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Theory and implementation of orthotropic materials in growing continua

Most biological tissues show a material behavior which is characterized through a pronounced anisotropy. In particular hard tissues such as bones or soft tissues as muscles are commonly modeled as either transversely isotropic or even orthotropic. In contrast to engineering materials, however, biological tissues possess the ability to adapt, e.g. their density, to the current loading situation. Based on a formulation for growth in isotropic continua, see for instance Kuhl, Menzel & Steinmann [3], and transversely isotropic continua as discussed e.g. in Himpel [2], we attend to a model for the functional adaption of orthotropic biomaterials. The material model has been implemented in a finite element code and is studied by means of a numerical example. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)