An anisotropic elastic-viscoplastic damage model for bone tissue

  title={An anisotropic elastic-viscoplastic damage model for bone tissue},
  author={Johann Jakob Schwiedrzik and Philippe K. Zysset},
  journal={Biomechanics and Modeling in Mechanobiology},
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… 
Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone
This computational study enhances the current knowledge on the macroscopic damage behavior of trabecular bone by developing relationships of damage progression with bone's micro-architectural indices and provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.
Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model
This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.
Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone
Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination.
A rate-independent continuum model for bone tissue with interaction of compressive and tensile micro-damage.
  • P. Zysset, U. Wolfram
  • Materials Science, Engineering
    Journal of the mechanical behavior of biomedical materials
  • 2017
Experimental validation of a nonlinear μFE model based on cohesive‐frictional plasticity for trabecular bone
The ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors is demonstrated, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.
An explicit micro‐FE approach to investigate the post‐yield behaviour of trabecular bone under large deformations
The potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses is demonstrated and the proper account of the mesh sensitivity remains challenging for practical computing times.
Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine
The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine and can enable efficient investigation of human bone using finite element analysis (FEA).
Nonlinear micro finite element models based on digital volume correlation measurements predict early microdamage in newly formed bone
The ability of the nonlinear μFE model to capture local microdamage in newly formed bone tissue can be exploited to improve the current understanding of healing bone and mechanical competence and ultimately aid the development of BMPs delivery systems for bone defect treatment.


A three-dimensional elastic plastic damage constitutive law for bone tissue
A 3D constitutive law describing the macroscopic mechanical behaviour of both cortical and trabecular bone in cyclic (not fatigue) overloads is developed and numerical resolutions of several boundary value problems and a biomechanical application are presented to illustrate the potential of the constitutive model and demonstrate the expected quadratic convergence of the algorithm.
A nonlocal constitutive model for trabecular bone softening in compression
A constitutive law is proposed, which captures the compressive behavior of trabecular bone as a porous material with accumulation of irreversible strain and loss of stiffness beyond its yield point and softening beyond its ultimate point.
A constitutive law for trabecular bone
Motivated by applications in orthopaedic surgery, new constitutive laws for trabecular (or spongious) bone are developed in the framework of continuum mechanics, implemented in a mechanical analysis
Constitutive modelling of inelastic behaviour of cortical bone.
Elastic plastic damage laws for cortical bone
Motivated by applications in orthopaedic and maxillo-facial surgery, the mechanical behaviour of cortical bone tissue in cyclic overloads at physiological strain rates is investigated. The emphasis
A damage model for nonlinear tensile behavior of cortical bone.
The results demonstrate that the 2-ISV model combining damage (stiffness loss) with slip and viscous behavior could capture the nonlinear tensile behavior of cortical bone in axial and bending loading.
A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behavior of the tissue.
The numerical model presented in this paper shows that the probe tip-tissue friction and the post-yield deformation modes play a relevant role in this respect; in particular, a small dilatation angle, ruling the volumetric inelastic strain, is required to approach the experimental findings.
Characterization of indentation response and stiffness reduction of bone using a continuum damage model.
Strain- and stress-based continuum damage models—I. Formulation