Realizing the Willis equations with pre-stresses
Realizing the Willis equations with pre-stresses
复制标题
DOI：
10.1016/j.jmps.2015.10.010
复制
发表时间：
2014-11
影响因子：
5.3
通讯作者：
Z. Xiang;Ruiwen Yao
中科院分区：
文献类型：
--
作者：
Z. Xiang;Ruiwen Yao
本文证明了非均匀预应力材料的线弹性行为可以用 Willis 方程描述。在这种情况下，与均匀介质的经典线弹性方程相比，威利斯方程中的附加项与预应力梯度有关。这样，材料长度尺度自然就纳入了连续介质力学的框架中。这些发现也与变换弹动力学的结果相吻合，从而满足物质客观性原理和广义不变性原理的要求。
This paper proves that the linear elastic behavior of the material with inhomogeneous pre-stresses can be described by the Willis equations. In this case, the additional terms in the Willis equations, compared with the classical linear elastic equations for homogeneous media, are related to the gradient of pre-stresses. In this way, the material length scale is naturally incorporated in the framework of continuum mechanics. All these findings also coincide with the results of transformation elastodynamics, so that they can meet the requirement of the principle of material objectivity and the principle of general invariance.