From classical to Voigt’s molecular models in elasticity

Capecchi, Danilo; Ruta, Giuseppe; Trovalusci, Patrizia

doi:10.1007/s00407-010-0065-y

Cited by 47 publications

(35 citation statements)

References 9 publications

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“…His results in terms of number of elastic constants ('multi-constant' theory [5,22,38]) were confirmed by experiments.…”

Section: Introductionsupporting

confidence: 63%

“…In the present paper, we will sketch Voigt's refined molecular approach [5,38] and Poincaré's energetic approach to linear elasticity. The original texts are re-interpreted and re-written in terms of modern tensor algebra in order to understand how these approaches can be still valid and predictive in the theories of new, non-standard materials.…”

Section: Introductionmentioning

confidence: 99%

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Voigt and Poincaré’s mechanistic–energetic approaches to linear elasticity and suggestions for multiscale modelling

2011

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Many modern theories for "complex" materials rely on the construction of specific potentials for inner actions by resorting to mechanistic/corpuscular descriptions of the matter at different length scales. Techniques allowing the dialogue among different material scales on the basis of energetic equivalence criteria play a central role in mechanics of materials. These multiscale techniques can be seen as originated from the molecular theories of the nineteenth century and in particular by the suggestions of Voigt and Poincaré, to deal with the paradoxes coming from the search of the exact number of elastic constants in linear elasticity. In this paper, we examine both Voigt and Poincaré's mechanistic-energetic approaches to the standard linear theory of elasticity in contrast with the mechanistic molecular model by Navier, Cauchy and Poisson. We also try to provide some conceptual guidelines among these approaches and the contemporary theories of complex material behaviour.

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“…His results in terms of number of elastic constants ('multi-constant' theory [5,22,38]) were confirmed by experiments.…”

Section: Introductionsupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Voigt and Poincaré’s mechanistic–energetic approaches to linear elasticity and suggestions for multiscale modelling

2011

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“…However, the theory of elasticity has been remarkably successful in describing the mechanical properties of real materials, all discretely composed of atoms. Indeed, much of the early development of the theory of elasticity-including the models of Fresnel, Navier, Cauchy, Poisson, Voigt, Born, and von Karman-occurred in the context of discrete, atomic media (30,31), with continuum theories arising as a limit of molecular models. Moreover, the calculation of strain tensors can readily be extended to granular media (32), and strains remain highly useful in describing granular materials' deformations.…”

Section: Strainmentioning

confidence: 99%

Strain analysis of protein structures and low dimensionality of mechanical allosteric couplings

Mitchell

Tlusty

Leibler

2016

Proc. Natl. Acad. Sci. U.S.A.

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In many proteins, especially allosteric proteins that communicate regulatory states from allosteric to active sites, structural deformations are functionally important. To understand these deformations, dynamical experiments are ideal but challenging. Using static structural information, although more limited than dynamical analysis, is much more accessible. Underused for protein analysis, strain is the natural quantity for studying local deformations. We calculate strain tensor fields for proteins deformed by ligands or thermal fluctuations using crystal and NMR structure ensembles. Strains-primarily shears-show deformations around binding sites. These deformations can be induced solely by ligand binding at distant allosteric sites. Shears reveal quasi-2D paths of mechanical coupling between allosteric and active sites that may constitute a widespread mechanism of allostery. We argue that strain-particularly shear-is the most appropriate quantity for analysis of local protein deformations. This analysis can reveal mechanical and biological properties of many proteins.strain | protein mechanics | protein allostery | elasticity

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“…Alternatively, the identification of the stress-strain relationships of the multifield continuum can be based on the definition of a direct energy equivalence with discrete descriptions of the matter [11,12]. Such energy-based lattice-continuum approaches have their origin in the non-standard molecular models of elasticity of the eighteenth and nineteenth century [22][23][24] and, also at present, are among the most promising approaches in materials science [25,26]. The basic idea of these approaches is the assumption that there is an implicit mapping from the set of degrees of freedom of the discrete model to the displacement vector fields, like the so-called Cauchy-Born rule used in crystal elasticity.…”

Section: Introductionmentioning

confidence: 99%

Block masonry as equivalent micropolar continua: the role of relative rotations

Pau

Trovalusci

2012

Acta Mech

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A description of brick/block masonry by continua equivalent to discrete systems made of blocks of different geometry and texture is proposed in this paper. Here, the reasons for the selection of a micropolar continuum with respect to the classical continuum are discussed. As recent research in various micromorphic multifield formulations shows, the problem of the choice of the most appropriate continuum to model masonry mechanical behavior is still open, and the advantages of non-classical continuum modeling are not yet completely ascertained. Earlier analyses performed on masonry panels in the presence of load and geometrical singularities pointed out the significant role of the additional degree of freedom of the micropolar continuum (microrotation) and of its gradient. The present study aims to expand the investigation into the consequences of changes in blocks' shape, size and arrangement on the response of block masonry panels under shear forces. This analysis points out the greater effectiveness of micropolar models in capturing the gross structural response of masonry, with respect to the classical modeling. The cases analyzed herein show that apart from the very peculiar case of orthotetragonal symmetry, not only the gradient of microrotation but also the relative rotation between the local rigid rotation and the microrotation, to which relevant non-symmetric strains correspond, are predominant in the majority of the performed numerical tests. Models lacking in these strain measures are therefore inappropriate. The results obtained, ascertained by analyses performed on discrete block assemblies, point out that the micropolar continuum provides a proper description of the masonry behavior. Moreover, the differences between micropolar and classical models remain when the internal lengths vanish.

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From classical to Voigt’s molecular models in elasticity

Cited by 47 publications

References 9 publications

Voigt and Poincaré’s mechanistic–energetic approaches to linear elasticity and suggestions for multiscale modelling

Voigt and Poincaré’s mechanistic–energetic approaches to linear elasticity and suggestions for multiscale modelling

Strain analysis of protein structures and low dimensionality of mechanical allosteric couplings

Block masonry as equivalent micropolar continua: the role of relative rotations

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