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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Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics
Anil Misra,Payam Poorsolhjouy +1 more
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A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model
TL;DR: In this article, the second-order displacement second-gradient model is extended to the case of a scalar damage field and two internal variables, i.e., accumulated plastic tension and the accumulated plastic compression, and the softening matrix is introduced as the coefficient matrix in front of the quadratic terms of the two plastic internal variables.
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Two-dimensional strain gradient damage modeling: a variational approach
TL;DR: In this paper, the authors formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage, defined as the condition in which the damage parameter reaches 1, at least in one point of the domain.
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Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity
Ugo Andreaus,Francesco dell’Isola,Ivan Giorgio,Luca Placidi,Tomasz Lekszycki,Nicola Luigi Rizzi +5 more
TL;DR: In this article, a two-dimensional solid consisting of a linear elastic isotropic material is considered and the strain energy is expressed as a function of the strain and the gradient of strain.
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The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics
TL;DR: In this paper, a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor is studied.
References
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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.