Exact controllability of vibrations of thin bodies.
Existence theorem in the linear theory of multipolar elasticity
Fluid flow in macromolecular systems and related perturbation problems
Generic properties of von Kármán equations
Geometrical modeling of material aging.
Ground states in complex bodies
A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance...
Ground states in complex bodies
A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance...
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...
Inequalities of Korn's type, uniform with respect to a class of domains
Inequalities of Korn's type involve a positive constant, which depends on the domain, in general. A question arises, whether the constants possess a positive infimum, if a class of bounded two-dimensional domains with Lipschitz boundary is considered. The proof of a positive answer to this question is shown for several types of boundary conditions and for two classes of domains.
Instability critical loads of the fiber reinforced elastic composites.
Integrazione del problema dell'elastostatica nel caso asimmetrico e con coppie di contatto. Applicazione al problema delle piastre. IIa parte
Isoperimetric distributions of loads in elastostatics
Kelvin's solution and nuclei of strain in a solid mixture
Korn's inequality uniform with respect to a class of axisymmetric bodies
The Korn's inequality involves a positive constant, which depends on the domains, in general. We prove that the constants have a positive infimum, if a class of bounded axisymmetric domains and axisymmetric displacement fields are considered.
Mathematical analysis for the peridynamic nonlocal continuum theory
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical analysis for the peridynamic nonlocal continuum theory*
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures
A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.
Mixed interface problems for anisotropic elastic bodies.
Morphological analysis and variational formulation in heterogeneous thermoelasticity.
This paper is devoted to several applications of morphological analysis applied to the bounding of the overall behaviour of composite materials. In particular we focus our attention to the generalization of the Hashin-Shtrikmann variational principles to thermoelasticity.