Continua with latent microstructure

Capriz, Gianfranco

doi:10.1007/bf00281586

Cited by 90 publications

(57 citation statements)

References 5 publications

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“…with f a differentiable function, we recover strain-gradient elasticity as a special case of the general format of the elasticity of complex materials, as shown in [51]. In this case, the microstress becomes the third-rank hyperstress appearing in the direct formulation of strain-gradient elasticity (the proof of the existence of S indicated above applies).…”

Section: (B) the Relative Power And Its Invariancementioning

confidence: 99%

Trends and challenges in the mechanics of complex materials: a view

Mariano

2016

Phil. Trans. R. Soc. A.

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Section: (B) the Relative Power And Its Invariancementioning

confidence: 99%

Trends and challenges in the mechanics of complex materials: a view

Mariano

2016

Phil. Trans. R. Soc. A.

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“…It applies to phenomena implying addition or subtraction of material points to the reference control volume, as for example cases in which there is crack growth 5 or evolution of a surface across which phase transitions occur. In such a way, Gurtin extends to non conservative setting the concept of configurational forces 6 , representing the action of the body on its part changing structure with a kinematical mechanism independent on the external forces. Such an independence implies that configurational forces appear explicitly in the expression of the power.…”

Section: General Remarksmentioning

confidence: 99%

“…(4.30) 49 The interpretation of div(Sφ) as interstitial working is due to Capriz [1985] in a paper in which a bridge among multifield theories and the Dunn's and Serrin's theory of continua with higher order gradients [Dunn and Serrin, 1985] has been established.…”

Section: P M Mariano Zampmentioning

confidence: 99%

Configurational forces in continua with microstructure

Mariano¹

2000

Z. angew. Math. Phys.

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The action exerted on a defect or inclusion in an elastic solid by the surrounding medium can be expressed by means of the space-like part of the Noether energy momentum tensor, the so-called Eshelby tensor 1 . The theory by Eshelby is variational in essence and has been formulated for materials of grade n. It is based on Noether theorem that establishes the existence of a second order tensor quantity which is invariant along the trajectories, under conditions of homogeneity, if the equations of motion are satisfied. As well known, this theorem (a central result in Hamiltonian mechanics) states that every group of transformations under which the Lagrange density function is invariant generates a conserved quantity 2 .Gurtin has proved the validity of Eshelby relation in non conservative setting 3 . His argument is based on • the time variation of a reference control volume, interpreting the evolution of defects or interface surfaces, and the action of the associated material observer 4 ; • a mechanical version of the second law of thermodynamics;• the requirement of invariance under re-parametrization of the boundary of the reference control volume. It applies to phenomena implying addition or subtraction of material points to the reference control volume, as for example cases in which there is crack growth 5 or evolution of a surface across which phase transitions occur. In such a way, 1 [Eshelby, 1975] 2 [Marsden and Hughes, 1983] 3 [Gurtin, 1995] 4 [Gurtin, 1997] 5 Podio-Guidugli, 1996] [Gurtin andYatomi, 1980]

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“…49, [ 12]). To proceed, we use (4.7) to replace ~i by z i in the constrained directed rod so that the field equations (4.8) are altered to the following form n' + 2pf = 0; (4.12)…”

Section: Comparison Of Constrained Directed Rods With Ordinary Rods Amentioning

confidence: 99%

“…However, (4.12)4 indicates that the tensor P* in the constrained directed rod is no longer symmetric due to the extra terms pertaining to the director d3. In fact, the discrepancy between the theory of continua without microstructure and that of continua with latent microstructure has been discussed by Capriz [12]. It is dear that if 13 = ld3 and m 3 = rnd3 where I and m are arbitrary scalars, (4.12)4,5 are reduced to (4.1)3,4, respectively.…”

Section: Comparison Of Constrained Directed Rods With Ordinary Rods Amentioning

confidence: 99%