Related papers: Integral representation for a relaxed optimal desi…
We obtain a measure representation for a functional arising in the context of optimal design problems under linear growth conditions. The functional in question corresponds to the relaxation with respect to a pair $(\chi,u)$, where $\chi$…
The paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in…
In this paper we investigate the possibility of obtaining a measure representation for function- als arising in the context of optimal design problems under non-standard growth conditions and perimeter penalization. Applications to…
We obtain an integral representation for certain functionals arising in the context of optimal design and damage evolution problems under non-standard growth conditions and perimeter penalisation. Under our hypotheses, the integral…
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincar\'e inequality. Such a functional is defined through relaxation, and it defines a Radon measure on…
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
In this work we consider an optimal design problem for two-component fractured media for which a macroscopic strain is prescribed. Within the framework of structured deformations, we derive an integral representation for the relaxed energy…
This paper joins some concepts from Mechanics, Partial Differential Equations and Control Theory in order to solve bi-time optimization problems related to stress tensor in plastic deformations. The main goal is to analyze some optimal…
We report a method for describing plasticity in a broad class of amorphous materials. The method is based on nonlinear (geometric) deformation theory allowing the separation of the plastic deformation from the general deformation tensor.…
This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…
An integral representation result is obtained for the relaxation of a class of energy functionals depending on two vector fields with different behaviors which appear in the context of thermochemical equilibria and are related to image…
We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an…
We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…
Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…
The paper deals with the determination of integral functional quality for control system of generalized linear dynamic object with exponential activation function by solving the inverse problem of dynamic programming. The obtained…
We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(\Omega)T^q(\Omega)|\Omega|^{-2q-1/2}$ and the class of…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure…
Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…
Stress and strain fields in a two-dimensional pixelwise disordered system are computed by a Fast Fourier Transform method. The system, a model for a ductile damaged medium, consists of an elastic-perfectly matrix containing void pixels. Its…