Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model

Misra, Anil; Singh, Viraj

doi:10.1007/s00161-014-0360-y

Cited by 75 publications

(46 citation statements)

References 82 publications

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“…A review of results on the theoretical foundation of a variational approach for higher gradient theories is [71]. Besides, the use of the methods of metamaterials [72][73][74] like those for pantographic structures [75][76][77] could be considered even to take into account the effects of damage [78][79][80][81][82]. Another possible extension of this model is to include surface effects [83][84][85][86][87][88][89] and the anisotropy induced by the orientation of the NLC directors, as in [90] , or as it is done in granular materials [91].…”

Section: Numerical Simulationsmentioning

confidence: 99%

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

Rosi

Placidi

Dell’Isola

2017

Z. Angew. Math. Phys.

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Section: Numerical Simulationsmentioning

confidence: 99%

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

Rosi

Placidi

Dell’Isola

2017

Z. Angew. Math. Phys.

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“…Works in the literature since this pioneering contribution witness a diversity of definitions and derivations of the stress tensor using a molecular viewpoint, see the recent critical overview [29] and references therein. Such an interpretation of the stress tensor based on the connection between discrete and continuum systems has been given for the specific case of granular materials [27,28]. In particular, when micro-macro-identifications processes are considered, higher gradient theories naturally arise in which to Cauchy stress tensor one needs to add a family of hyper stresses, as already remarked by Gabrio Piola in his pioneering works [10,11].…”

Section: Introductionmentioning

confidence: 99%

On the generalized virial theorem for systems with variable mass

Ganghoffer

Rahouadj

2015

Continuum Mech. Thermodyn.

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We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209-1220. The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem. List of symbols R, R i (r, r i )Material (resp. spatial) position vectors X, x Referential and actual position of material points for a continuum J Inertia tensorMomentum for a single particlê V ,V Respectively, the scalar and tensorial virialŝ V int ,V ext Respectively, the internal and external scalar virials · Ensemble averaging (equivalent to time averaging according to ergodicity) V 0 (resp. V 0 ) Average scalar (resp. tensorial) material virial V (resp. V ) Average scalar (resp. tensorial) spatial virial Communicated by Victor Eremeyev, Peter Schiavone and Francesco dell'Isola.

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“…The macroscopic scale can be interpreted as the length scale of a representative volume element (RVE) of the polycrystal. Expressing the macroscopic free energy in terms of the mesoscopic free energies in the constitutive grains is a long-standing topic in the study of polycrystals and granular materials (see e.g., [18] for a recent work in the field of granular materials).…”

Section: Peigney (B)mentioning

confidence: 99%

“…Using the quasiconvexity of the function h in (6), upper bounds onK that take one-point statistics of the functions χ r can be derived [22]. Let indeedF be inK and consider a deformation gradient field F in A (F) such that F(x) ∈K (x) for all x (recall that such F exists by (18)). Using the property (7) and noting that…”

Section: Polycrystalmentioning

confidence: 99%

Improved bounds on the energy-minimizing strains in martensitic polycrystals

Peigney

2015

Continuum Mech. Thermodyn.

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International audienceThis paper is concerned with the theoretical prediction of the energy-minimizing (or recoverable) strains in martensitic polycrystals, considering a nonlinear elasticity model of phase transformation at finite strains. The main results are some rigorous upper bounds on the set of energy-minimizing strains. Those bounds depend on the polycrystalline texture through the volume fractions of the different orientations. The simplest form of the bounds presented is obtained by combining recent results for single crystals with a ho-mogenization approach proposed previously for martensitic polycrystals. However, the polycrystalline bound delivered by that procedure may fail to recover the monocrystalline bound in the homogeneous limit, as is demonstrated in this paper by considering an example related to tetragonal martensite. This motivates the development of a more detailed analysis, leading to improved polycrystalline bounds that are notably consistent with results for single crystals in the homogeneous limit. A two-orientation polycrystal of tetragonal martensite is studied as an illustration. In that case, analytical expressions of the upper bounds are derived and the results are compared with lower bounds obtained by considering laminate textures

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Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model

Cited by 75 publications

References 82 publications

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

On the generalized virial theorem for systems with variable mass

Improved bounds on the energy-minimizing strains in martensitic polycrystals

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