Anisotropic elastic behaviour using the four-dimensional formalism of differential geometry
Anisotropic elastic behaviour using the four-dimensional formalism of differential geometry
复制标题
使用微分几何的四维形式的各向异性弹性行为
DOI：
10.1016/j.commatsci.2014.03.016
复制
发表时间：
2014
影响因子：
3.3
通讯作者：
O. Ameline
中科院分区：
文献类型：
--
作者：
M. Wang;E. Rouhaud;A. Roos;B. Panicaud;R. Kerner;O. Ameline
本文讨论了连续介质力学中的协变性和物质客观性。其目的是将本构关系的数学框架扩展到广义相对论的四维（4D）形式。首先，证明了可以获得4D一般线性或非线性、各向同性或各向异性关系，无论参考系如何，例如惯性、用刚体运动和对流或一般曲线动画，并且无论起始点如何，例如热力学势的变化或类应力张量和类应变张量之间的直接耦合等。然后，总是可以对各向异性行为进行建模，而这在某些3D经典方法中并不总是可能的。为了证明这种4D方法，不同的弹性关系，不同的观察者进行了研究分析和数值。
This paper discusses covariance and material objectivity in continuum mechanics. The aim is to extend the mathematical framework of constitutive relations to the four-dimensional (4D) formalism of the General Relativity theory. First, it is demonstrated that 4D general linear or non-linear, isotropic or anisotropic relations can be obtained, no matter the reference frame, such as inertial, animated with a rigid body motion and convective or generally curvilinear, and no matter the starting point, for instance a variation of a thermodynamic potential or a direct coupling between stress-like and strain-like tensors, etc. Second, it is then always possible to model anisotropic behaviour, which is not always possible in some of the 3D classical approaches. In order to demonstrate this 4D approach, different elastic relations for different observers have been investigated analytically and numerically.