The simulation of growth processes within soft biological tissues is of utmost importance for many applications in the medical sector. Within this contribution we propose a new macroscopic approach fro modelling stress-driven volumetric growth occurring in soft tissues. Instead of using the standard approach of a-priori defining the structure of the growth tensor, we postulate the existance of a general growth potential. Such a potential describes all eligable homeostatic stress states that can ultimately be reached as a result of the growth process. Making use of well established methods from visco-plasticity, the evolution of the growth related right Cauchy-Green tensor is subsequently defined as a time dependent associative evolution law with respect to the introduced potential. This approach naturally leads to a formulation that is able to cover both, isotropic and anisotropic growth related changes in geometry. It furthermore allows the model to flexibly adapt to changing boundary and loading conditions. Besides the theoretical development, we also describe the algorithmic implementation and furthermore compare the newly derived model with a standard formulation of isotropic growth.

翻译：软生物组织内生长过程的模拟对于医疗部门的许多应用至关重要。在这一贡献中,我们提议采用一种新的宏观方法,模拟软组织内产生的压力驱动的体积增长。我们不使用标准方法,优先界定增长结构的振幅,而是假定存在总体增长潜力。这种潜力描述了所有可自由的自制压力状态,这些压力状态最终可以因增长过程而达到。利用成熟的透视性方法,与增长有关的Caoci-Green Excor的演进后来被定义为一种与引入的潜力有关的、取决于时间的联动演进法。这种方法自然导致一种配方,能够涵盖与几何学有关的增长结构、异性增长和异性增长变化。此外,它使模型能够灵活地适应变化的边界和负荷条件。除了理论发展外,我们还描述了算法的实施,并进一步将新衍生的模型与标准的异位增长的配方加以比较。