Related papers: Intrinsic nonlinear elasticity: An exterior calcul…
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
A theoretical description of the weakly nonlinear and mode-dependent dynamics of a nanoscale beam that is under intrinsic tension is developed. A full analysis of the dynamic range of the beam over a wide range of conditions is presented.…
We consider a Kelvin-Voigt model for viscoelastic second-grade materials, where the elastic and the viscous stress tensor both satisfy frame indifference. Using a rigidity estimate by [Ciarlet-Mardare '15], existence of weak solutions is…
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these…
Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and…
We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
There is described a spacetime formulation of both nonrelativistic and relativistic elasticity. Specific attention is devoted to the causal structure of the theories and the availability of local existence theorems for the initial-value…
Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with…
The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long range correlations, which behave as $\sim 1/r$ in three and $\sim \ln(L/r)$ in two dimensions. We calculate the…
We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global…
We start from a variational model for nematic elastomers that involves two energies: mechanical and nematic. The first one consists of a nonlinear elastic energy which is influenced by the orientation of the molecules of the nematic…
Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their…
We present an overdamped continuum description of oriented active solids in which interactions respect the symmetries of space but do not obey the principle of action and reaction. Taking position and orientation as kinematic variables, we…
The mathematical formulation of constitutive models to describe the path-dependent, i.e., inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased…
Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…
We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework…