A novel anisotropic stress‐driven model for bioengineered tissues accounting for remodeling and reorientation based on homeostatic surfaces

PAMM, vol. 22

Abstract

Abstract A co‐rotated formulation of the intermediate configuration is derived in a thermodynamically consistent manner. As a result of this formulation, algorithmic differentiation (AD) and the equations of the material model can be combined directly, i.e., the equations can be implemented into the AD tool and the corresponding derivatives can be calculated using AD. This is not possible when the equations are given in terms of the intermediate configuration, since the multiplicative decomposition suffers from an inherent rotational non‐uniqueness. Moreover, a novel stress‐driven kinematic growth model is presented that takes homeostasis and fiber reorientation into account and is based on the co‐rotated formulation. A numerical example reveals the promising potential of both the co‐rotated formulation and the stress‐driven growth model.

Authors 5

1. Hagen Holthusen corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Email: [email protected]

   Fax: +49 241 80 22001

   Hagen Holthusen

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

   Telephone: +49 241 80 25016

2. Christiane Rothkranz Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

3. Lukas Lamm Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

4. Tim Brepols Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

5. Stefanie Reese Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany