The method of virtual power in continuum mechanics application to media presenting singular surfaces and interfaces
The method of virtual power in continuum mechanics application to media presenting singular surfaces and interfaces
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连续介质力学中的虚拟力方法应用于呈现奇异表面和界面的介质
DOI：
10.1007/bf01176354
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发表时间：
1986
期刊：
影响因子：
2.7
通讯作者：
G. Maugin
中科院分区：
文献类型：
--
作者：
N. Daher;G. Maugin
本文发展了简单材料（或第一梯度理论）有限速度场的虚幂原理，当物体被一个奇异表面扫过时，该表面可以是自由奇异表面（如连续介质力学中常见的强不连续面），也可以是热力学奇异表面（所谓的相间界面）。在典型情况下给出的公式首先表明如何系统地构造存在于不连续处的新的“内部”接触力，以及奇异表面上的质量传递和附着在其上的粒子的加速度所产生的新的惯性贡献.然后，它被示出了各种虚拟速度场如何产生所有的动力场方程以及横截性条件时的描述外部力量允许他们。这里的虚功率原理是这样表述的，当它与整体形式的热力学第一原理结合起来时，对于真实的速度场，它直接产生所谓的能量定理，无论是在体还是在奇异表面。在引入热力学第二原理的基础上，推导出了相应的熵产生率。虽然没有人声称在这里获得本质上新的方程，但虚功率原理的本公式为通过其他途径难以处理的有用的复杂扩展铺平了道路（例如，电磁连续体与诸如压电半导体的“结”）。
SummaryThe work develops the principle of virtual power for finite velocity fields for so-called simple materials (or first-gradient theory) without further constitutive assumptions when the body is swept out by a singular surface which is either afree singular surface (such as usual strong discontinuities of continuum mechanics) or athermodynamical singular surface (a so-called interface between phases). The formulation given on exemplary cases first shows how to systematically construct the new “internal” contact forces which exist at the discontinuity, as well as the new inertial contributions which arise from mass transfer across the singular surface and the acceleration of particles attached to it. Then it is shown how various virtual velocity fields generate all the dynamical field equations as well as transversality conditions when the description of external forces allows for them. The principle of virtual power here is so formulated that, when combined, forreal velocity fields, with the first principle of thermodynamics in global form, it yields directly the socalled energy theorem both in the bulk and at the singular surface. Then the corresponding rates of entropy production are deduced after introduction of the second principle of thermodynamics. While one does not claim to obtain here essentially new equations, the present formulation of the principle of virtual power paves the way for useful complex extensions which are difficult to deal with through other avenues (e.g., electromagnetic continua with “junctions” such as piezoelectric semiconductors).