Related papers: Special Cosserat rods with rate-dependent evolving…
In a previous paper, field theory in curved space was considered, and a formula that expresses the first order variation of correlation functions with respect to the external metric was postulated. The formula is given as an integral of the…
We propose two parameter-robust mixed finite element methods for linear Cosserat elasticity. The Cosserat coupling constant $\mu_c$, connecting the displacement $u$ and rotation vector $\omega$, leads to possible locking phenomena in finite…
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time-reversibility over the phase space is equivalent to the…
We continue our investigation of finite deformation linear viscoelastodynamics by focusing on constructing accurate and reliable numerical schemes. The concrete thermomechanical foundation developed in the previous study paves the way for…
We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the…
We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a…
This paper introduces a Cosserat rod based mathematical model for modeling a self-controllable variable curvature soft continuum robot. This soft continuum robot has a hollow inner channel and was developed with the ability to perform…
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…
We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P,…
We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium problem as a minimization problem. Applying the direct methods of the calculus of variations we show the existence of…
This article answers the question of whether homogenization of discrete fine-scale mechanical models, such as particle or lattice models, gives rise to an equivalent continuum that is of Cauchy-type or Cosserat-type. The study employs the…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
We generalize Tadmor's algebraic numerical flux condition for entropy-conservative discretizations of conservation laws to a broader class of secondary structures, i.e. possibly non-convex secondary quantities whose evolution can consist of…
By making use of the chiral kinetic theory in the relaxation-time approximation, we derive an Israel-Stewart type formulation of the hydrodynamic equations for a chiral relativistic plasma made of neutral particles (e.g., neutrinos). The…
This paper studies the dissipative structure of the system of equations that describes the motion of a compressible, isothermal, viscous-capillar fluid of Korteweg type in one space dimension. It is shown that the system satisfies the…
A toy-model is used for describing the steps achieving the no-reversible-direction axiom in a tutorial manner: i) choice of a state space results in the balance equations on state space which are linear in the process directions, ii) a…
The characteristic ``in-plane" bending associated with soft robots' deformation make them preferred over rigid robots in sophisticated manipulation and movement tasks. Executing such motion strategies to precision in soft deformable robots…
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes…
We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group…