Abstract
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 for 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 existence of a general growth potential. Such a potential describes all eligible 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.
Highlights
The production and use of artificially grown biological tissue has become an important research topic in the medical context over the last two decades
During the first loading period, the accumulated Cauchy stress zz rises to a value of approximately 300 MPa, which is due to a contraction induced by the volumetric growth process
We developed a novel model for the description of stress-driven volumetric growth
Summary
The production and use of artificially grown biological tissue has become an important research topic in the medical context over the last two decades. This is achieved by using a temporal homogenization of the mass increments alongside with the same multiplicative split as described by Rodriguez et al (1994) This approach overcomes the limitations of the classical constrained mixture theory in terms of computational costs, it still suffers from the need to a-priori define the structure of the growth tensor. Recent versions of this framework, as described e.g. in the work of Braeu et al (2019), were able to modify this approach such that the growth tensor adapts automatically to the given boundary value problem.
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