Related papers: A consistent variational formulation of Bishop non…

This paper presents a study on the backstepping control of tendon-driven continuum robots for large deflections using the Cosserat rod model. Continuum robots are known for their flexibility and adaptability, making them suitable for…

Motivated by problems in machine learning, we study a class of variational problems characterized by nonlocal operators. These operators are characterized by power-type weights, which are singular at a portion of the boundary. We identify a…

It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the…

We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of…

In this work, we study the Dirichlet problem associated with a strongly coupled system of nonlocal equations. The system of equations comes from a linearization of a model of peridynamics, a nonlocal model of elasticity. It is a nonlocal…

With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the…

Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…

A well-posed stress-driven mixture is proposed for Timoshenko nano-beams. The model is a convex combination of local and nonlocal phases and circumvents some problems of ill-posedness emerged in strain-driven Eringen-like formulations for…

Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances. This review illustrates different…

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…

The classical continuum models used for the woven fabrics do not fully describe the whole set of phenomena that occur during the testing of those materials. This incompleteness is partially due to the absence of energy terms related to some…

Random packings of stiff rods are self-supporting mechanical structures stabilized by long range interactions induced by contacts. To understand the geometrical and topological complexity of the packings, we first deploy X-ray computerized…

Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle…

We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing the thin infinite elastic rod with material coefficients which periodically highly oscillate…

The design and control of soft robots operating in fluid environments requires a careful understanding of the interplay between large elastic body deformations and hydrodynamic forces. Here we show that this interplay leads to novel…

As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by…

We study three-dimensional deformations of thin inextensible elastic rods with non-vanishing spontaneous curvature and torsion. In addition to the usual description in terms of curvature and torsion which considers only the configuration of…

Beam theory has traditionally been restricted to small elastic strains and rigid cross-sections. Relaxing these assumptions within closed-form analytical frameworks remains challenging. In contrast, the cross-sectional warping problem…

We develop a new method to isolate localized defects from extended vibrational modes in disordered solids. This method augments particle interactions with an artificial potential that acts as a high-pass filter: it preserves small-scale…

Topological growth control allows to produce a narrow distribution of outgrown colloidal rods with defined and adjustable length. We use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of a chosen…