Faculty of Mechanical Engineering , Technion - Israel Institute of Technology , 32000 Haifa , Israel.
Philos Trans A Math Phys Eng Sci. 2019 May 6;377(2144):20180071. doi: 10.1098/rsta.2018.0071.
The purpose of this paper is to review and contrast the Lagrangian and Eulerian formulations of inelasticity as they apply to metal plasticity and growth of biological tissues. In contrast with the Lagrangian formulation of inelasticity, the Eulerian formulation is unaffected by arbitrary choices of the reference configuration, an intermediate configuration, a total deformation measure and an inelastic deformation measure. Although the Eulerian formulation for growth of biological tissues includes a rate of mass supply and can be used to understand the mechanics of growth, it does not yet model essential mechanobiological processes that control growth. Much research is needed before this theory can help design medical treatments for growth related disease. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.
本文旨在综述和对比非弹性力学的拉格朗日和欧拉表述，特别针对金属塑性和生物组织生长。与非弹性力学的拉格朗日表述不同，欧拉表述不受参考构形、中间构形、总变形度量和非弹性变形度量的任意选择的影响。尽管生物组织生长的欧拉表述包括质量供应率，可以用于理解生长的力学，但它尚未模拟控制生长的基本的机械生物学过程。在该理论能够帮助设计与生长相关疾病的医学治疗方法之前，还需要开展大量的研究。本文是主题为“里夫林在连续介质力学和应用数学方面的遗产”的一部分。
