Prediction of stress shielding around an orthopedic screw: Using stress and strain energy density as mechanical stimuli

2013 ◽  
Vol 43 (11) ◽  
pp. 1748-1757 ◽  
Author(s):  
Kristina Haase ◽  
Gholamreza Rouhi
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Stress Shielding ◽  
Stress And Strain ◽  
Mechanical Stimuli

scholarly journals Biomechanical investigation of extragraft bone formation influences on the operated motion segment after anterior cervical spinal discectomy and fusion

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Won Man Park ◽  
Yong Jun Jin
Keyword(s):  
Energy Density ◽  
Bone Formation ◽  
Trabecular Bone ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Rotation Angle ◽  
Von Mises Stress ◽  
Stress And Strain ◽  
Mechanical Stimuli ◽  
Motion Segment

AbstractAlthough the clinical importance of extragraft bone formation (ExGBF) and bridging (ExGBB) has been reported, few studies have investigated the biomechanical influences of ExGBF on the motion segment. In this study, ExGBF was simulated at the C5-C6 motion segment after anterior cervical discectomy and fusion using a developed finite element model and a sequential bone-remodelling algorithm in flexion and extension. The computer simulation results showed that extragraft bone was primarily formed in the extension motion and grew to form ExGBB. A stepwise decrease in the intersegmental rotation angle, maximum von Mises stress and strain energy density on the trabecular bone with ExGBF were predicted in extension. When ExGBB was formed in the trabecular bone region, the intersegmental rotation angle slightly decreased with additional bone formation. However, the stress and strain energy density on the trabecular bone region decreased until ExGBB reached the peripheral cortical margin. The results offer a rationale supporting the hypothesis that mechanical stimuli influence ExGBF. ExGBF was helpful in increasing the stability of the motion segment and decreasing the fracture risk of trabecular bones, even in cases in which ExGBB was not formed. ExGBB can be classified as either soft or hard bridging based on a biomechanical point of view.

Mechanical states encoded by stretch-sensitive neurons in feline joint capsule

1996 ◽  
Vol 76 (1) ◽  
pp. 175-187 ◽  
Author(s):  
P. S. Khalsa ◽  
A. H. Hoffman ◽  
P. Grigg
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Neuronal Response ◽  
Neural Response ◽  
Joint Capsule ◽  
Stress And Strain ◽  
Mechanical State ◽  
Simple Correlation ◽  
Strain Components

1. The sensitivity of group II joint afferents innervating cat knee joint capsule to in-plane stretch was studied in vitro. Single afferents were recorded from teased filaments of the posterior articular nerve. The capsule was stretched by applying forces through tabs along the edges of the capsule (3 tabs/edge) with the use of an apparatus that allowed for independent control of each load. The relationships between the neural responses of these afferents and the local continuum mechanical state of the joint capsule have been investigated. By appropriately loading the tissue margins, it was possible to establish states of uniaxial and biaxial tension, including shear. 2. Plane stress was calculated from the loads along the tissue margins. Stress at the location of the mechanoreceptor ending was estimated by interpolation. Strain was calculated from deformations of the capsule measured by tracking markers on its surface. Full characterization of tissue stress and strain made it possible to determine strain energy density and the magnitudes of other coordinate invariant mechanical quantities. 3. Individual afferents (n = 15) exhibited pronounced selectivity to the direction of applied stress and strain. There was no overall preferred orientation across neurons, and simple correlation of individual stress or strain components with the neuronal response revealed no consistent relationship between neuronal response and any single tensor component. However, linear multiple regression of the combined stress and strain components with the neuronal response revealed high correlation (mean R = 0.91), indicating that the measured mechanical states strongly determine the neuronal response. There was a much stronger relationship between neuronal response and stress variables than with strain variables. Simple correlation of the first invariant of the stress tensor with neuronal response had the highest mean correlation of the tensor quantities (R = 0.51). On average, strain energy density was only modestly correlated with the neural response (R = 0.28). 4. These findings indicate that capsule mechanoreceptors are encoding the local continuum mechanical state in the joint capsule. The neural response of these mechanoreceptors is more strongly correlated to local stress than to local strain.

Spectral decomposition of the linear elastic tensor for monoclinic symmetry

1999 ◽  
Vol 55 (4) ◽  
pp. 635-647 ◽  
Author(s):  
Pericles S. Theocaris ◽  
Dimitrios P. Sokolis
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Stress And Strain ◽  
Monoclinic Symmetry ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Elastic Strain Energy Density

The compliance fourth-rank tensor related to crystalline or other anisotropic media belonging to the monoclinic crystal system is spectrally decomposed for the first time, and its characteristic values and idempotent fourth-rank tensors are established. Further, it is proven that the idempotent tensors resolve the stress and strain second-rank tensors into eigentensors, thus giving rise to a decomposition of the total elastic strain-energy density into non-interacting strain-energy parts. Several examples of representative inorganic crystals of the monoclinic system illustrate the results of the theoretical analysis. It is also proven that the essential parameters required for a coordinate-invariant characterization of the elastic properties of a crystal exhibiting monoclinic symmetry are both the six characteristic values of the compliance tensor and seven dimensionless parameters. These material constants, referred to as the eigenangles, are shown to be accountable for the orientation of the stress and strain eigentensors, when represented in a stress coordinate system. Finally, the restrictions dictated by the classical thermodynamical argument on the elements of the compliance tensor, which are necessary and sufficient for the elastic strain-energy density to be positive definite, are investigated for the monoclinic symmetry.

scholarly journals Volume free strain energy density method for applications to blunt V-notches

2020 ◽  
Vol 28 ◽  
pp. 734-742
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

2021 ◽  
Vol 230 ◽  
pp. 111716
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Majid Reza Ayatollahi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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