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Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…
This paper introduces a three-dimensional (3-D) mathematical and computational framework for the characterization of crack-tip fields in star-shaped cracks within porous elastic solids. A core emphasis of this model is its direct…
An experimental technique is presented to quantify the lateral restraint provided by a geogrid embedded in granular soil at the particle level. Repeated load triaxial tests were done on transparent sand specimens with geosynthetic…
Constitutive tensors are of common use in mechanics of materials. To determine the relevant symmetry class of an experimental tensor is still a tedious problem. For instance, it requires numerical methods in three-dimensional elasticity. We…
We present a quantitative geometric rigidity estimate in dimensions $d=2,3$ generalizing the celebrated result by Friesecke, James, and M\"uller to the setting of variable domains. Loosely speaking, we show that for each $y \in…
Electromagnetic crimping is a high-velocity joining method to join highly conductive workpieces where a pulsed magnetic field is applied without any working medium or mechanical contact to deform the workpiece. This work explores…
We present a new first-order approach to strain-engineering of graphene's electronic structure where no continuous displacement field $\mathbf{u}(x,y)$ is required. The approach is valid for negligible curvature. The theory is directly…
This paper investigates nonlinear bending and buckling behaviours of composite plates characterized by a thickness variation. Layer interfaces are described as functions of inplane coordinates. Top and bottom surfaces of the plate are…
In this paper, we extend the tangential-displacement normal-normal-stress continuous (TDNNS) method from [26] to nonlinear elasticity. By means of the Hu-Washizu principle, the distibutional derivatives of the displacement vector are lifted…
A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the…
The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the `standard model' of condensed matter physics. The model has been remarkably…
A comprehensive 3-D finite element formulation for the coupled thermoelastic system is proposed based on the Total Lagrangian framework to study the thermoelastic damping (TED) in small scale structures. The proposed formulation takes into…
In this paper we define distance expanding random dynamical systems. We develop the appropriate thermodynamic formalism of such systems. We obtain in particular the existence and uniqueness of invariant Gibbs states, the appropriate…
The problem of the detachment of a sufficiently large flat indenter from a plane adhesive viscoelastic strip of thickness "b" is studied. For any given retraction speed, three different detachment regimes are found: (i) for very small "b"…
Structural transitions are invariably affected by lattice distortions. If the body is to remain crack-free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility…
A simple position-dependent body force-based confinement for simulating triaxial tests using the Discrete Element Method is presented. The said method is used to perform triaxial simulations on mono-disperse and segregated assemblies of…
It is often stated that if one is presented with a snapshot of the positions of the molecules of a glass and one of a liquid, one is unable to tell the difference. Here we argue instead that given several such snapshots taken over a…
The role of image charges in nanoporous semiconductor materials is investigated within the framework of the effective mass and envelope function approximations. We show that nanometric air bubbles in these materials can act as…
Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML…
Grain boundaries can block slip-band propagation and generate intense local stress and strain fields that influence subsequent deformation and damage initiation in polycrystalline metals. Conventional geometric criteria, such as Schmid…