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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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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An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids
TL;DR: In this paper, qualitative features of solutions exhibiting strong discontinuities in rate-independent inelastic solids are identified and exploited in the design of a new class of finite element approximations.
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Nonlocal Continuum Damage, Localization Instability and Convergence
TL;DR: In this paper, a nonlocal damage formulation was extended to a more general form in which the strain remains local while any variable that controls strain-softening is nonlocal, and it was shown that the energy dissipation and damage cannot localize into regions of vanishing volume.
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The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure
TL;DR: The advantages of a systematic application of the method of virtual power are exemplified by the study of continuous media with microstructure, and the equations of motion for the general micromorphic medium are established for the first time.
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A finite element method for localized failure analysis
TL;DR: In this paper, a bifurcation analysis is used to determine the geometry of the localized deformation modes, and suitably defined shape functions are added to the element interpolation which closely reproduce the localized modes.
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Continuum Theory for Strain‐Softening
TL;DR: In this article, it is shown that failure occurs by progressive distributed damage during which the material exhibits strain-softening, i.e., a gradual decline of stress at increasing strain.