Related papers: 3D mixed finite elements for curved, flat piezoele…
We explore the possibilities of using energy minimization for the numerical modeling of strain localization in solids as a sharp discontinuity in the displacement field. For this purpose, we consider (regularized) strong discontinuity…
Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
A layer of dielectric elastomer can be voltage actuated to behave as actuators, but needs to avoid the electromechanical instability of excessively thin down accompanied with electric breakdown. We develop a true method to analyze the…
For layered materials, the interlayer stacking is a critical degree of freedom tuning electronic properties, while its microscopic characterization faces great challenges. The transition-metal dichalcogenide 1T-TaS$_2$ represents a novel…
The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic…
We present a framework for the multiscale modeling of finite strain magneto-elasticity based on physics-augmented neural networks (NNs). By using a set of problem specific invariants as input, an energy functional as the output and by…
The ability in experiments to control the relative twist angle between successive layers in two-dimensional (2D) materials offers a new approach to manipulating their electronic properties; we refer to this approach as "twistronics". A…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…
Each element in tensioned structural networks -- such as tensegrity, architectural fabrics, or medical braces/meshes -- requires a specific tension level to achieve and maintain the desired shape, stability, and compliance. These structures…
Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress…
Mesh-based 3D static analysis methods have recently emerged as efficient alternatives to traditional computational numerical solvers, significantly reducing computational costs and runtime for various physics-based analyses. However, these…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…
The wide adoption of thermoplastic composites to reduce weight in structural parts requires reliable numerical methods to account for debonding between overmolded parts. Although cohesive elements are effective for debonding, the need for…
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…
A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses,…
In this paper, we propose a multiphysics finite element method for a quasi-static thermo-poroelasticity model with a nonlinear convective transport term. To design some stable numerical methods and reveal the multi-physical processes of…
We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…