Related papers: Partial constraint singularities in elastic rods
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with…
In the special relativity, a rigid rod slides upon itself, with one extremity oscillating harmonically. We discovered restrictions in the amplitude of the motion and in the length of the rod, essential to eliminate unphysical solutions.…
We present a general energy approach to study the unsteady adhesive contact of viscoelastic materials. Under the assumption of infinitely short-range adhesive interactions, we exploit the principle of virtual work to generalize Griffith…
A popular problem asks for the equilibrium separation between two identical (mutually repelling) charges suspended by strings fastened to a common point. We slightly modify this problem by considering two opposite (mutually attracting)…
We present a phenomenological model for granular suspension rheology in which particle interactions enter as constraints to relative particle motion. By considering constraints that are formed and released by stress respectively, we derive…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…
On the retention problem, we study the case of a functional constraint on the set of disturbances. A construction of resolving quasistrategy based on the method of programmed iterations is proposed.
In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of…
In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of…
This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and…
We solve the stochastic equations for a cluster of parallel bonds with shared constant loading, rebinding and the completely dissociated state as an absorbing boundary. In the small force regime, cluster lifetime grows only logarithmically…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
Features of rheological laws applied to solid-like granular materials are recalled and confronted to microscopic approaches via discrete numerical simulations. We give examples of model systems with very similar equilibrium stress transport…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions…
We study the vibrations of a hanging thin flexible rod, in which the dominant restoring force in most of the domain is tension due to the weight of the rod, while bending elasticity plays a small but non-negligible role. We consider a…
An elastic rod, straight in its undeformed state, has a mass attached at one end and a variable length, due to a constraint at the other end by a frictionless sliding sleeve. The constraint is arranged with the sliding direction parallel to…