Elastic Media with Microstructure I

Kunin, Isaak A.

doi:10.1007/978-3-642-81748-9

Cited by 369 publications

(278 citation statements)

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“…Besides nonlocal models in elasticity, Bazant and Jirasek (2002) review models in nonlocal plasticity and damage, including cohesive zone models for fracture. Analytical results are possible for special cases for nonlocal models and some are presented in, for example, the monographs by Kunin (1982), and by Erofeyev (2003) which discusses wave processes in solids with microstructure. One of the factors that have delayed the widespread adoption of nonlocal formulations by industry has been the difficulty of correlating them to existing constitutive models that have performed well under certain strain rates and thermal ranges.…”

Section: Nonlocal Modelsmentioning

confidence: 99%

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Impact Mechanics and High-Energy Absorbing Materials: Review

2008

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Section: Nonlocal Modelsmentioning

confidence: 99%

“…In the peridynamic model, all forces are long-range as in other nonlocal continuum theories, such as those described in Kunin (1982) and Rogula (1982). A discussion of the relation between nonlocal theories and atomistic models can be found in, e.g., Chen et al (2004).…”

Section: Nonlocal Modelsmentioning

confidence: 99%

Impact Mechanics and High-Energy Absorbing Materials: Review

2008

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“…Since the publication of the landmark book of Cosserat brothers [4] in literature there are various known generalizations and applications of the classical or Cauchy continuum which are summarized in many books [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and papers [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Especially we must mention remarkable books of Eringen [38,39] and Nowaski [40] and fundamental treatise of Truesdell and Toupin [3].…”

Section: Introductionmentioning

confidence: 99%

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya

2017

Curved and Layered Structures

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New models for plane curved rods based on linear couple stress theory of elasticity have been developed. 2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and EulerBernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

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“…In the case of Cosserat continua the degree of freedom for each material point are six: three translations and three microrotations. The domain of applicability of the theory of continua with inner structure has investigated by Fischer-Hjalmars (1982), Kunin (1983), Eringen (1999), Dyszlewicz (2004) and Chen et al (2004). The classical theory of Cosserat elastic solids is characterized by constitutive functions which depend on the deformation gradient, microrotation vector and gradient of microrotation.…”

Section: Introductionmentioning

confidence: 99%

Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

Ieşan

Quintanilla

2016

Journal of Mathematical Analysis and Applications

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In this paper, we use the Green-Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of Cosserat thermoelastic bodies. The theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor. The constitutive equations for isotropic chiral thermoelastic materials are presented. In this case, in contrast with the classical Cosserat thermoelasticity, a thermal field produces a microrotation of the particles. The thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory. Existence and uniqueness results are established. The theory is used to study the effects of a concentrated heat source in an unbounded homogenenous and isotropic chiral solid.

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Elastic Media with Microstructure I

Cited by 369 publications

References 0 publications

Impact Mechanics and High-Energy Absorbing Materials: Review

Impact Mechanics and High-Energy Absorbing Materials: Review

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

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