Related papers: The Elastic Theory of Shells using Geometric Algeb…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
In this work, we systematically treat the ambiguities that generically arise in the gradient expansion of any hydrodynamic theory. While these ambiguities do not affect the physical content of the equations, they induce two types of…
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…
The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe, including the accelerated expansion. The analogy is manifested…
We study the $\Gamma$-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.
We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled…
We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with…
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…
We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…
Accurate finite element analysis of refined shell theories is crucial but often hindered by membrane and shear locking effects. While various element-based locking-free techniques exist, this work addresses the problem at the theoretical…
We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory…
The elastohydrodynamics of slender bodies in a viscous fluid have long been the source of theoretical investigation, being pertinent to the microscale world of ciliates and flagellates as well as to biological and engineered active matter…
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…
Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic…
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
Three general modes are distinguished in the deformation of a thin shell; these are stretching, drilling, and bending. Of these, the drilling mode is the one more likely to emerge in a soft matter shell (as compared to a hard, structural…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
We present an edge-based framework for the study of geometric elastic network models to model mechanical interactions in physical systems. We use a formulation in the edge space, instead of the usual node-centric approach, to characterise…
This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…