Huang Ruoyu, Ogden Raymond W, Penta Raimondo
Lightweight Manufacturing Centre, University of Strathclyde, Renfrew, PA4 8DJ UK.
School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ UK.
J Elast. 2021;145(1-2):223-241. doi: 10.1007/s10659-021-09834-8. Epub 2021 May 20.
Growth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the "opening-angle" in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.
自然界中的生长与残余应力的发展相关联，并且在所有尺度上通常都是非均匀和各向异性的。生长材料在无载荷构型下的残余应力为生长的非均匀性和各向异性的力学调节提供了直接证据。本研究基于无载荷构型探索了一种应力介导生长模型，该模型将残余应力或相对于无载荷构型的变形梯度视为生长变量。这使得在无需引入虚构的无应力生长构型的情况下分析应力介导生长成为可能。此外，基于所提出理论框架的应用直接涉及到实际实验场景，其中将动脉中的“开口角”作为残余应力的一种度量。然后通过考虑受不可压缩性约束的球对称厚壁壳的生长来提供该理论的初步例证。
