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We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $\Gamma$-convergence we derive a one-dimensional limit theory and show that…
In this paper we study the homogenization of the Dirichlet problem for the Stokes equations in a perforated domain with multiple microstructures. First, under the assumption that the interface between subdomains is a union of Lipschitz…
Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…
A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a condition number that is bounded independently of the…
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a…
Curved thin sheets are ubiquitously found in nature and manmade structures. Within the framework of classical thin plate theory, the stiffness of thin sheets is independent of its bending state. This assumption, however, goes against…
The k-truss model is one of the most important models in cohesive subgraph analysis. The k-truss decomposition problem is to compute the trussness of each edge in a given graph, and has been extensively studied. However, the conventional…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
In this investigation, a data-driven turbulence closure framework is introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical…
Advances in manufacturing techniques may now realize virtually any imaginable microstructures, paving the way for architected materials with properties beyond those found in nature. This has lead to a quest for closing gaps in…
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling…
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…
Poroelasticity problems play an important role in various engineering, geophysical, and biological applications. Their full discretization results in a large-scale saddle-point system at each time step that is becoming singular for locking…
Due to time-reversal symmetry (TRS), two dimensional topological insulators support counter-propagating helical edge modes. Here we show that, unlike the infinitely sharp edge potential utilized in traditional calculations, an…
The preconditioned iterative solution of large-scale saddle-point systems is of great importance in numerous application areas, many of them involving partial differential equations. Robustness with respect to certain problem parameters is…
Lower bounds for the factors entering the standard notions of shear and torsion stiffness for a linearly elastic rod are established in a new and simple way. The proofs are based on the following criterion to identify the stiffness…
It is well known that the use of a consistent tangent stiffness matrix is critical to obtain quadratic convergence of the global Newton iterations in the finite element simulations of problems involving elasto-plastic deformation of metals,…
We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient…
Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…