Relativistic shells: Dynamics, horizons, and shell crossing

We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived, and subsequently specialized to the vacuum case. We first examine the relative motion of two dust shells by focusing on the dynamics of the exterior shell, whereby the problem is reduced to that of a single shell with different active Schwarzschild masses on each side. We then examine the dynamics of shells with non-vanishing tangential pressure $p$, and show that there are no stable--stationary, or otherwise--solutions for configurations with a strictly linear barotropic equation of state, $p=\alpha\sigma$, where $\sigma$ is the proper surface energy density and $\alpha\in(-1,1)$. For {\em arbitrary} equations of state, we show that, provided the weak energy condition holds, the strong energy condition is necessary and sufficient for stability. We examine in detail the formation of trapped surfaces, and show explicitly that a thin boundary layer causes the apparent horizon to evolve discontinuously. Finally, we derive an analytical (necessary and sufficient) condition for neighboring shells to cross, and compare the discrete shell model with the well-known continuous Lema\^{\i}tre-Tolman-Bondi dust case.Comment: 25 pages, revtex4, 4 eps figs; published in Phys. Rev.

Break-up of shells under explosion and impact

A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on brown and white hen egg-shells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class different from that of two- and three-dimensional bulk systems.Comment: 11 pages, 14 figures in eps forma

Напряженное состояние цилиндров слоистой структуры с межфазными дефектами

On the basis of the discrete-structural theory of the thin shells the variant of the settlement model of multy-layer thin-walled elements from several rigid anisotropic layers is offered. It is considered, that the voltage of cross shift and pressure on the border of contact are equal among themselves. Elastic slipping is admitted on a surface of contact of adjacent layers. The decision of the task is got in vectorially nonlinear production with account of deformations' influence of cross shift and pressure. The status of two-layer transversally isotropic cylindrical shells with interphasal defects of material's structure is investigated. The results of the theoretical researches are compared to experimental dat

Один вариант уравнений устойчивости оболочек слоистой структуры с межфазными дефектами

On the basis of the discrete-structural theory of thin shells the variant of the equations of stability of settlement model of multy-layer thin-walled elements with several rigid anisotropic layers is offered. It is considered, that the pressure of cross shift and pressure on border of contact are equal among themselves. It is supposed elastic slipping on a surface of contact of adjacent layers. The permitting equations of stability are received with the account of nonlinear deformations and deformations of cross shift and pressur

Dynamics of a developable shell with uniform curvatures

International audienceMany surface-like objects around us such as leaves, garments, or boat sails, may easily bend but hardly stretch. One is thus faced with the need for numerical models able to handle inextensibility constraints properly. In the present work we restrict ourselves to the modeling of elastic developable surfaces, i.e., surfaces which always remain isometric to a planar configuration. Our surfaces of interest may however take a non-planar rest configuration, hence we shall model them as developable thin elastic shells. Our goal is to design a both robust and efficient discrete model for simulating the motion of such objects. This work presents a first step towards this direction, by introducing a perfectly inextensible patch for a developable thin elastic shell

On large deformations of thin elasto-plastic shells: Implementation of a finite rotation model for quadrilateral shell element

A large-deformation model for thin shells composed of elasto-plastic material is presented in this work, Formulation of the shell model, equivalent to the two-dimensional Cosserat continuum, is developed from the three-dimensional continuum by employing standard assumptions on the distribution of the displacement held in the shell body, A model for thin shells is obtained by an approximation of terms describing the shell geometry. Finite rotations of the director field are described by a rotation vector formulation. An elasto-plastic constitutive model is developed based on the von Mises yield criterion and isotropic hardening. In this work, attention is restricted to problems where strains remain small allowing for all aspects of material identification and associated computational treatment, developed for small-strain elastoplastic models, to be transferred easily to the present elasto-plastic thin-shell model. A finite element formulation is based on the four-noded isoparametric element. A particular attention is devoted to the consistent linearization of the shell kinematics and elasto-plastic material model, in order to achieve quadratic rate of asymptotic convergence typical for the Newton-Raphson-based solution procedures. To illustrate the main objective of the present approach-namely the simulation of failures of thin elastoplastic shells typically associated with buckling-type instabilities and/or bending-dominated shell problems resulting in formation of plastic hinges-several numerical examples are presented, Numerical results are compared with the available experimental results and representative numerical simulations

Effects of scars on crystalline shell stability under external pressure

We study how the stability of spherical crystalline shells under external pressure is influenced by the defect structure. In particular, we compare stability for shells with a minimal set of topologically-required defects to shells with extended defect arrays (grain boundary "scars" with non-vanishing net disclination charge). We perform Monte Carlo simulations to compare how shells with and without scars deform quasi-statically under external hydrostatic pressure. We find that the critical pressure at which shells collapse is lowered for scarred configurations that break icosahedral symmetry and raised for scars that preserve icosahedral symmetry. The particular shapes which arise from breaking of an initial icosahedrally-symmetric shell depend on the F\"oppl-von K\'arm\'an number.Comment: 8 pages, 6 figure