A combined model of multiplicative growth and fiber remodeling in the sense of a reorientation of the collagen fibers is proposed for the simulation of adaptation processes in arterial tissues, where both mechanisms are supposed to be governed by the intensity and the direction of the principal stresses. The generalized formulation of the growth tensor includes up to three perpendicular anisotropy directions, which are defined based on the local principal stress state. Remodeling is incorporated in a straightforward manner by formulating a scalar evolution equation for the angle between the existing and the target fiber orientation vectors. In numerical examples on idealized arterial segments, the fiber remodeling algorithm is illustrated and a comparison of different approaches for the growth tensor with respect to stresses in the loaded state, fiber angles and residual stresses is conducted.

Based on the multiplicative decomposition of the deformation gradient, a local formulation for anisotropic growth in soft biological tissues is formulated by connecting the growth tensor to the main anisotropy directions. In combination with an anisotropic driving force, the model enables an effective stress reduction due to growth-induced residual stresses. A method for the imitation of opening angle experiments in numerically simulated arterial segments, visualizing the deformations related to residual stresses, is presented and illustrated in a numerical example.

With the aim of obtaining a general local formulation for anisotropic growth in soft biological tissues, a model based on the multiplicative decomposition of the growth tensor is formulated. The two parts of the growth tensor are associated with the main anisotropy directions. Together with an anisotropic driving force, the model enables an effective stress reduction by including growth‐induced residual stresses, which is demonstrated in a numerical example of an idealized arterial segment. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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A combined framework for stress-induced growth and fiber reorientation in arterial walls is presented. Assuming that the reduction of stress peaks and gradients in different loading situations is the main purpose of an effective adaptation process, a simplified study of model variants is performed on idealized arterial geometries.