Higher integrability of determinants and weak convergence in L1.
Higher integrability of the gradient in linear elasticity.
Homogenization of linear elasticity equations
The homogenization problem (i.e. the approximation of the material with periodic structure by a homogeneous one) for linear elasticity equation is studied. Both formulations in terms of displacements and in terms of stresses are considered and the results compared. The homogenized equations are derived by the multiple-scale method. Various formulae, properties of the homogenized coefficients and correctors are introduced. The convergence of displacment vector, stress tensor and local energy is proved...
Homogenization of linearized elasticity systems with traction condition in perforated domains.
Homogenization of many-body structures subject to large deformations
We give a first contribution to the homogenization of many-body structures that are exposed to large deformations and obey the noninterpenetration constraint. The many-body structures considered here resemble cord-belts like they are used to reinforce pneumatic tires. We establish and analyze an idealized model for such many-body structures in which the subbodies are assumed to be hyperelastic with a polyconvex energy density and shall exhibit an initial brittle bond with their neighbors. Noninterpenetration...
Homogenization of many-body structures subject to large deformations
We give a first contribution to the homogenization of many-body structures that are exposed to large deformations and obey the noninterpenetration constraint. The many-body structures considered here resemble cord-belts like they are used to reinforce pneumatic tires. We establish and analyze an idealized model for such many-body structures in which the subbodies are assumed to be hyperelastic with a polyconvex energy density and shall exhibit an...
Homogenization of some contact problems for the system of elasticity in perforated domains