Related papers: Nitsche's method method for mixed dimensional anal…
We study a force-based hybrid method that couples atomistic models with nonlinear Cauchy-Born elasticity models. We show that the proposed scheme converges quadratically to the solution of the atomistic model, as the ratio between lattice…
We develop a diffuse solid method that is versatile and accurate for modeling wetting and multiphase flows in highly complex geometries. In this scheme, we harness N + 1-component phase field models to investigate interface shapes and flow…
The simulation of geometrically resolved rigid particles in a fluid relies on coupling algorithms to transfer momentum both ways between the particles and the fluid. In this article, the fluid flow is modeled with a parallel Lattice…
Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled…
We apply the well-established theoretical method developed for geometrical nonlinearities of micro/nano-mechanical clamped beams to circular drums. The calculation is performed under the same hypotheses, the extra difficulty being to…
A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based…
Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non Uniform Rational B-splines) to generate cohesive elements…
This work introduces a scaffolding framework to compactly parametrise solid structures with conforming NURBS elements for isogeometric analysis. A novel formulation introduces a topological, geometrical and parametric subdivision of the…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…
A geometrically nonlinear finite element model is developed for the bending analysis of micropolar Timoshenko beams using the principle of virtual displacements and linear Lagrange interpolation functions. The nonlinearity enters the model…
This paper proposes a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy…
In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
We consider two methods for treating elastic contact problems with the finite element method; the penalty method and Nitsche's method. For the penalty method we discuss how the penalty parameter should be chosen. Both the theoretical…
This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a…
The present article proposes a partitioned Dirichlet-Neumann algorithm, that allows to address unique challenges arising from a novel mixed-dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar-type…
We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…
In this paper, we study the stability of the non symmetric version of the Nitsche's method without penalty for domain decomposition. The Poisson problem is considered as a model problem. The computational domain is divided into two…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…