Relaxation et existence pour le problème des matériaux à blocage
Relaxation of convex functionals : the gap problem
Relaxation of elastic energies with free discontinuities and constraint on the strain
As a model for the energy of a brittle elastic body we consider an integral functional consisting of two parts: a volume one (the usual linearly elastic energy) which is quadratic in the strain, and a surface part, which is concentrated along the fractures (i.e. on the discontinuities of the displacement function) and whose density depends on the jump part of the strain. We study the problem of the lower semicontinuous envelope of such a functional under the assumptions that the surface energy density...
Relaxation of free-discontinuity energies with obstacles
Given a Borel function ψ defined on a bounded open set Ω with Lipschitz boundary and , we prove an explicit representation formula for the L1 lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint
Relaxation of vectorial variational problems
Multidimensional vectorial non-quasiconvex variational problems are relaxed by means of a generalized-Young-functional technique. Selective first-order optimality conditions, having the form of an Euler-Weiestrass condition involving minors, are formulated in a special, rather a model case when the potential has a polyconvex quasiconvexification.
Relaxation theorems in nonlinear elasticity
Relaxed hyperelastic curves
We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.
Reliable computation and local mesh adaptivity in limit analysis
The contribution is devoted to computations of the limit load for a perfectly plastic model with the von Mises yield criterion. The limit factor of a prescribed load is defined by a specific variational problem, the so-called limit analysis problem. This problem is solved in terms of deformation fields by a penalization, the finite element and the semismooth Newton methods. From the numerical solution, we derive a guaranteed upper bound of the limit factor. To achieve more accurate results, a local...
Reliable solution of an elasto-plastic Reissner-Mindlin beam for Hencky's model with uncertain yield function
We apply the method of reliable solutions to the bending problem for an elasto-plastic beam, considering the yield function of the von Mises type with uncertain coefficients. The compatibility method is used to find the moments and shear forces. Then we solve a maximization problem for these quantities with respect to the uncertain input data.
Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function
Maximization problems are formulated for a class of quasistatic problems in the deformation theory of plasticity with respect to an uncertainty in the material function. Approximate problems are introduced on the basis of cubic Hermite splines and finite elements. The solvability of both continuous and approximate problems is proved and some convergence analysis presented.
Remark to the comparison of solution properties of Love's equation with those of wave equation
In the paper some solution properties of the Love's equation are compared with those of the classical wave equation for a certain class of boundary conditions. The method of small parameter is used.
Remarks about Signorini's problem in linear elasticity
Remarks on a Nonlinear Theory of Thin Elastic Plates
Remarks on Carleman estimates and exact controllability of the Lamé system
In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.
Remarks on materials with memory
The mistaken notion that consistency with fading memory should require uniqueness is refuted by citation of the sources. Indeed, insistence on uniqueness would exclude many examples from non-linear elasticity and would exclude materials capable of exhibiting hysteresis.
Remarks on nonlinear biharmonic evolution equation of Kirchhoff type in noncylindrical domain.
Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory
Remarks on the existence and decay of the nonlinear beam equation.
Remarks on the theory of elasticity
In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some -norm of the gradient with is controlled...
Remarks on -quasiconvexity, interpenetration of matter, and function spaces for elasticity