Equilibrium of immersed hyperelastic solids

Equilibria of charged hyperelastic solids

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in Eulerian coordinates. The ensuing electroelastic energy is then of mixed Lagrangian-Eulerian type. We prove that minimizers exist by investigating the continuity properties of the capacitary terms under convergence of the deformations

Equilibrium for multiphase solids with Eulerian interfaces

We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove the existence of energy minimizing equilibrium states and $Γ$-convergence of diffuse-interface approximations to the sharp-interface limit.

Control at a distance of the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid

We consider the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid with Navierslip-with-friction conditions at the solid boundary. The fluid-solid system occupies the whole plane. We provethe small-time exact controllability of the position and velocity of the solid when the control takes the form of adistributed force supported in a compact subset (with nonvoid interior) of the fluid domain, away from the body.The strategy relies on the introduction of a small parameter: we consider fast and strong amplitude controls forwhich the ``Navier-Stokes+rigid body'' sys…

弹性固体中依赖曲率的欧拉界面

Curvature-dependent Eulerian interfaces in elastic solids

本文提出一种两相超弹性材料的锐界面模型，在变形构型中处理相界面以构建完全欧拉界面能，并引入曲率变分几何项惩罚大曲率，通过最小化证明平衡解存在，最后将其应用于含曲率惩罚的欧拉拓扑优化问题。

二维不可压缩理想流体中小物体的运动

On the motion of a small body immersed in a two dimensional incompressible perfect fluid

本文证明了二维不可压缩理想流体中固体的运动，当固体收缩到一个具有固定质量和环量的点时，收敛到涡波系统的一个变形，在这个变形中，位于收缩体所占据的点上的涡被一个类似于无旋理论中的Kutta-Joukowski力的升力加速。

Viscoelastodynamics of swelling porous solids at large strains by an Eulerian approach

A model of saturated hyperelastic porous solids at large strains is formulated and analysed. The material response is assumed to be of a viscoelastic Kelvin-Voigt type and inertial effects are considered, too. The flow of the diffusant is driven by the gradient of the chemical potential and is coupled to the mechanics via the occurrence of swelling and squeezing. Buoyancy effects due to the evolving mass density in a gravity field are covered. Higher-order viscosity is also included, allowing for physically relevant stored energies and local invertibility of the deformation. The whole system i…