On the continuum mechanics of growing plant-like structures

Abstract

The contribution at hand focuses on the introduction of a novel approach to model biological growth. The proposed formulations are chosen to represent plant like structures. Therefore, thermomechanically open systems are considered. The balance laws are presented for such systems. Furthermore, the proposed formulations are coupled with an adaptive meshing framework. Therefore, a so-called structural generator is presented and utilized in this work. Since no growth formulations within the framework of continuum mechanics exist so far for plant like systems, a novel set of constitutive equations is shown. The newly described principles are the phototropism and graviotropism. In the numerical examples, it is shown that the proposed formulation yields physically meaningful results. The combination of different growth principles results in plausible interactions of the aforementioned principles. Furthermore, results of numerical simulations are shown, which represent the growth process of plant like biological structures.