Related papers: Moving frames applied to shell elasticity
Measurements of the time of arrival of shock waves from explosions can serve as powerful markers of the evolution of the shock front for determining crucial parameters driving the blast. Using standard theoretical tools and a simple ansatz…
The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. It allows to control contribution from each scale of underlying…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essentially these models are tranport equations, coupled with the…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal…
Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
Elastic models of the glass transition relate the relaxation dynamics and the elastic properties of structural glasses. They are based on the assumption that the relaxation dynamics occurs through activated events in the energy landscape…
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…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
The formation and evolution of nonlinear and turbulent dynamical structures in two-dimensional complex plasmas and fluids is explored by means of generalised (drift) fluid simulations. Recent numerical results on turbulence in dusty…
The uniaxial elastic-plastic deformation process is considered. Mathematical model of this process was built. According to this model all stable static states form the lattice, which is called the delta-lattice.
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
The conformations and dynamics of semiflexible filaments subject to a homogeneous external (gravitational) field, e.g., in a centrifuge, are studied numerically and analytically. The competition between hydrodynamic drag and bending…
Soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric, from polymers to space tethers. We present a practical numerical approach to simulate…
The systematic errors due to the practical implementation of the Contact Dynamics method for simulation of dense granular media are examined. It is shown that, using the usual iterative solver to simulate a chain of rigid particles,…
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…