On Singularities in 2D Linearized Elasticity

2016 ◽  
pp. 35-47
Author(s):  
Hiromichi Itou
Keyword(s):  
Linearized Elasticity

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

2014 ◽  
Vol 25 (01) ◽  
pp. 1-38 ◽  
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.

Linearized Elasticity

2015 ◽  
pp. 308-685
Author(s):  
Chandrashekhar S. Jog
Keyword(s):  
Linearized Elasticity

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

2004 ◽  
Vol 134 (6) ◽  
pp. 1041-1083 ◽  
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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