Related papers: General theory for plane extensible elastica with …
It is stated in the main in essence new approach to mechanics of the stressed state of the solid body from statistically isotropic material and the homogeneous liquid dynamics. The approach essence is in the detected property of the…
A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energy of an hyperelastic material body subject to an equilibrated force field. We show that the strains of minimizing sequences associated to re-scaled…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a…
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 homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a…
Fundamental solutions for two- and three-dimensional linear isotropic size-dependent couple stress elasticity are derived, based upon the decomposition of displacement fields into dilatational and solenoidal components. While several…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
It is shown that when the well-known minimal complementary energy variational principle in linear elastostatics is written in a different form with the strain tensor as an independent variable and the constitutive relation as one of the…
We present a new one-dimensional model for elastic strips based on a nondevelopable ruled surface. An auxiliary field regularizes the Sadowsky narrow-strip model to allow nonzero twist with vanishing curvature. The energy exhibits the…
Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean…
Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating non-linear elasticity using geometric invariant quantities. Solutions are generally…
The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…
A stiff one-armed swimmer in glycerine goes nowhere, but if its arm is elastic, exerting a restorative torque proportional to local curvature, the swimmer can go on its way. Considering this happy consequence and the principles of…
We derive a continuum-level plasticity model for polycrystalline materials in the high energy density regime, based on a single dislocation density and single mobility mechanism, with an evolution model for the dislocation density. The…
This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…
One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed…
We present a geometrically exact nonlinear analysis of elastic in-plane beams in the context of finite but small strain theory. The formulation utilizes the full beam metric and obtains the complete analytic elastic constitutive model by…
This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically…
Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure…