Polyconvexity and Existence Theorem for Nonlinearly Elastic Shells
نویسندگان
چکیده
منابع مشابه
Contact between nonlinearly elastic bodies
We study the contact between nonlinearly elastic bodies by variational methods. After the formulation of the mechanical problem we provide existence results based on polyconvexity and on quasiconvexity. Then we derive the Euler-Lagrange equation as a necessary condition for minimizers. Here Clarke’s generalized gradients are the essential tool to treat the nonsmooth obstacle condition.
متن کاملDamage of nonlinearly elastic materials at small strain – Existence and regularity results –
In this paper an existence result for energetic solutions of rate-independent damage processes is established and the temporal regularity of the solution is discussed. We consider a body consisting of a physically nonlinearly elastic material undergoing small deformations and partial damage. The present work is a generalization of [MiR06] concerning the properties of the stored elastic energy d...
متن کاملElastic platonic shells.
On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic s...
متن کاملStraight Configurations of Shearable Nonlinearly Elastic Rods
Investigating obstacle problems for elastic rods we are sometimes confronted with the question to look for a solution which has a prescribed shape along some part of it. In the simplest case the rod is enforced to be straight along some contact area (cf., e.g., Gastaldi & Kinderlehrer [3]). Motivated by such applications we study straight configurations of elastic rods in this paper. More preci...
متن کاملModels for elastic shells with incompatible strains.
The three-dimensional shapes of thin lamina, such as leaves, flowers, feathers, wings, etc., are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Elasticity
سال: 2017
ISSN: 0374-3535,1573-2681
DOI: 10.1007/s10659-017-9664-z