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Research Papers

Constitutive Models for Constrained Compression of Unimpacted and Impacted Human Morselized Bone Grafts

[+] Author and Article Information
Knut B. Lunde

Department of Structural Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway

Olav A. Foss, Lars Fosse

Norwegian Orthopaedic Implant Research Unit, NKSOI, St. Olav University Hospital, 7489 Trondheim, Norway

Bjørn Skallerud1

Department of Structural Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norwaybjorn.skallerud@ntnu.no

1

Corresponding author.

J Biomech Eng 130(6), 061014 (Oct 15, 2008) (8 pages) doi:10.1115/1.2979878 History: Received November 21, 2007; Revised May 18, 2008; Published October 15, 2008

Morselized corticocancellous bone (MCB) is widely used in revision surgery with and without impaction. In the current study material parameters for the nonlinear viscoelastic and plastic responses of impacted and unimpacted human MCBs were determined during constrained compression. These models may be useful in finite element analyses of surgical constructs involving impacted and unimpacted MCBs. MCB is impacted layer by layer in the femoral canal during revision surgery. The influence of different layers on the mechanical properties was therefore also examined by comparing the relaxation strength and elastic and plastic strains for bone pellets impacted in one and two layers during constrained compression of human MCB. The relaxation strength was found to increase significantly by 14% for two layer pellets compared to one layer pellets, and the plastic strains decreased significantly by 15%, while the elastic strains were similar.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Experimental apparatus used

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Figure 2

The stress and strain distribution in the experiment and the notation used

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Figure 3

Loading scheme used. Stresses (solid line) and strains (dotted line) plotted versus time.

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Figure 4

The figure shows how the total (ϵtot), viscous (ϵvisco) and plastic (ϵp) strains are determined as a function of σi at load level i. The elastic strains at the beginning of step i are then calculated as ϵe(σi)=ϵtot(σi)−ϵp(σi)−ϵvisco(σi).

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Figure 5

Yield surface for the Drucker–Prager model

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Figure 6

The determined mean elastic and plastic strains for the three different pellet constructions

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Figure 7

Constrained elastic stiffness at the end of each step for each pellet (left) and σ plotted versus the evolution of the plastic strains (right). The mean values with standard deviations are illustrated by the error bars. (a) Virgin pellets, elasticity, R2>0.999 (b) Virgin pellets, plasticity, R2>0.999 (c) One layer pellets, elasticity, R2>0.98 (d) One layer pellets, plasticity, R2>0.98 (e) Two layer pellets, elasticity, R2>0.98 (f) Two layer pellets, plasticity, R2>0.98

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Figure 8

Comparison of the elastic stiffness and hardening behavior for the three different pellet constructions. The models resulting from the data found by Phillips (29) are also included. (a) Hardening behavior. (b) Elastic stiffness.

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Figure 9

Prony fit for one of the one layer pellets at load step 7, σ=1380kPa, R2>0.998, and C=0.083

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Figure 10

Mean C as a function of σ for the three different pellet constructions. The standard deviations are illustrated by the error bars. For all impacted pellets R2>0.99 for all load steps except the first. For the virgin pellets R2>0.96 for load steps 2–4 and >0.99 for the four last steps, i.e., σ⩾490kPa. The fit was not as good for the first step; here, R2>0.85 for all pellets in all the studies. (a) Virgin pellets (b) One layer pellets (c) Two layer pellets

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