Related papers: Rotational elasticity
We consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle…
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…
In this paper we study a coupled system modeling the movement of a deformable solid immersed in a fluid. For the solid we consider a given deformation that has to obey several physical constraints. The motion of the fluid is modeled by the…
A circular elastic disk is coated with an elastic beam, absorbing shear and normal forces without deformation and linearly reacting to a bending moment with a change in curvature. The inexstensibility of the elastic beam introduces an…
In this paper, we investigate well-posedness of time-harmonic scattering of elastic waves by unbounded rigid rough surfaces in three dimensions. The elastic scattering is caused by an $L^2$ function with a compact support in the…
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…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
In this study, the authors employ the analogy between continuum mechanics and general relativity to investigate, from the perspective of elasticity and crystal plasticity, the deformations of space measured by LIGO/VIRGO interferometers…
A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…
One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range…
We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are…
The dynamics of filaments in flow are central to understanding a wide range of biological and soft-matter systems, yet their behavior under time-dependent forcing remains poorly understood. Here, we investigate the long-time dynamics of…
We prove long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the…
Considering the importance of correctly understanding the dynamics of microstructure materials for their applications in related technologies, by eliminating the shortcomings and some overlooked physical concepts in the existing asymmetric…
The linear equations of motion of a uniformly rotating, elastic and self-gravitating earth model are analyzed under minimal regularity assumptions. We present existence and uniqueness results for the system, energy estimates, convergence of…
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec \tau}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system.…
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…
Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical…