-plane analysis for the fundamental problems of a stretched infinite plate weakened by curvilinear holes.
Scaling laws for non-euclidean plates and the isometric immersions of riemannian metrics
Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its Γ-convergence under the proper...
Scaling laws for non-Euclidean plates and the W2,2 isometric immersions of Riemannian metrics
Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its Γ-convergence under the proper scaling....
Semicontinuity theorem in the micropolar elasticity
In this paper we investigate the equivalence of the sequential weak lower semicontinuity of the total energy functional and the quasiconvexity of the stored energy function of the nonlinear micropolar elasticity. Based on techniques of Acerbi and Fusco [Arch. Rational Mech. Anal.86 (1984) 125–145] we extend the result from Tambača and Velčić [ESAIM: COCV (2008) DOI: 10.1051/cocv:2008065] for energies that satisfy the growth of order p≥ 1. This result is the main step towards the general existence...
Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization
Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used for numerical realization. Numerical results of model examples are shown.
Solution of mechanical problems in fractured rock with the user-defined interface of COMSOL multiphysics
This paper presents the main concept and several key features of the user-defined interface of COMSOL Java API for the solution of mechanical problems in fractured rock. This commercial computational system based on FEM has yet to incorporate fractures in mechanical problems. Our aim is to solve a 2D mechanical problem with a fracture which is defined separately from finite-element discretization and the fracture properties are included through the constitutive laws. This will be performed based...
Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method
A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.
Solvability and asymptotics of solutions of crack-type boundary-contact problems of the ocuple-stress elasticity.
Some dynamic problems of the theory of electroelasticity.
Some problems of thermoelastic equilibrium of a rectangular parallelepiped in terms of asymmetric elasticity.
Some regularity results for minimal crystals
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space ( a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is empty...
Some regularity results for minimal crystals
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space (i.e. a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is...
Spatial heterogeneity in 3D-2D dimensional reduction
A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem...
Spatial heterogeneity in 3D-2D dimensional reduction
A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem...
Stability of microstructure for tetragonal to monoclinic martensitic transformations
Stability of microstructure for tetragonal to monoclinic martensitic transformations
We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to...
Stability properties of a class of viscoelastic beams of the hereditary type
The paper deals with the problem of equilibrium stability of prismatic, homogeneous, intrinsically isotropic, viscoelastic beams subjected to the action of constant compressive axial force in the light of Lyapounov's stability theory. For a class of functional expressions of creeping kernels characteristic of no-aging viscoelastic materials of the hereditary type, solution of the governing integro-differential equations is given. Referring to polymeric materials of the PMMA type, numerical results...
Stable and unstable bifurcation in the von Kármán problem for a circular plate.
Structure of stable solutions of a one-dimensional variational problem
We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...
Sugli atti di moto, eventualmente isocori, più rigidi possibile