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The paper presents a numerical study for the finite element method with anisotropic meshes. We compare the accuracy of the numerical solutions on quasi-uniform, isotropic, and anisotropic meshes for a test problem which combines several…
Mechanical interactions between rigid rings and flexible cables find broad application in both daily life (hanging clothes) and engineering systems (closing a tether-net). A reduced-order method for the dynamic analysis of sliding rings on…
We propose a generalized finite element method for linear elasticity equations with highly varying and oscillating coefficients. The method is formulated in the framework of localized orthogonal decomposition techniques introduced by…
We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on…
We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…
This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…
Young's classic analysis of the equilibrium of a three-phase contact line ignores the out-of-plane component of the liquid-vapor surface tension. While it has long been appreciated that this unresolved force must be balanced by elastic…
A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength $\lambda$. As the confinement…
We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without…
We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also…
We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on…
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…
An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the…
In this paper, we deal with the inverse problem of the shape reconstruction of inclusions in elastic bodies. The main idea of this reconstruction is based on the monotonicity property of the Neumann-to-Dirichlet operator presented in a…
This paper deals with the mathematical modelling of large strain magneto-viscoelastic deformations. Energy dissipation is assumed to occur both due to the mechanical viscoelastic effects as well as the resistance offered by the material to…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…