Related papers: Linearization of finite elasticity with surface te…
This work is concerned with an asymptotic analysis, in the sense of $\Gamma$-convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity. The study is performed as the damaged zone concentrates…
Disordered networks of fragile elastic elements have been proposed as a model of inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221, http://xyz.lanl.gov]. It is shown that the ratio $\Gamma$ of responses of such a…
Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are…
In this thesis, we consider the thin-film equation with nonlinear surface tension term in one space dimension. Relying on the corresponding energy and entropy estimates, we prove existence of weak solutions as well as nonnegativity results.
In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate-of-strain, as…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
A unifying framework to describe dense flows of dry, deformable grains is proposed. Perturbative analysis of a granular temperature equation describing flows with contact stresses, supported by the recovery of the nonlocal granular fluidity…
The elastic response is studied of a single flexible chain grafted on a rigid plane and an ensemble of non-interacting tethered chains. It is demonstrated that the entropic theory of rubber elasticity leads to conclusions that disagree with…
We investigate the effective coupling between heat and fluid dynamics within a thin fluid layer in contact with a solid structure via a rough surface. Moreover, the opposing vertical surfaces of the thin layer are in relative motion. This…
We analyze a term penalizing surface self-penetration, as a soft constraint for models of hyperelastic materials to approximate the Ciarlet-Ne\v{c}as condition (almost everywhere global invertibility of deformations). For a linear elastic…
We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…
In this paper we derive the one-dimensional bending-torsion equilibrium model modeling the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a…
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…
The internal motions of biomatter immersed in biofluid are investigated. The interactions between the fragments of biomatter and its surrounding biofluid are modeled using field theory. In the model, the biomatter is coupled to the gauge…
A mathematical model for an elastoplastic continuum subject to large strains is presented. The inelastic response is modeled within the frame of rate-dependent gradient plasticity for nonsimple materials. Heat diffuses through the continuum…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for…
This work is motivated by discrete-to-continuum modeling of the mechanics of a graphene sheet, which is a single-atom thick macromolecule of carbon atoms covalently bonded to form a hexagonal lattice. The strong covalent bonding makes the…
The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6]…
A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elastic stresses satisfy static frame-indifference, while the…