Re-interpretation of the Homogenized Constrained Mixture Theory within the plasticity framework and application to soft tissue growth and remodeling

Abstract

The homogenized constrained mixture theory (H-CMT) is an attractive and efficient computational framework to simulate growth and remodeling (G&R) of soft tissues within finite deformations. It considers several prestressed constituents within a mixture and it enables their continuous individual mass removal and production to be taken into account. However, the referred theory was developed for specific mixtures, whose remodeling occurred on unidimensional constituents (fibers) only, while being embedded in an isotropic matrix. As the microstructure of soft tissues is generally more complex, we propose an extension of the H-CMT, which enables remodeling to occur on tridimensional constituents. This was achieved by manipulating the remodeling stress rate equation of the H-CMT. By rearranging the tensorial expression, it was possible to re-interpret its terms as variables of the classical plasticity theory and the resulting equation is a particular case of kinematic hardening. This interpretation, in turn, enables standard return mapping algorithms, which are classical in plasticity, to be quickly adapted to G&R problems. Therefore, not only we explore the intersection of both the H-CMT and the plasticity frameworks, but we also propose new algorithmic implementations of G&R that closely resemble those used in standard elasto-plastic problems. Applications to the simulation of G&R in mixtures composed of anisotropic constituents are eventually shown to demonstrate the capabilities of the new algorithms.