Continua with Latent Microstructure

Capriz, Gianfranco

doi:10.1007/978-3-642-61598-6_9

Cited by 11 publications

(25 citation statements)

References 4 publications

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“…A continuum with latent microstructure is a continuum subject to internal constraints relating the order parameters to the macroscopic deformation [Capriz 1985;. By effect of the constraint, the internal forces decompose into the sum of an active part and a reactive part.…”

Section: Continua With Latent Microstructurementioning

confidence: 99%

Nonclassical continua, pseudobalance, and the law of action and reaction

Piero

2014

Math. Mech. Compl. Sys.

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Section: Continua With Latent Microstructurementioning

confidence: 99%

Nonclassical continua, pseudobalance, and the law of action and reaction

Piero

2014

Math. Mech. Compl. Sys.

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“…The scheme is suitable to cover various cases such as the one of bodies with dense polymeric linear chains discussed above or fullerene-reinforced composites. A basic interest to mention this special model is that when there is an internal constraint of the type ν = f (F ), so that the substructure becomes latent in the sense of Capriz [6]. In this case the energy density reduces to the one of a second-grade Cauchy body, namely e = e (x, F, ∇F ).…”

Section: Taxonomy Of Special Casesmentioning

confidence: 99%

“…For this reason one finds reasonable to consider each material element as a system and to describe its inner geometry at least at coarse grained level. Descriptors of the substructural morphology are selected here as elements of a finite-dimensional differentiable manifold, the manifold of substructural shapes, by following this way the general model-building framework of the mechanics of complex bodies in [7,38,42] (see also [5,6,12,33,41,51]). …”

Section: Introductionmentioning

confidence: 99%

Ground states in complex bodies

Mariano

Modica

2008

ESAIM: COCV

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Abstract.A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end.

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“…The internal microstructure then becomes 'latent' (see [17]) with the consequence that the 2D continuum results to be of the second gradient type [18][19][20][21][22][23][24][25][26][27][28]. Using the reduced kinematics, an expression of the kinetic energy of the 2D body is derived from the one of the network by following an equivalence procedure analogous to that used for the strain energy described before.…”

Section: Introductionmentioning

confidence: 99%

Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis

Giorgio¹,

2017

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To cite this version:I. Giorgio, N. Rizzi, E. Turco. Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2017The, , 473 (2207The, ), 10.1098The, /rspa.2017 Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis Giorgio, I. and Rizzi, N. L. and Turco, E.Abstract A nonlinear 2D continuum with a latent internal structure is introduced as a coarse model of a plane network of beams which, in turn, is assumed as a model of a pantographic structure made up by two families of equispaced beams, superimposed and connected by pivots. The deformation measures of the beams of the network and that of the 2D body are introduced and the former are expressed in terms of the latter by making some kinematical assumptions. The expressions for the strain and kinetic energy densities of the network are then introduced and given in terms of the kinematic quantities of the 2D continuum. In order to account for the modelling abilities of the 2D continuum in the linear range, the eigenmode and eigenfrequencies of a given specimen are determined. The buckling and postbuckling behaviour of the same specimen, subjected to two di↵erent loading conditions are analysed as tests in the nonlinear range. The problems have been solved numerically by means of COMSOL Multiphysics FE software.

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Continua with Latent Microstructure

Cited by 11 publications

References 4 publications

Nonclassical continua, pseudobalance, and the law of action and reaction

Nonclassical continua, pseudobalance, and the law of action and reaction

Ground states in complex bodies

Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis

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