Related papers: Training nonlinear elastic functions: nonmonotonic…
We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
This paper investigates the effects of geometric nonlinearity and structural flexibility on the flight dynamics of high-aspect-ratio wings representative of high-altitude long endurance aircraft configurations. A coupled aeroelastic flight…
We study the deformations of elastic filaments confined within slowly-shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of…
The classical flexure problem of non-linear incompressible elasticity is revisited for elastic materials whose mechanical response is different in tension and compression---the so-called bimodular materials. The flexure problem is chosen to…
We learn parameterized nonlinear elasticity on curved surfaces using a physics-informed neural network that enforces governing equations and boundary conditions directly through the loss function, enabling a single trained model to…
Trainable activation functions, whose parameters are optimized alongside network weights, offer increased expressivity compared to fixed activation functions. Specifically, trainable activation functions defined as ratios of polynomials…
The classical flexure problem of non-linear incompressible elasticity is revisited assuming that the bending angle suffered by the block is specified instead of the usual applied moment. The general moment-bending angle relationship is then…
Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or non-uniform (non-affine) under…
In theory and practice of elastic straight rods, the statically indeterminate reactions acted by perfect constraints are commonly believed not to depend on the flexural stiffness $EJ$. We solve exactly two elastica problems in order to…
This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy…
Filamentous bio-materials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses…
Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic…
Crumpled paper or drapery patterns are everyday examples of how elastic sheets can respond to external forcing. In this Letter, we study experimentally a novel sort of forcing. We consider a circular flexible plate clamped at its center and…
A nonlinear frequency response based adaptive vibration controller is proposed for a class of nonlinear mechanical systems. In order to obtain the nonlinear Frequency Response Function (FRF), the convergence properties of the system are…
We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition…
In this paper, first, it is shown that if a nonlinear time-varying system is contractive, then it is incrementally exponentially stable. Second, leveraging this result, under mild restrictions, an approach is proposed to design feedforward…
Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and…
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…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes,…