How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”

Dell’Isola, Francesco; Seppecher, Pierre; Madeo, Angela

doi:10.1007/s00033-012-0197-9

Cited by 244 publications

(231 citation statements)

References 107 publications

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“…For negligible diffusion along the junction curve, the dissipation inequality (3.27) simplifies to F J · q p ≥ 0. Assuming linear kinetics we postulate that 16) where M J is the positive semi-definite junction mobility tensor. An analogous treatment in a two-dimensional setting can be seen in [30] (see also [2]).…”

Section: (B) Bicrystal-iimentioning

confidence: 99%

A three-dimensional study of coupled grain boundary motion with junctions

Basak

Gupta

2015

Proc. R. Soc. A.

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A novel continuum theory of incoherent interfaces with triple junctions is applied to study coupled grain boundary (GB) motion in three-dimensional polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and migration of the boundary and junction evolution are developed. In doing so, a vectorial form of the geometrical coupling factor, which relates the tangential motion at the GB to the migration, is also obtained. Diffusion along the GBs and the junctions is allowed so as to prevent nucleation of voids and overlapping of material near the GBs. The coupled dynamics has been studied in detail for two bicrystalline and one tricrystalline arrangements. The first bicrystal consists of two cubic grains separated by a planar GB, whereas the second is composed of a spherical grain embedded inside a larger grain. The tricrystal has an arbitrary-shaped grain embedded inside a much larger bicrystal made of two cubic grains. In all these cases, analytical solutions are obtained wherever possible while emphasizing the role of various kinetic coefficients during the coupled motion.

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Section: (B) Bicrystal-iimentioning

confidence: 99%

A three-dimensional study of coupled grain boundary motion with junctions

Basak

Gupta

2015

Proc. R. Soc. A.

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“…All macroscopic (continuous) models to be used in this context must belong to the class of generalized continua (see, e.g., [93][94][95][96]). The main problem to be confronted when modeling with continua fabrics having a complex microstructure consists in the determination of macroscopic constitutive equations in terms of the microscopic mechanical and geometrical features of considered mechanical systems.…”

Section: Dynamic Behavior Instabilities and Wrinkling In (Non)linearmentioning

confidence: 99%

“…The possibility of describing a whole and large range of physical states of considered deformable bodies by means of a unique constitutive equation is essential if one wants to establish a mathematical model which is able to forecast the localization of the aforementioned regions. In this context, the general framework can be found in the papers [95,96]: perturbation techniques able to determine boundary layers by means of inner and outer expansions are needed to perform qualitative studies on this phenomenon.…”

Section: Localization Problems In Solids and Structuresmentioning

confidence: 99%

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

Piccardo

D’Annibale

Zulli

2014

Continuum Mech. Thermodyn.

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This paper intends to summarize the scientific production of Angelo Luongo on the occasion of his Sixtieth Birthday, focusing on his main contributions in the field of Mechanics. The task will not be easy because of the breadth of his scientific production, only apparently attributable to a restricted number of keywords. In fact, even when the work seems purely algorithmic, speculation on the physical and mechanical aspects of the problem is always present, providing new interpretations and innovative openings to a careful reader. Similarly, also the works, which apparently seem to be high-level applications, always reserve methodological aspects that are not negligible. The editorial choice to divide his papers through a small number of keywords is certainly simplistic, but offers the possibility to better highlight all the connections among his variegated production. The most original contributions of Angelo Luongo in the context of perturbation methods, linear and nonlinear dynamics and control, elastic buckling and structural analysis, bifurcation and stability of non-conservative systems, are discussed in detail. Finally, the Angelo Luongo's central role in the creation and development of activities of the international research center M&MoCS is pointed out.

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“…In Section 2, the required kinematics of the continuum is introduced. Section 3 proposes a variational theory of mechanics, mainly based on the insights of [Germain 1972;dell'Isola et al 2012], with the principle of virtual work and the variational law of interaction as the basic axioms. The core of this paper is formulated in Section 4: based on an alternative definition of stress on the micro level of infinitesimal volume elements and Piola's micro-macro identification procedure, the virtual work contribution of the stress is derived on the macro level, together with the emerging stress tensor.…”

Section: Introductionmentioning

confidence: 99%

On the notion of stress in classical continuum mechanics

Eugster

Glocker

2017

Math. Mech. Compl. Sys.

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A variational formulation of continuum mechanics, in which the principle of virtual work and the variational law of interaction are postulated as the basic axioms, is still controversially discussed. In particular, not widely accepted is the internal virtual work contribution of a continuum, as postulated as a smooth density integrated over the deformed configuration of the body, in which the stress field is defined as the quantity dual to the gradient of the virtual displacement field. The question arises whether this internal virtual work can be deduced, rather than just postulated, from already known mechanical concepts completely within the variational framework. To achieve such a derivation, we give in this paper an interpretation of Piola's micro-macro identification procedure in view of the Riemann integral, which naturally provides in its mathematical definition a micro-macro relation between the discrete system of infinitesimal volume elements and the continuum. Accordingly, we propose a definition of stress on the micro level of the infinitesimal volume elements. In particular, the stress is defined as the internal force effects of the body that model the mutual force interaction between neighboring infinitesimal volume elements. The internal virtual work of the continuum is then obtained by Piola's micro-macro identification procedure, where in the limit of vanishing volume elements the virtual work of the continuous macromodel is identified with the virtual work of the discrete micromodel. In the course of this procedure, the stress tensor emerges directly as the quantity dual to the gradient of the virtual displacement field. Furthermore, we try to gather important results of variational continuum mechanics, which have appeared here and there in very diverse forms, in order to underline once more the strength of a variational formulation of continuum mechanics.

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How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”

Cited by 244 publications

References 107 publications

A three-dimensional study of coupled grain boundary motion with junctions

A three-dimensional study of coupled grain boundary motion with junctions

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

On the notion of stress in classical continuum mechanics

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