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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A frictional Cosserat model for the slow shearing of granular materials
TL;DR: In this paper, a rigid-plastic Cosserat model for slow frictional flow of granular materials is proposed, where the hydrodynamic fields of a classical continuum are supplemented by the couple stress and intrinsic angular velocity fields.
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Embedded localization band in undrained soil based on regularized strong discontinuity theory and FE-analysis
TL;DR: A novel approach to the analysis of a developing localization zone in undrained soil considered as a mixture of a solid skeleton and fluid-filled pores, where the solid phase is considered as elastic-plastic.
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A study on finite elements for capturing strong discontinuities
TL;DR: In this article, the authors focus on the presently existing families of finite elements with embedded discontinuities and explore the possibilities of obtaining symmetric statically consistent finite elements that alleviate the stress-locking problem.
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A finite element model of localized deformation in frictional materials taking a strong discontinuity approach
TL;DR: In this paper, a finite element analysis of localized deformation occurring in a more complex model problem of slope stability is conducted in a nearly mesh-independent manner, where the effect of dilatancy on the orientation of slip lines is demonstrated for the slope stability problem.
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Two gradient plasticity theories discretized with the element-free Galerkin method
TL;DR: 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.