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Originalpublikation
Bittens, M.; Nackenhorst, U.: A fully implicit and thermodynamically consistent finite element framework for bone remodeling simulations. In: Computational Mechanics 71 (2023), Nr. 5, S. 853-866. DOI: https://doi.org/10.1007/s00466-022-02263-x
This work addresses the thermodynamically consistent formulation of bone remodeling as a fully implicit finite element material model. To this end, bone remodeling is described in the framework of thermodynamics for open systems resulting in a thermodynamically consistent constitutive law. In close analogy to elastoplastic material modeling, the constitutive equations are implicitly integrated in time and incorporated into a finite element weak form. A consistent linearization scheme is provided for the subsequent incremental non-linear boundary value problem, resulting in a computationally efficient description of bone remodeling. The presented model is suitable for implementation in any standard finite element framework with quadratic or higher-order element types. Two numerical examples in three dimensions are shown as proof of the efficiency of the proposed method.