大应变下的粘弹性动力学
Visco-elastodynamics at large strains Eulerian
摘要：
在Kelvin-Voigt流变学中的等温粘弹动力学在空间欧拉坐标中以速度和变形梯度表示。一个一般非凸（也可能是帧无关）存储的能量是允许的。该模型考虑了非线性二阶非简单（多极）粘性，使速度场具有较好的规则性。为了简化分析论证，利用半可压缩材料的概念，假设固体材料的体积变化仅相当小，使得质量密度恒定。利用Galerkin方法结合适当的正则化，利用光滑速度场输运的非平凡结果证明了弱解的存在性.
英文摘要：
Isothermal visco-elastodynamics in the Kelvin-Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted. The model involves a nonlinear 2nd-grade nonsimple (multipolar) viscosity so that the velocity field is well regular. To simplify analytical arguments, volume variations of the solid material are assumed to be only rather small so that the mass density is constant, exploiting the concept of semi-compressible materials. Existence of weak solutions is proved by using the Galerkin method combined with a suitable regularization, using nontrivial results about transport by smooth velocity fields.
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