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
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At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola
TL;DR: Gabrio Piola's scientific papers have been underestimated in mathematical physics literature as mentioned in this paper, but a careful reading of them proves that they are original, deep and far-reaching, and even even...
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At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola
TL;DR: In this paper, the authors show that non-local and higher gradient continuum mechanics was conceived already in Piola's works and explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of Piola contribution.
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Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium
TL;DR: In this article, the authors considered a discrete spring model for extensible beams and proposed a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model.
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Analytical continuum mechanics à la Hamilton-Piola least action principle for second gradient continua and capillary fluids
TL;DR: In this article, a Lagrangian action is proved to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments.
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Dynamic problems for metamaterials: Review of existing models and ideas for further research
TL;DR: In this article, the authors focus on the design of wave-guides aimed to control wave propagation in micro-structured continua, with particular attention to piezoelectromechanical structures, having a strong coupling between macroscopic motion and some internal degrees of freedom.
References
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The element free galerkin method for dynamic propagation of arbitrary 3-d cracks
Petr Krysl,Ted Belytschko +1 more
TL;DR: In this article, a technique for modeling arbitrary three-dimensional dynamically propagating cracks in elastic bodies by the Element-Free Galerkin (EFG) method with explicit time integration is described.
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Uniqueness and localization—I. Associative and non-associative elastoplasticity
Davide Bigoni,Tomasz Hueckel +1 more
TL;DR: In this paper, the authors studied the critical hardening modulus for deformation into a planar band in the incremental response of elasto-plastic material in the case of small strains and rotations.
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Strong discontinuities and continuum plasticity models: the strong discontinuity approach
TL;DR: The Strong Discontinuity Approach for the analysis and simulation of strong discontinuities in solids using continuum plasticity models has been proposed in this paper, where a regularized kinematic state of discontinuity is proposed as a mean to model the formation of a strong discontinuity as the collapsed state of a weak discontinuity induced by a bifurcation of the stress-strain field, which propagates in the solid domain.
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A simplified mesh-free method for shear bands with cohesive surfaces
TL;DR: In this article, a mesh-free particle method is proposed to model shear bands as strong displacement discontinuities in a mesh free particle method, where the loss of material stability is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation law acting on the discontinuity surface.