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...
Posted Content
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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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Gradient enhanced damage for quasi-brittle materials
TL;DR: In this article, a consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena, and the introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models.
Book
An Introduction to Meshfree Methods and Their Programming
Gui-Rong Liu,YuanTong Gu +1 more
TL;DR: This book provides first the fundamentals of numerical analysis that are particularly important to meshfree methods, and provides most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of mesh free methods.
Journal ArticleDOI
Gradient-dependent plasticity: formulation and algorithmic aspects
René de Borst,Hans Muhlhaus +1 more
TL;DR: In this paper, the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof, and the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity.
MonographDOI
An introduction to nonlinear finite element analysis
TL;DR: The Finite Element Method: A Review 3. Heat Transfer and other Field Problems in One Dimension 4. Nonlinear Bending of Straight Beams 5. Bending Elastic Plates 7. Flows of Viscous Incompressible Fluids 8. Non-linear Analysis of Time-Dependent Problems 9. Finite Elements Formulations of Solids and Structures 10. Material Nonlinearities and Coupled Problems as mentioned in this paper
Journal ArticleDOI
Material rate dependence and mesh sensitivity in localization problems
TL;DR: In this paper, the role of material rate dependence in setting the character of governing equations is illustrated in the context of a simple one-dimensional problem, and numerical results are presented that illustrate the localization behavior of slightly rate-dependent solids under both quasi-static and dynamic loading conditions.