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We characterize the general solutions to certain symmetric systems of linear partial differential equations with tensor functionals as unknowns. Then we determine the solutions that are physically meaningful in suitable senses related with the constitutive functionals of two simple thermodynamic bodies with fading memory that are globally equivalent, i.e. roughly speaking that behave in the same way along processes not involving cuts. The domains of the constitutive functionals are nowhere dense...
We introduce the space of generalized functions of bounded deformation and study the structure properties of these functions: the rectiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for , which leads to a compactness result for the space of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational...
The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.
We deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations.
We restrict our analysis to the case of a cylindrical symmetry for the crystal under study, so that the mathematical formulation will involve a two-dimensional variational problem.
The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so-called core region. We show that the -limit of this
energy (suitably rescaled),...
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...
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...
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