engleski

On numerical modelling of nonlinear behaviour of cortical bone

Damage accumulation is a critical component of the fracture process in a bone under monotonic, creep and fatigue load conditions. In recent years, it has been accepted that the damage mechanics approach using finite element method is a potential tool to analyse the strength and stiffness of the bone material as well as its adaptation due to microdamage. The presented research is motivated by the experimental data and the constitutive model for viscoelastic-damage response of human cortical bone reported by Parsamian [1]. As shown, the bone behaves as a linear viscoelastic material for stress levels below some threshold value of stress, and it behaves as a viscoelastic damaging material beyond the threshold. The derived model is based on ideas and approaches from Abdel-Tawab and Weitsman [2], developed for the swirl-mat composites. The bone behaviour is modelled by using the theory of viscoelasticity and non-linear effects within the theory of continuum damage mechanics. In the present paper, the computational algorithm for the integration of the Parsamian’ s viscoelastic-damage constitutive model at the material point level is derived. Small strains are assumed where the total strain is decomposed into time-dependent viscoelastic and non-linear damage components. It was assumed that the time-dependent stress and damage influence the viscoelastic strain through the time-dependent effective stress. The derived algorithm is implemented in the finite element code ABAQUS [3] by using a user subroutine CREEP. Additionally, for the implicit integration algorithm the Jacobian matrix is derived and applied thereby. The computational strategy is based on the time hardening integration approach. The accuracy of the computational procedure is tested by comparing the computed results with the real experimental data ([1], [4]). Thereby, creep deformation processes in cortical bone under different loading levels are considered.

cortical bone; viscoelasticity; damage; creep; finite element analysis

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