Damage as Γ-limit of Microfractures in Anti-plane Linearized Elasticity
نویسندگان
چکیده
A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Γ-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.
منابع مشابه
Damage as Γ-limit of Microfractures in Linearized Elasticity under the Non-interpenetration Constraint
A homogenization result is given for a material having soft inclusions arranged in a periodic structure, under the requirement that the interpenetration of matter is forbidden. According to the relation between the softness parameter and the size of the microstucture, three different limit models are deduced via Γ-convergence.
متن کاملA Γ-Convergence Result for Thin Martensitic Films in Linearized Elasticity
The elastic energy of a thin film Ωh of thickness h with displacement u : Ωh → R is given by the functional E(u) = ∫ Ωh W (∇u). We consider materials whose energy density W is linearly frame indifferent and vanishes on two linearized wells which are compatible in the plane but incompatible in the thickness direction. We prove compactness of displacement sequences u : Ωh → R satisfying E(u) ≤ Ch...
متن کاملAsymptotic Models for Curved Rods Derived from Nonlinear Elasticity by Γ-convergence
We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elast...
متن کاملA Note on Anti-plane Shear for Compressible Materials in Finite Elastostatics
This note gives a necessary and sufficient condition that a compressible, isotropic elastic material should admit non-trivial states of finite anti-plane shear. One of the simplest classes of deformations of solids is that of anti-plane shear, in which each particle of a cylindrical body undergoes a displacement parallel to the generators of the cylinder and independent of the axial position of...
متن کاملPlane Strain Deformation of a Poroelastic Half-Space Lying Over Another Poroelastic Half-Space
The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...
متن کامل