Related papers: Elastica catastrophe machine: theory, design and e…
Faults are complex systems embedded in an evolving medium fractured by seismic ruptures. This off-fault damage zone is shown to be thermo-hydro-mechano-chemically coupled to the main fault plane by a growing number of studies. Yet,…
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
Understanding the fracture mechanics of soft solids remains a fundamental challenge due to their complex, nonlinear responses under large deformations. While multiaxial loading is key to probing their mechanical behavior, the role of such…
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…
The review is devoted to the theory of collective and it local pinning effects in various disordered non-linear driven systems. Although the emphasis is put on charge and spin density waves and magnetic domain walls, the theory has also…
We introduce a new class of (dynamical) systems that inherently capture cascading effects (viewed as consequential effects) and are naturally amenable to combinations. We develop an axiomatic general theory around those systems, and guide…
A key feature of mechanical structures ranging from crumple zones in cars to padding in packaging is their ability to provide protection by absorbing mechanical energy. Designing structures to efficiently meet these needs has profound…
Elasto-plastic models are among the most successful ways to study the critical properties of the plastic yielding transition of amorphous solids. Typically these models are studied under a condition of constant transition rates from one…
Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…
This paper presents a theoretical study on the influence of a discrete element in the nonlinear dynamics of a continuous mechanical system subject to randomness in the model parameters. This system is composed by an elastic bar, attached to…
Perturbing the external control parameters of nonlinear systems leads to dramatic changes of its bifurcations. A branch of singular theory, the catastrophe theory, analyses the generating function that depends on state and control…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
This contribution investigates the extension of the microplane formulation to the description of transversely isotropic materials such as shale rock, foams, unidirectional composites, and ceramics. Two possible approaches are considered: 1)…
We investigate the morphology and mechanics of a naturally curved elastic arch loaded at its center and frictionally supported at both ends on a flat, rigid substrate. Through systematic numerical simulations, we classify the observed…
Friction plays a fundamental role in many natural processes, including earthquakes, landslides, and volcanic eruptions. Earthquakes occur when highly compressed fault surfaces accumulate large enough shear stresses, causing the faults to…
We initiate the development of a theory of the elasticity of nanoscale objects based upon new physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in…
Despite the apparent ease with which a sheet of paper is crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This complexity arises from the infinite number of configurations a disordered crumpled…
We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of…