Geometrically nonlinear higher-gradient elasticity with energetic boundaries

Javili, Ali; Dell’Isola, Francesco; Steinmann, Paul

doi:10.1016/j.jmps.2013.06.005

Cited by 190 publications

(116 citation statements)

References 146 publications

(108 reference statements)

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“…The elastic and plastic regimes are defined, respectively, as the regimes where the constitutive relation is characterized by linear and nonlinear stress-strain relations, and fracture is considered as an independent phenomenon where a preexisting crack grows by itself. For each regime, a specific theory is used: continuum mechanics [Spencer 1980;Landau and Lifshitz 1986] for the elastic regime, various theories of plasticity [Hill 1998;Lubliner 2008] for the plastic regime and fracture mechanics [Griffith 1921;Irwin 1948] for the fracturing regime. When an external load is applied to a solid object and the resultant deformation is viewed as the response of the entire object, it is true that the deformation mechanics undergone in these regimes exhibits the stress-strain characteristics of the respective regimes.…”

Section: Introductionmentioning

confidence: 99%

“…In the tensile or compression mode of deformation where the stress increases with the passage of time, the deformation exhibits this pattern of progression as a function of the increasing stress. Even in the fatigue mode of deformation where the magnitude of the external load remains the same, most solids follow the same pattern of progression [Ichinose et al 2006]. In engineering, often analysis of the transitional stage from one regime to the next is more important than analysis within a certain regime.…”

Section: Introductionmentioning

confidence: 99%

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Comprehensive description of deformation of solids as wave dynamics

Yoshida

2015

Math. Mech. Compl. Sys.

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Deformation and fracture of solids are discussed as comprehensive dynamics based on a field theory. Applying the principle of local symmetry to the law of elasticity and using the Lagrangian formalism, this theory derives field equations that govern dynamics of all stages of deformation and fracture on the same theoretical foundation. Formulaically, these field equations are analogous to the Maxwell equations of electrodynamics, yielding wave solutions. Different stages of deformation are characterized by differences in the restoring mechanisms responsible for the oscillatory nature of the wave dynamics. Elastic deformation is characterized by normal restoring force generating longitudinal waves; plastic deformation is characterized by shear restoring force and normal energy-dissipative force generating transverse, decaying waves. Fracture is characterized by the final stage of plastic deformation where the solid has lost both restoring and energy-dissipative force mechanisms. In the transitional stage from the elastic regime to the plastic regime where both restoring and energydissipative normal force mechanisms are active, the wave can take the form of a solitary wave. Experimental observations of transverse, decaying waves and solitary waves are presented and discussed based on the field theory.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comprehensive description of deformation of solids as wave dynamics

Yoshida

2015

Math. Mech. Compl. Sys.

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“…In particular, surface material parameters can be negative where the analogous bulk material parameters are strictly positive. This can be justified by the fact that the surface cannot exist independent of the bulk and the overall response of the bulk together with the surface need to be positive definite [37][38][39].…”

Section: Dielectric Constant Of Batio 3 Particle Compositesmentioning

confidence: 99%

Interface properties influence the effective dielectric constant of composites

Chatzigeorgiou

Javili

Steinmann

2015

Philosophical Magazine

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Erlangen-Nuremberg, Egerlandstr. 5, 91058 Erlangen, Germany In this work we propose a micromechanics model, based on the composite spheres assemblage method, for studying the electrostatic behaviour of particle and porous composites when the interface between the particle (or the pore) and the matrix has its own independent behaviour. Examples from experimental results in porous media and particle composites are utilized to demonstrate the model's capabilities. The current model shows a better agreement with experiments compared with other available studies. Furthermore, it is shown that the interface dielectric constant is independent of the experiments which prove its nature as a material parameter.

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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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Geometrically nonlinear higher-gradient elasticity with energetic boundaries

Cited by 190 publications

References 146 publications

Comprehensive description of deformation of solids as wave dynamics

Comprehensive description of deformation of solids as wave dynamics

Interface properties influence the effective dielectric constant of composites

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

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