117,418 research outputs found
Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density
Full text linkThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional converge to critical points of the Γ-limit. This is proved under the physical assumption that the energy density blows up as the determinant of the deformation gradient becomes infinitesimally small
An extension theorem in SBV and an application to the homogenization of the Mumford-Shah functional in perforated domains
Full text linkThe aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a non coercive homogenization problem
The Equilibrium Measure for a Nonlocal Dislocation Energy
Full text linkIn this paper we characterize the equilibrium measure for a nonlocal and anisotropic weighted energy describing the interaction of positive dislocations in the plane. We prove that the minimum value of the energy is attained by a measure supported on the vertical axis and distributed according to the semicircle law, a well-known measure that also arises as the minimizer of purely logarithmic interactions in one dimension. In this way we give a positive answer to the conjecture that positive dislocations tend to form vertical walls. This result is one of the few examples where the minimizer of a nonlocal energy is explicitly computed and the only one in the case of anisotropic kernels. © 2018 Wiley Periodicals, Inc
The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity
Full text linkThe problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the diameter of the beam goes to zero, a nonlinear model for strings and a bending-torsion theory for rods are deduced
Damage as the Γ-limit of microfractures in linearized elasticity under the non-interpenetration constraint
Full text linkA homogenization result is given for a material with brittle periodic inclusions, under the requirement that the interpenetration of matter is forbidden. According to the ratio between the softness of the inclusions and the size of the microstucture, three different limit models are deduced via Gamma-convergence. In particular it is shown that in the limit the non-interpenetration constraint breaks the symmetry between states where the material is in extension and in compression
Recensione di L. Pessoa da Silva Pinto - D. Scialabba (eds.), New Avenues in Biblical Exegesis in Light of the Septuagint (The Septuagint in its Ancient Context. Philological, Historical and Theological Approaches 1; Turnhout: Brepols, 2022), 345 pp.
No full textQuasistatic delamination problem
Full text linkWe study delamination of two elastic bodies glued together by an adhesive that can undergo a unidirectional inelastic rate-independent process. The quasistatic delamination process is thus activated by time-dependent external loadings, realized through body forces and displacements prescribed on parts of the boundary. The novelty of this work consists of considering the glue as infinitesimally thin and ideally rigid in the sense that a crack in the glue cannot be seen before, speaking ``microscopically'', all macromolecular links of the adhesive are fully debonded. The concept of energetic solution is applied and existence of such solutions is proved by showing Gamma-convergence of a suitable approximation that, in addition, allows for a direct computer implementation, unlike the original problem
Damage as Gamma-limit of microfractures in anti-plane linearized elasticity
Full text linkA homogenization result is given for a material having brittle inclusions arranged in a periodic structure.
<br/>
According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence.
<br/>
In particular, damage is obtained as limit of periodically distributed
microfractures
Boundary layer energies for nonconvex discrete systems
No full textIn this work we consider a one-dimensional chain of atoms which interact through nearest and next-to-nearest neighbour interactions of Lennard-Jones type. We impose Dirichlet boundary conditions and in addition prescribe the deformation of the second and last but one atoms of the chain. This corresponds to prescribing the slope at the boundary of the discrete setting. We compute the Gamma-limits of zero and first order, where the latter leads to the occurrence of boundary layer contributions to the energy. These contributions depend on whether the chain behaves elastically close to the boundary or whether there is a crack. This in turn depends on the given boundary data. We also analyse the location of fracture in dependence on the prescribed discrete slopes
- …
