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The complicated mesoscopic configurations of composite plate and shell structures requires a huge amount of computational overhead for directly simulating their mechanical problems. In this paper, a unified high-order multi-scale method,…
As a model of composite material, the fiber bundle model has been chosen -where a bundle of fibers is subjected to external load and fibers have distributed thresholds. For different loading conditions, such a system shows few precursors…
Strain localization is an instability phenomenon occurring in deformable solid materials which undergo dissipative deformation mechanisms. Such instability is characterized by the localization of the displacement or velocity fields in a…
An elastic membrane that is forced to reside in a container smaller than its natural size will deform and, upon further volume reduction, eventually crumple. The crumpled state is characterized by the localization of energy in a complex…
Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two `self-equilibrated' states, one natural and the other inside out (or `everted'). Though this is…
Linear complexions are defect phases that form in the presence of dislocations and thus are promising for the direct control of plasticity. In this study, atomistic simulations are used to model the effect of linear complexions on…
Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for…
Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and Dynamical reduction models propose a…
We investigate the buckling and post-buckling properties of a hyperelastic half-space coated by two hyperelastic layers when the composite structure is subjected to a uniaxial compression. In the case of a half-space coated with a {\it…
We investigate localised bulging or necking in an incompressible, hyperelastic cylindrical tube under axial stretching and surface tension. Three cases are considered in which the tube is subjected to different constraints. In case 1 the…
We study a three-dimensional barotropic compressible Navier-Stokes flow interacting with a viscoelastic shell that occupies a portion of the fluid boundary. The analysis is entirely Eulerian and the moving interface is parametrised by a…
Liquid crystal elastomer films that morph into cones are strikingly capable lifters. Thus motivated, we combine theory, numerics, and experiments to reexamine the load-bearing capacity of conical shells. We show that a cone squashed between…
Bolted joints are critical in engineering for maintaining structural integrity and reliability. Accurate prediction of parameters influencing their function and behavior is essential for optimal performance. Traditional methods often fail…
The paper proposes a novel adaptive search space decomposition method and a novel gradient-free optimization-based formulation for the pre- and post-buckling analyses of space truss structures. Space trusses are often employed in structural…
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining dynamical systems machinery…
Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as uniaxially compressed soft-film/stiff-substrate systems. This can be explained by curvature effects. To…
Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field,…
Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure…
Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Here we show that a machine learning model,…
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context of nonlinear entropy-stable discretizations, we argue that…