Related papers: Unbiased higher-order frictional contact using mid…
In this work, we design and analyze a Discrete de Rham (DDR) scheme for a contact mechanics problem involving fractures along which a model of Tresca friction is considered. Our approach is based on a mixed formulation involving a…
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…
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…
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
The friction force observed at macroscale is the result of interactions at various lower length scales that are difficult to model in a combined manner. For this reason, simplified approaches are required, depending on the specific aspect…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
In this paper, a direct finite element method is proposed for solving interface problems on unfitted meshes. This new method treats the two interface conditions as an $H^{\frac12}(\Gamma)\times H^{-\frac12}(\Gamma)$ pair for the mutual…
Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code…
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange…
In this two part series, we present a contact model able to capture the response of interacting adhesive elastic-perfectly plastic particles under a variety of loadings. In Part I, we focus on elastic through fully-plastic contact with and…
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable…
Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…
Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A…
The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
Force modulation of robotic manipulators has been extensively studied for several decades. However, it is not yet commonly used in safety-critical applications due to a lack of accurate interaction contact modeling and weak performance…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…