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有关，并且通常在所有尺度上都是不均匀和各向异性的。生长材料的卸载配置中的残余应力提供了生长的异质性和各向异性的机械调节的直接证据。本研究探讨了基于卸载配置的应力介导增长模型，该模型将相对于卸载配置的残余应力或变形梯度视为增长变量。这使得分析压力介导的生长成为可能，而无需调用虚构的无压力生长配置的存在。此外，基于所提出的理论框架的应用直接涉及实际实验场景，涉及动脉中的“张角”作为残余应力的量度。然后通过考虑受不可压缩约束的球对称厚壁壳的生长来提供该理论的初步说明。