54 research outputs found
Quasistatic delamination of sandwich-like Kirchhoff-Love plates
A quasistatic rate-independent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rate-independent delamination model for a laminated Kirchhoff-Love plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguishe
Shape-topological differentiability of energy functionals for unilateral problems in domains with cracks and applications
International audienceA review of results on first order shape-topological differentiability of energy functionals for a class of variational inequalities of elliptic type is presented.The velocity method in shape sensitivity analysis for solutions of elliptic unilateral problems is established in the monograph (SokoĆowski and ZolĂ©sio, Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992). The shape and material derivatives of solutions to frictionless contact problems in solid mechanics are obtained. In this way the shape gradients of the associated integral functionals are derived within the framework of nonsmooth analysis. In the case of the energy type functionals classical differentiability results can be obtained, because the shape differentiability of solutions is not required to obtain the shape gradient of the shape functional (SokoĆowski and ZolĂ©sio, Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992). Therefore, for cracks the strong continuity of solutions with respect to boundary variations is sufficient in order to obtain first order shape differentiability of the associated energy functional. This simple observation which is used in SokoĆowski and ZolĂ©sio (Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992) for the shape differentiability of multiple eigenvalues is further applied in Khludnev and SokoĆowski (Eur. J. Appl. Math. 10:379â394, 1999; Eur. J. Mech. A Solids 19:105â120, 2000) to derive the first order shape gradient of the energy functional with respect to perturbations of the crack tip. A domain decomposition technique in shape-topology sensitivity analysis for problems with unilateral constraints on the crack faces (lips) is presented for the shape functionals.We introduce the Griffith shape functional as the distributed shape derivative of the elastic energy evaluated in a domain with a crack, with respect to the crack length. We are interested in the dependence of this functional on domain perturbations far from the crack. As a result, the directional shape and topological derivatives of the nonsmooth Griffith shape functional are obtained with respect to boundary variations of an inclusion
Optimal location of a rigid inclusion in equilibrium problems for inhomogeneous twoâdimensional bodies with a crack
Controlling the shape of a crack in an elastic body under the condition of a possible contact of edges
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