Material symmetries of micropolar continua equivalent to lattices

Trovalusci, Patrizia; Masiani, Renato

doi:10.1016/s0020-7683(98)00073-0

Cited by 67 publications

(101 citation statements)

References 15 publications

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“…Within the framework of rigid body kinematics, the strain measures of the discrete system can be defined as the relative displacements and rotations between blocks. The details of the equivalence procedure are reported in the paper [27]. The interactions between blocks, contact forces and couples are assumed to be linear functions of these strain measures.…”

Section: Identification Of the Equivalent Continuummentioning

confidence: 99%

“…Drawing from the latter idea originally suggested by Voigt, in the present paper, we adopt a model proposed in the past, developed in [27] and further extended to the nonlinear constitutive case in [11,12]. Starting from a system of interacting rigid blocks (micromodel), a micropolar anisotropic continuum (macromodel) is identified by equating, through the localization theorem, the mean virtual work of the internal actions of the fine micromodel over a representative volume element to the internal virtual work density of the coarse macromodel.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Identification Of the Equivalent Continuummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Pau

Trovalusci

2012

Acta Mech

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“…Finally, an advantage of the energy equivalence procedure is that this ensures the preservation of the material symmetry class in the transition from the discrete to the continuum description [90]. From a more general point of view, this apprach could allow one to properly account for symmetry-induced instabilities describing important features related to re-arrangements of the material microstructure, such as a symmetrybreaking phase transition [51,94], a defect-induced damage [95] or other material instabilities [96].…”

Section: A Model For Masonry-like Materials Based On Voigt's Approachmentioning

confidence: 99%

“…It can be shown that if the central symmetry for the module holds, the tensor B is null and the strain energy function is a quadratic form[90]. Such a material symmetry characterizes periodic lattices.…”

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confidence: 99%

Genesis of the multiscale approach for materials with microstructure

2008

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This paper presents an overview of the origin of multiscale approaches in mechanics. While the pioneer molecular models of linear elastic bodies by Navier, Cauchy and Poisson were contradicted by experiments, the phenomenological energetic approach by Green still seems suitable for simple materials only. Voigt's molecular model, here reinterpreted in the light of contemporary mechanics, reconciled the two approaches providing a conceptual guideline for developing constitutive models based on a direct link between continuum and discrete solid mechanics. Such a theoretical background proves to be especially suitable for new complex materials. An example referred to masonry-like materials is given.

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“…This is done mostly to describe phenomena beyond elasticity, like plasticity, damage, fracture [24], but also elastic phenomena in the presence of load and geometrical singularities [35]. Not very differently than in the past, experimental discrepancies still call for the need of defining appropriate intermolecular potentials by-passing the above limitations.…”

Section: A Mention To Modern Discrete-continuum Theoriesmentioning

confidence: 99%

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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Material symmetries of micropolar continua equivalent to lattices

Cited by 67 publications

References 15 publications

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

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

Genesis of the multiscale approach for materials with microstructure

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

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