Equilibria of charged hyperelastic solids

Equilibrium of immersed hyperelastic solids

We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we discuss free-floating bodies, anchored solids, and floating vessels. Conditions for the existence of local and global energy minimizers are presented.

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.

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。

流固耦合问题中平衡态的稳定性与分岔

Stability of equilibria and bifurcations for a fluid-solid interaction problem

本文研究无界三维黏性流中受弹性恢复力作用的刚体平衡态，证明当无量纲来流速度低于临界值时存在唯一稳定定常解且无振荡流动，并给出定态分岔发生的充要条件。

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…

利用欧拉增量公式建模大变形的流体饱和多孔介质

Modelling large-deforming fluid-saturated porous media using an Eulerian incremental formulation

本文提出利用欧拉增量公式建模大变形流体饱和多孔介质，通过Biot模型描述扰动，结合有限元方法验证了数值模型的准确性。