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In this note, we address several issues, including some raised in recent works and commentary, related to bending measures and energies for plates and shells, and certain of their invariance properties. We discuss overlaps and distinctions…
We propose a novel variationally consistent membrane wrinkling model for analyzing the mechanical responses of wrinkled thin membranes. The elastic strain energy density is split into tensile and compressive terms via a spectral…
This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…
Motivated by the analysis of thin structures, we study the variational dimension reduction of hyperelastic energies involving nonlocal gradients to an effective membrane model. When rescaling the thin domain, isotropic interaction ranges…
The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions…
This paper presents a pure complementary energy variational method for solving anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconex partial…
We propose a novel optimization framework for computing the medial axis transform that simultaneously preserves the medial structure and ensures high medial mesh quality. The medial structure, consisting of interconnected sheets, seams, and…
Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be…
Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interations deform vesicle membrane is a fundamental question in biophysics. In this article we developed a fast algorithm to…
We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by…
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…
Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response.…
Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…