Related papers: Elastica-based strain energy functions for soft bi…
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…
Connecting cell behavior to tissue shape and mechanics is a key challenge in the physics of morphogenesis. Cytoskeletal turnover precludes a fixed reference state, and tensions are actively generated independently of strain; so conventional…
The extensive application of surfactants motivates comprehensive and predictive theoretical studies that improve our understanding of the behaviour of these complex systems. In this study, an expression for the elastic free-energy density…
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…
The yielding of foams, concentrated emulsions, pastes and other soft materials under applied strain is often characterized by measuring the complex shear modulus as a function of strain amplitude at low frequency. Results obtained for…
Ab initio density functional theory has been used to analyze flexural modes, elastic constants, and atomic corrugations on single and bi-layer graphene. Frequencies of flexural modes are sensitive to compressive stress; its variation under…
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation…
We develop an instanton technique for calculations of correlation functions characterizing statistical behavior of the elastic string in disordered media and apply the proposed approach to correlations of string free energies corresponding…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
We study the elasticity of fibrous materials composed of generalized stiff polymers. It is shown that in contrast to cellular foam-like structures affine strain fields are generically unstable. Instead, a subtle interplay between the…
Disordered networks of fragile elastic elements have been proposed as a model for inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221]. In numerical studies, weakening of such networks is seen to be accompanied by…
We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy…
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…
The capillary forces exerted by liquid drops and bubbles on a soft solid are directly measured using molecular dynamics simulations. The force on the solid by the liquid near the contact line is not oriented along the liquid vapor interface…
The deep energy method (DEM) has been used to solve the elastic deformation of structures with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on the principle of minimum potential energy. In this…
The discovery of configurational forces acting on elastic structures and its initial applications are reviewed. Configurational forces are related to the possibility that an elastic structure can change its configuration, thus inducing a…
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 investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition…
This paper proposes that elastic potentials, which may be rigorously formulated using the negative Gibbs free energy or the complementary strain energy density, should be used as the basis for the plastic part of elasto-plastic constitutive…
Kinetic energy functionals of the electronic density are used to model large systems in the context of density functional theory, without the need to obtain electronic wavefunctions. We discuss the problems associated with the application…