An anisotropic stress-driven growth model of living tissue is presented for tissue engineering based on Eulerian deformation tensor and growth potential. The evolution of growth is simply defined by the homeostatic pressure and Cauchy stress caused by the left Cauchy–Green deformation tensor that is an Eulerian deformation measure. For more generality, anisotropy is considered by proposing the concept of growth flow and growth potential that are inspired by the flow rule of plasticity theory. This method is then able to make three-dimensional anisotropic growth modeling. The Eulerian tensor-based characteristic enables easy implementation into finite element method (FEM). The presented model was implemented into an FEM code and validated by a theoretical solution of thick-walled hollow tubes of soft tissue in homeostatic state, and aortic stenting simulation was also performed for biomedical engineering application. The simulation results show good agreement with the references. The effect of the anisotropic function is also discussed with one element tension simulation. Finally, it is shown that the proposed model can capture experimental data of a growing tumor tissue, and a future work is discussed.

中文翻译：

---

基于欧拉变​​形张量和生长势的软组织各向异性应力驱动生长模型

提出了一种基于欧拉变​​形张量和生长潜力的活组织各向异性应力驱动生长模型，用于组织工程。生长的演变简单地由作为欧拉变形量度的左柯西-格林变形张量引起的稳态压力和柯西应力定义。更一般地说，各向异性是通过提出受塑性理论流动规律启发而提出的增长流和增长潜力的概念来考虑的。该方法然后能够进行三维各向异性生长建模。基于欧拉张量的特性可以轻松实现有限元方法 (FEM)。所提出的模型被实施到有限元代码中，并通过稳态软组织厚壁空心管的理论解决方案进行验证，并且还进行了主动脉支架模拟用于生物医学工程应用。仿真结果与参考文献吻合良好。各向异性函数的影响也通过单元张力模拟进行了讨论。最后，表明所提出的模型可以捕获生长肿瘤组织的实验数据，并讨论了未来的工作。