Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity
Yang Yang,Anil Misra +1 more
TLDR
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.About:
This article is published in International Journal of Solids and Structures.The article was published on 2012-09-15 and is currently open access. It has received 121 citations till now. The article focuses on the topics: Elasticity (physics) & Continuum mechanics.read more
Citations
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Book ChapterDOI
Dynamical Vector Fields on Pantographic Sheet: Experimental Observations.
TL;DR: In this paper, the authors present and discuss some experimental observations of the dynamical displacement vector field on a pantographic sheet and qualitatively describe the observed behavior for a set of relevant frequencies.
Journal ArticleDOI
Approach à la Piola for the equilibrium problem of bodies with second gradient energies. Part II: Variational derivation of second gradient equations and their transport
TL;DR: In this article , a variational derivation of the equilibrium equations for second gradient materials and their transformation from the Eulerian to the Lagrangian form was presented, where volume, face and edge contributions to the inner virtual work were provided through integration by parts and by repeated applications of the divergence theorem extended to curved surfaces with border.
Journal ArticleDOI
Piola’s approach to the equilibrium problem for bodies with second gradient energies. Part I: First gradient theory and differential geometry
Journal ArticleDOI
On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure
Luca Placidi,Emilio Barchiesi,Francesco dell’Isola,Valerii Maksimov,Anil Misra,Nasrin Rezaei,Angelo Scrofani,Dmitry Timofeev +7 more
TL;DR: In this paper , a continuum theory for 2D strain gradient materials accounting for a class of dissipation phenomena is presented, which is constructed by means of a (reversible) placement function and by reversible damage and plastic functions.
Book ChapterDOI
A still topical contribution of Gabrio Piola to Continuum Mechanics: the creation of peri-dynamics, non-local and higher gradient continuum mechanics
TL;DR: In this article, the authors show that non-local and higher gradient continuum mechanics is rigorously formulated already in Piola's works and explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of his contribution.
References
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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.
Book
Mechanics of Solid Materials
TL;DR: In this article, the physical mechanisms of deformation and fracture are discussed, including linear elasticity, thermo-elasticity, and viscoelastic properties of real solids.
Journal ArticleDOI
A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
Satya N. Atluri,T. Zhu +1 more
TL;DR: In this article, a local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy.