Related papers: Data Driven Finite Element Method: Theory and Appl…
We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a…
We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
This paper proposes a data-adaptive factor model (DAFM), a novel framework for extracting common factors that explain the structures of high-dimensional data. DAFM adopts a composite quantile strategy to adaptively capture the full…
Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…
Sintering of printed porcelain filaments can be strongly affected by overhang geometry, thin features, and printing-induced anisotropy. These effects are particularly difficult to simulate because they require accurately capturing the…
One of the enticing features common to most of the two-dimensional electronic systems that are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in…
Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by…
The expansion of programmatically-accessible materials data has cultivated opportunities for data-driven approaches. Highly-automated frameworks like AFLOW not only manage the generation, storage, and dissemination of materials data, but…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
In this paper we present a finite element method (FEM) for two-phase incompressible flows with moving contact lines. We use a sharp interface Navier-Stokes model for the bulk phase fluid dynamics. Surface tension forces, including Marangoni…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
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…
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…
The abundance of observed data in recent years has increased the number of statistical augmentations to complex models across science and engineering. By augmentation we mean coherent statistical methods that incorporate measurements upon…
In this paper, size-dependent dynamic responses of small-size frames are modelled by stress-driven nonlocal elasticity and assessed by a consistent finite-element methodology. Starting from uncoupled axial and bending differential…
We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…