of failure in non-local and gradient-enhanced media
TL;DR: In this article, the authors investigated damage initiation and propagation in a class of non-local and gradient-enhanced media and showed that the use of a nonlocal dissipation-driving state variable leads to an incorrect failure characterisation in terms of damage initiation.
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Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity
Yang Yang,Anil Misra +1 more
TL;DR: In this paper, a second gradient stress-strain damage elasticity theory based on the method of virtual power is proposed. But the authors consider the strain gradient and its conjugated double stresses instead of introducing an intrinsic material length scale into the constitutive law in an ad hoc fashion.
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Higher-Order Continuum Theory Applied to Fracture Simulation of Nanoscale Intergranular Glassy Film
TL;DR: In this article, the authors applied microstructural granular mechanics-based higher-order continuum theory to model the failure behavior of nanophased ceramics, and compared the results obtained from the ab-initio simulations with those predicted by the higherorder continuum theories.
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A direct finite element implementation of the gradient-dependent theory
TL;DR: In this paper, a non-local gradient-dependent approach is proposed to bridge the gap between the micromechanical theories and the classical (local) continuum, which is successful in explaining the size effects encountered at the micron scale and in preserving the well-posedeness of the (I) BVP governing the solution of material instability triggering strain localization.
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Strain gradient continuum plasticity theories: Theoretical, numerical and experimental investigations
George Z. Voyiadjis,Yooseob Song +1 more
TL;DR: A review of the theoretical developments by several research groups and their applications to the finite element method is presented in this article, where a review of various experimental methodologies to study the size effects is presented.
References
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Journal ArticleDOI
A finite element method for crack growth without remeshing
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
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Meshless methods: An overview and recent developments
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.
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The Partition of Unity Method
Ivo Babuška,Jens Markus Melenk +1 more
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
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Second gradient of strain and surface-tension in linear elasticity
TL;DR: In this article, a linear theory of deformation of an elastic solid was formulated, in which the potential energy-density is a function of the strain and its first and second gradients.