Related papers: A mortar-type finite element approach for embeddin…
In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite…
A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic…
This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using $C^1$-continuous finite elements constructed from NURBS interpolation. Both displacement-based and…
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
We propose a novel cut finite element method for the numerical solution of the Biot system of poroelasticity. The Biot system couples elastic deformation of a porous solid with viscous fluid flow and commonly arises on domains with complex…
Bio-inspired composites are a great promise for mimicking the extraordinary and highly efficient properties of natural materials. Recent developments in voxel-by-voxel 3D printing have enabled extreme levels of control over the material…
Basket weaving is a traditional craft used to create practical three-dimensional (3D) structures. While the geometry and aesthetics of baskets have received considerable attention, the underlying mechanics and modern engineering potential…
The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These…
Numerical simulations of flow and transport in porous media usually rely on hybrid-dimensional models, i.e., the fracture is considered as objects of a lower dimension compared to the embedding matrix. Such models are usually combined with…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
We present a hybrid Eulerian-Lagrangian method for the direct simulation of three-dimensional, heterogeneous structures made of soft fibers and immersed in incompressible viscous fluids. Fiber-based organization of matter is pervasive in…
We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
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…
An integrated mechanical model for fiber-laden membranes is presented and representative predictions of relevance to cellulose ordering and orientation in the plant cell wall are presented. The model describes nematic liquid crystalline…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
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…