An anisotropic elastic-viscoplastic damage model for bone tissue

Schwiedrzik, J. J.; Zysset, P. K. (2013). An anisotropic elastic-viscoplastic damage model for bone tissue. Biomechanics and Modeling in Mechanobiology, 12(2), pp. 201-213. Springer-Verlag 10.1007/s10237-012-0392-9

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A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Item Type:

Journal Article (Original Article)


04 Faculty of Medicine > Pre-clinic Human Medicine > Institute for Surgical Technology & Biomechanics ISTB [discontinued]

Graduate School:

Graduate School for Cellular and Biomedical Sciences (GCB)

UniBE Contributor:

Schwiedrzik, Johann Jakob, Zysset, Philippe


500 Science > 570 Life sciences; biology
600 Technology > 610 Medicine & health
600 Technology > 620 Engineering








Johann Jakob Schwiedrzik

Date Deposited:

21 Apr 2014 08:39

Last Modified:

05 Dec 2022 14:28

Publisher DOI:


PubMed ID:





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