相关论文: Shells without drilling rotations: a representatio…
We present an existence theorem for a large class of nonlinearly elastic shells with low regularity in the framework of a two-dimensional theory involving the mean and Gaussian curvatures. We restrict our discussion to hyperelastic…
A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot strains, truncated at quadratic order. The primary motivation is the desire for a clean separation between stretching and bending energies for…
In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wavenumber shells in incompressible fluid turbulence. The computation has been done using first-order perturbative…
We study the effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed…
We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using the variational asymptotical method. Biological materials may exhibit remarkable compressibility when under…
In Euclidean space we study surfaces with constant anisotropic mean curvature $\Lambda$ of the Dirichlet energy $\int_\Omega( |Du|^2+\Lambda u)$. We prove the existence of non-rotational surfaces with $\Lambda=0$ and foliated by a…
Accurate description of deformed atomic nuclei by the orbital-free density functional theory has been a longstanding textbook challenge, due to the difficulty in accounting for the intricate quantum shell effects that are present in such…
We prove smoothness of $W^{2,2}$ isometric immersions of surfaces endowed with a smooth Riemannian metric of positive Gauss curvature. We then derive the $\Gamma$-limit of three dimensional nonlinear shells with inhomogeneous energy…
We study the $\Gamma$-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.
We construct the theory of dissipative hydrodynamics of uncharged fluids living on embedded space-time surfaces to first order in a derivative expansion in the case of codimension-1 surfaces (including fluid membranes) and the theory of…
This paper is concerned with an asymptotic analysis of the dispersion relation for wave propagation in an elastic layer of uniform thickness. The layer is subject to an underlying simple shear deformation accompanied by an arbitrary uniform…
In this paper, 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 in exam, so that the mathematical formulation…
Though highly impacting our lives, rotating turbulent flows are not well understood. These anisotropic three-dimensional disordered flows are governed by different nonlinear processes, each of which can be dominant in a different range of…
How much energy does it take to stamp a thin elastic shell flat? Motivated by recent experiments on the wrinkling patterns of floating shells, we develop a rigorous method via $\Gamma$-convergence for answering this question to leading…
We examine long-time properties of the ideal dynamics of three--dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases the results agree with…
We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells.…
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a…
Soft materials exhibit significant nonlinear geometric deformations and stress-strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau's and Murnaghan's formulations, advancing…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…