# From non-linear elasticity to linear elasticity with initial stress via Î“-convergence

## Related Articles

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The authors propose a procedure for estimating stresses, load bearing capacity and remaining life of lining in long-term operated underground tunnels using the analytical calculations based on solving the plane elastic problem on stress-strain state of a non-circular variable-thickness ring...

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We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical Îµ-periodically distributed fibres of size rÎµ, with 0 < rÎµ < Îµ, filled in with some different elastic material, when this small parameter Îµ goes to 0. The case of small deformations and...

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The solution of a plane problem of elasticity theory for an orthotropic plane with semiinfinite rounded V-notch under the action of symmetric loads is obtained by the method of singular integral equations. By using this solution, we deduce the relations between the stress intensity factor at the...

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Generalization of the formula of Euler on not elastic area and definition of critical force in the compression member behind a limit of elasticity is considered in article. It is set an example of calculation in which comparison of the decisions received by methods of F.Engessera, T.Karmana and...

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- Application of triangular element invariants for geometrically nonlinear analysis of functionally graded shells. Levyakov, S.; Kuznetsov, V. // Computational Mechanics;Oct2011, Vol. 48 Issue 4, p499
This paper is an attempt to construct a computationally effective curved triangular finite element for geometrically nonlinear analysis of elastic shear deformable shells fabricated from functionally graded materials. The focus is on the concise finite-element formulation under the demand of...

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The problem of determining the stressâ€”strain state of a multilayered shell is solved. It is assumed that the layer material is nonlinearly elastic and the strainâ€”displacement relations are nonlinear. The displacements are expanded in terms of the functions of transverse coordinate...

- MULTI-COMPONENT ALLEN-CAHN EQUATION FOR ELASTICALLY STRESSED SOLIDS. Blesgen, Thomas; Weikard, Ulrich // Electronic Journal of Differential Equations;2005, Vol. 2005, p1
The vector-valued Allen-Cahn equations are combined with elasticity where a linear stress-strain relationship is assumed. A short physical derivation of the generalised model is given and global existence and uniqueness of the solution are shown under suitable growth conditions on the nonlinearity.