论文标题
粘弹性固体的热力学，其欧拉制剂和弱溶液的存在
Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions
论文作者
论文摘要
有限菌株的粘弹性变形固体的热力学模型以完全欧拉的方式制定。还涵盖了由于重力场中不断发展的质量密度而引起的热膨胀或浮力的影响。使用具有高阶粘度（利用多极材料的概念）的开尔文 - voigt流变性，从而允许物理相关的框架不相同的存储能量和局部变形的可逆性。该模型符合节能和Clausius-Duhem熵不等式。 FAEDO-GALERKIL半污垢和合适的正则化证明了存在和弱解的某些规律性。模型的细微物理局限性在热膨胀的新霍克材料或具有相变的材料上说明。
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The Kelvin-Voigt rheology with a higher-order viscosity (exploiting the concept of multipolar materials) is used, allowing for physically relevant frame-indifferent stored energies and for local invertibility of deformation. The model complies with energy conservation and Clausius-Duhem entropy inequality. Existence and a certain regularity of weak solutions is proved by a Faedo-Galerkin semi-discretization and a suitable regularization. Subtle physical limitations of the model are illustrated on thermally expanding neo-Hookean materials or materials with phase transitions.
