Seguin Brian, Hinz Denis F, Fried Eliot
Postdoctoral Fellow Division of Mathematics, University of Dundee , Dundee DD1 4HN, Scotland , UK e-mail:
Graduate Student Department of Mechanical Engineering, McGill University , Montréal, PQ H3A 0C3 , Canada e-mail:
Appl Mech Rev. 2014 Sep;66(5):0508021-5080216. doi: 10.1115/1.4026910. Epub 2014 May 29.
Transport theorems, such as that named after Reynolds, are an important tool in the field of continuum physics. Recently, Seguin and Fried used Harrison's theory of differential chains to establish a transport theorem valid for evolving domains that may become irregular. Evolving irregular domains occur in many different physical settings, such as phase transitions or fracture. Here, emphasizing concepts over technicalities, we present Harrison's theory of differential chains and the results of Seguin and Fried in a way meant to be accessible to researchers in continuum physics. We also show how the transport theorem applies to three concrete examples and approximate the resulting terms numerically. Furthermore, we discuss how the transport theorem might be used to weaken certain basic assumptions underlying the description of continua and the challenges associated with doing so.
诸如以雷诺兹命名的输运定理，是连续介质物理学领域的重要工具。最近，塞金和弗里德运用哈里森的微分链理论，建立了一个适用于可能变得不规则的演化域的输运定理。演化的不规则域出现在许多不同的物理情境中，比如相变或断裂。在此，我们更强调概念而非技术细节，以一种连续介质物理学领域的研究人员能够理解的方式，介绍哈里森的微分链理论以及塞金和弗里德的研究成果。我们还展示了输运定理如何应用于三个具体例子，并对所得项进行数值近似。此外，我们讨论了输运定理如何可能被用于弱化连续体描述背后的某些基本假设以及这样做所带来的挑战。
