Geometry of interactions in complex bodies

Fabritiis, Chiara de; Mariano, Paolo Maria

doi:10.1016/j.geomphys.2004.10.002

Cited by 31 publications

(35 citation statements)

References 36 publications

(61 reference statements)

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“…(1.15). 41 The indeterminacy can be eliminated by covariance techniques (de Fabritiis & Mariano, 2005), i.e., by requiring at least invariance with respect to the generalized class 1. 40 If we cancel w, P rel B (ẏ,ν, w) reduces to P ext B (ẏ,ν), already defined above, and P rel−int…”

Section: An Extended Version Of the Virtual Power Principle Holds Itmentioning

confidence: 99%

Mechanics of Material Mutations

Mariano

2014

Advances in Applied Mechanics

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Section: An Extended Version Of the Virtual Power Principle Holds Itmentioning

confidence: 99%

Mechanics of Material Mutations

Mariano

2014

Advances in Applied Mechanics

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“…Theorem 7 extends to complex bodies a companion result for simple elastic bodies in [31]. The extended Hamilton-Eshelby tensor P has been introduced in [38] (see also [12]) with reference to smooth minimizers. Here the configurational balance involving P is extended to irregular minimizers.…”

Section: Irregular Minimizers: Horizontal Variationsmentioning

confidence: 93%

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 U-relative form of the material time derivative of a spacelike vector field c : M → E is obtained by (17) and (21):…”

Section: Materials Time Derivativementioning

confidence: 99%

Absolute time derivatives

Matolcsi

Ván

2007

Journal of Mathematical Physics

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A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their coordinatized forms depends on the tensorial properties of the relevant physical quantities. We calculate the particular forms of objective time derivatives for scalars, vectors, covectors and different second order tensors from the point of view of a rotating observer. The relation of substantial, material and objective time derivatives is treated.

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Geometry of interactions in complex bodies

Cited by 31 publications

References 36 publications

Mechanics of Material Mutations

Mechanics of Material Mutations

Ground states in complex bodies

Absolute time derivatives

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