Cauchy: from Masslets and Springs to 2-D Linearized Elasticity

Expression of Dirichlet boundary conditions in terms of the strain tensor in linearized elasticity

Comptes Rendus Mathematique ◽

10.1016/j.crma.2013.04.015 ◽

2013 ◽

Vol 351 (7-8) ◽

pp. 329-334 ◽

Cited By ~ 2

Author(s):

Philippe Ciarlet ◽

Cristinel Mardare

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Strain Tensor ◽

Dirichlet Boundary Conditions ◽

Linearized Elasticity

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Complex potentials of plane linearized elasticity-theory problems (incompressible body)

Soviet Applied Mechanics ◽

10.1007/bf00883901 ◽

1980 ◽

Vol 16 (6) ◽

pp. 507-512

Author(s):

A. N. Guz'

Keyword(s):

Elasticity Theory ◽

Complex Potentials ◽

Linearized Elasticity ◽

Incompressible Body

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From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202515500013 ◽

2014 ◽

Vol 25 (01) ◽

pp. 1-38 ◽

Cited By ~ 7

Author(s):

V. Agostiniani ◽

T. Blass ◽

K. Koumatos

Keyword(s):

Coercivity Conditions ◽

Coercivity Condition ◽

Nematic Elastomers ◽

Linearized Elasticity ◽

Γ Convergence

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.

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On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement

Journal of Physics Conference Series ◽

10.1088/1742-6596/290/1/012005 ◽

2011 ◽

Vol 290 ◽

pp. 012005 ◽

Cited By ~ 2

Author(s):

M Ikehata ◽

H Itou

Keyword(s):

Linearized Elasticity

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Solutions of some boundary value problems for a new class of elastic bodies undergoing small strains. Comparison with the predictions of the classical theory of linearized elasticity: Part I. Problems with cylindrical symmetry

Acta Mechanica ◽

10.1007/s00707-014-1293-z ◽

2014 ◽

Vol 226 (6) ◽

pp. 1815-1838 ◽

Cited By ~ 18

Author(s):

R. Bustamante ◽

K. R. Rajagopal

Keyword(s):

Boundary Value Problems ◽

Classical Theory ◽

Boundary Value ◽

Cylindrical Symmetry ◽

New Class ◽

Small Strains ◽

Elastic Bodies ◽

Linearized Elasticity

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Linearized Elasticity

Continuum Mechanics ◽

10.1017/cbo9781316134054.007 ◽

2015 ◽

pp. 308-685

Author(s):

Chandrashekhar S. Jog

Keyword(s):

Linearized Elasticity

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Classical Linearized Elasticity

A Theory of Elasticity with Microstructure for Directionally Reinforced Composites ◽

10.1007/978-3-7091-4313-1_2 ◽

1975 ◽

pp. 13-20

Author(s):

J. D. Achenbach

Keyword(s):

Linearized Elasticity

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Homogenization of the anisotropic heterogeneous linearized elasticity system in thin reticulated structures

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500003620 ◽

2004 ◽

Vol 134 (6) ◽

pp. 1041-1083 ◽

Cited By ~ 4

Author(s):

J. Casado-Díaz ◽

M. Luna-Laynez

Keyword(s):

Asymptotic Behaviour ◽

Strain Tensor ◽

Relative Size ◽

Limit System ◽

Elasticity System ◽

Linearized Strain ◽

Linearized Elasticity ◽

Small Parameters ◽

Linearized Elasticity System ◽

Suitable Approximation

The aim of this paper is to study the asymptotic behaviour of the solutions of the linearized elasticity system, posed on thin reticulated structures involving several small parameters. We show that this behaviour depends on the relative size of the parameters. In each case, we obtain a limit system where the microstructure and macrostructure appear simultaneously. From it, we get a suitable approximation in L2 of the displacements and the linearized strain tensor.

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