On standard dissipative gradient models

Nguyen, Quoc Son

doi:10.1007/s12356-010-0006-0

Cited by 17 publications

(13 citation statements)

References 27 publications

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“…There exist alternative approaches to Gurtin's treatment. For instance, an entropy source term is added in the second principle by Ireman and Nguyen (2004), Nguyen (2010) and leads to a generalized heat equation that differs from both (52) and (69) but also removes the paradox of instantaneous propagation of heat.…”

Section: Discussionmentioning

confidence: 99%

Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

Forest

Aifantis

2010

International Journal of Solids and Structures

146

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International audienceThis work elaborates upon two robust models of gradient elasticity and gradient plasticity, and one gradient model of heat transfer, as originally advocated by the second author in the 1980's. The objective is, after recalling the links between these models and existing generalized continuum theories as developed in the 1960's and subsequently, to apply the same methodology to the case of diffusion with a view to establishing generalized transport equations. Aifantis double diffusivity and conductivity theory that provides generalized mass or heat transfer equations is compared to micromorphic-type hyper-temperature and micro-entropy proposals. The double temperature and the micromorphic thermal models are shown to lead to equations more general that Cattaneo's. The sign of the coefficient of the second time-derivative of temperature is found to differ according to both approaches. The double temperature model contains a fourth space derivative term not present in the micromorphic models. Such generalized equations can be useful, for example, in the interpretation of recent femtosecond laser experiments on metals

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Section: Discussionmentioning

confidence: 99%

Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

Forest

Aifantis

2010

International Journal of Solids and Structures

146

View full text Add to dashboard Cite

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“…fully characterise the boundary value problem associated to the variational principle (6). Note that by introducing (7), (8) and (9) in (16), (17), (18) and (19), the equilibrium equations for high order continua with inertia effects are recovered. The reader is referred to [21] for further details.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…The literature in the field is vast and it is not the goal of the present work to discuss every aspect of the theory itself. The interested reader can refer to [2,3,16,18,17,19,22,24], which address various theoretical and practical aspects of such formulations.…”

Section: Introductionmentioning

confidence: 99%

The method of multiscale virtual power for the derivation of a second order mechanical model

Blanco

Sánchez

Neto

et al. 2016

Mechanics of Materials

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • The Method of Multiscale Virtual Power is used to derive an RVEbased multiscale model of second-order continua. • Body forces are considered in the formulation of the problem. • The resulting model relies crucially on kinematical hypotheses and a Principle of Multiscale Virtual Power.

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“…This approach is based on purely variational arguments to define the kinematic transfer between scales and to naturally derive homogenization rules for the flux quantities (stress and heat flux in this case). The formulation proposed in [15] is in line with [31,51,84,85] in the sense that the continuum model at the macro-scale features a higher order thermal behavior, with the stress depending on the temperature gradient. This is consistent with an extended thermodynamics framework at the macroscale.…”

Section: Rve-based Multiscale Methods: a Brief Reviewmentioning

confidence: 89%

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

Blanco

Sánchez

Neto

et al. 2014

Arch Computat Methods Eng

133

113

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A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro-and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force-and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the wellknown Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force-and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations.

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On standard dissipative gradient models

Cited by 17 publications

References 27 publications

Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

The method of multiscale virtual power for the derivation of a second order mechanical model

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

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