A nonlinear theory of elastic materials with voids

Nunziato, Jace W.; Cowin, Stephen C.

doi:10.1007/bf00249363

Cited by 689 publications

(390 citation statements)

References 18 publications

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“…Nunziato and Cowin [14] have shown that this internal dissipation results in the material exhibiting a relaxation property similar to that associated with viscoelastic materials.…”

Section: Viscoporositymentioning

confidence: 93%

See 1 more Smart Citation

On the time decay of solutions for non-simple elasticity with voids

Liu

Magaña²,

Quintanilla³

2015

Z. Angew. Math. Mech.

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Abstract:In this work we consider the non-simple theory of elastic material with voids and we investigate how the coupling of these two aspects of the material affects the behavior of the solutions. We analyze only two kind of different behavior, slow or exponential decay. We introduce four different dissipation mechanisms in the system and we study, in each case, the effect of this mechanism in the behavior of the solutions.

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“…Nunziato and Cowin [14] have shown that this internal dissipation results in the material exhibiting a relaxation property similar to that associated with viscoelastic materials.…”

Section: Viscoporositymentioning

confidence: 93%

“…The classical setting of this theory was established by Nunziato and Cowin [14], Cowin and Nunziato [1] and Cowin [2]. The basic idea of these works is that the bulk density is the product of two scalar fields, the matrix material density and the volume fraction.…”

Section: Introductionmentioning

confidence: 99%

On the time decay of solutions for non-simple elasticity with voids

Liu

Magaña²,

Quintanilla³

2015

Z. Angew. Math. Mech.

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“…The theory of porous elastic material has been established by Cowin and Nunziato [12,13,14]. In this theory the bulk density is the product of two scalar fields, the matrix material density and the volume fraction field; it is studied in the book of Ciarletta and Iesan [15].…”

Section: Introductionmentioning

confidence: 99%

Exponential decay in one-dimensional porous-thermo-elasticity

Casas

Quintanilla

2005

Mechanics Research Communications

139

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This paper concerns the one dimensional problem of the porous-thermo-elasticity. Two kinds of dissipation process are considered: the viscosity type in the porous structure and the thermal dissipation. It is known that when only thermal damping is considered or when only porous damping is considered we have the slow decay of the solutions. Here we prove that when both kinds of dissipation terms are taken into account in the evolution equations the solutions are exponentially stable.

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“…In this case M reduces to the interval of the real axis [0, 1] (see [46]). The scheme of porous materials is useful when multiple phases (for example m phases) coexist within a body and phase transitions occur [22].…”

Section: Taxonomy Of Special Casesmentioning

confidence: 99%

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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A nonlinear theory of elastic materials with voids

Cited by 689 publications

References 18 publications

On the time decay of solutions for non-simple elasticity with voids

On the time decay of solutions for non-simple elasticity with voids

Exponential decay in one-dimensional porous-thermo-elasticity

Ground states in complex bodies

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