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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…
Understanding the fracture mechanisms in composite materials across scales, from nano- to micro-scales, is essential for an in-depth understanding of the reinforcement mechanisms and designing the next generation of lightweight,…
Modelling the large deformation of hyperelastic solids under plane stress conditions for arbitrary compressible and nearly incompressible material models is challenging. This is in contrast to the case of full incompressibility where the…
We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…
We propose mixed finite element methods for Cosserat materials that use suitable quadrature rules to eliminate the Cauchy and coupled stress variables locally. The reduced system consists of only the displacement and rotation variables.…
For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu:…
We determine how MRI-turbulent stresses depend on gas pressure via a suite of unstratified shearing box simulations. Earlier numerical work reported only a very weak dependence at best, results that call into question the canonical…
Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis.…
We consider the numerical approximation of acoustic wave propagation problems by mixed BDM(k+1)-P(k) finite elements on unstructured meshes. Optimal convergence of the discrete velocity and super-convergence of the pressure by one order are…
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The…
We use molecular dynamics simulations to study the behavior of a compressible Lennard-Jones fluid in simple shear flow in a two-dimensional nanochannel. The system is equilibrated in the fluid phase close to the triple point at which gas,…
Data-Driven Continuum Mechanics -- the continuous counterpart of Data-Driven Computational Mechanics -- is a modern paradigm that enhances classical continuum mechanics by incorporating finite sets of experimental material data directly,…
In magic angle twisted bilayer graphene, transport, thermodynamic and spectroscopic experiments pinpoint at a competition between distinct low-energy states with and without electronic order. We use Dynamical Mean Field Theory (DMFT) on the…
Upon loading, atomic networks can feature delayed viscoplastic relaxation. However, the effect of composition and structure on such a relaxation remains poorly understood. Herein, relying on accelerated molecular dynamics simulations and…
Deformation in the lithosphere-asthenosphere system can be accommodated by faulting and plastic flow. However, incorporating structural data in models of distributed deformation still represents a challenge. Here, I present solutions for…
Timoshenko's theory for bending vibrations of a beam has been extensively studied since its development nearly one hundred years ago. Unfortunately there are not many analytical results. The results above the critical frequency inclusive…
In this work we investigate the dynamical properties of a mixture of mutually interacting spherical molecules of different masses and sizes. From an analysis of the microscopic laws governing the motion of the molecules we derive a set of…
We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the…
A new family of mixed finite element methods$-$compatible-strain mixed finite element methods (CSFEMs)$-$are introduced for three-dimensional compressible and incompressible nonlinear elasticity. A Hu-Washizu-type functional is extremized…
Ion-beam irradiation of an amorphizable material such as Si or Ge may lead to spontaneous pattern formation, rather than flat surfaces, for irradiation beyond some critical angle against the surface normal. It is observed experimentally…