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In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic…
We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic…
A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We study the rheology of dry and wet granular materials in the steady quasistatic regime using the Discrete Element Method (DEM) in a split-bottom ring shear cell with focus on the macroscopic friction. The aim of our study is to understand…
A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass…
In this paper, the performance of different structural models based on global approach in evaluating the static response of curvilinear fibre composite laminates is analyzed. A Co shear flexible Quad-8 element developed based on…
We derive a mixture theory-based mathematical model of the degradation of a poroelastic solid immersed in a fluid bath. The evolution of the solid's mechanical and transport properties are also modeled. The inspiration for the model is the…
The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here, we use a discrete element model (DEM)…
The multi-scale nature of architectured materials raises the need for advanced experimental methods suitable for the identification of their effective properties, especially when their size is finite and they undergo extreme deformations.…
This paper investigates finite-element modeling of a vertically damped free-standing rocking column. The paper first derives the nonlinear equation of motion for the coupled system and then compares the analytical solution with…
Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a…
Accurate finite element analysis of refined shell theories is crucial but often hindered by membrane and shear locking effects. While various element-based locking-free techniques exist, this work addresses the problem at the theoretical…
Continuing the investigation started in a previous work, we consider form factors of integrable quantum field theories in finite volume, extending our investigation to matrix elements with disconnected pieces. Numerical verification of our…
An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box,…
We report experimental measurements of particle dynamics on slowly sheared granular matter in a three-dimensional (3D) Couette cell. A closely-packed ensemble of transparent spherical beads is confined by an external pressure and filled…