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Constitutive and closure models play important roles in computational mechanics and computational physics in general. Classical constitutive models for solid and fluid materials are typically local, algebraic equations or flow rules…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
Self-positioned nanomembranes such as rolled-up tubes and wrinkled thin films have been potential systems for a variety of applications and basic studies on elastic properties of nanometer-thick systems. Although there is a clear driving…
We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…
We present a novel formulation for the dynamics of geometrically exact Timoshenko beams and beam structures made of viscoelastic material featuring complex, arbitrarily curved initial geometries. An $\textrm{SO}(3)$-consistent and…
Cohesive zone models provide an illuminating and tractable way to include constitutive nonlinearity into continuum models of defects. Powerful insights have been gained by studying both dislocations and cracks using such analyses. Recent…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
The polymer dynamics of homogeneous C$_{60}$-polystyrene mixtures in the molten state are studied via molecular simulations using two interconnected levels of representation for polystyrene nanocomposites: (a) A coarse-grained…
Thermal greases, often used as thermal interface materials, are complex paste-like mixtures composed of a base polymer in which dense metallic (or ceramic) filler particles are dispersed to improve the heat transfer properties of the…
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results.…
We present neural network-based constitutive models for hyperelastic geometrically exact beams. The proposed models are physics-augmented, i.e., formulated to fulfill important mechanical conditions by construction, which improves accuracy…
In this paper, we investigate the rapid stabilization of N-layer Timoshenko composite beams with anti-damping and anti-stiffness at the uncontrolled boundaries. The problem of stabilization for a two-layer composite beam has been previously…
In their papers, Lu et al. analysed experimental data from in-situ transmission electron microscopy (TEM) and concluded that local stress concentration at grain boundary-twin boundary (GB-TB) intersections in nanotwinned (nt-) metals…
In this paper, the bending behaviour of small-scale Bernoulli-Euler beams is investigated by Eringen's two-phase local/nonlocal theory of elasticity. Bending moments are expressed in terms of elastic curvatures by a convex combination of…
We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…
We explore the dynamics of a nanoscale doubly-clamped beam that is under high tension, immersed in a viscous fluid, and driven externally by a spatially varying drive force. We develop a theoretical description that is valid for all…
We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly precise…