Dataset Information

Coiling of elastic rods on rigid substrates.

ABSTRACT: We investigate the deployment of a thin elastic rod onto a rigid substrate and study the resulting coiling patterns. In our approach, we combine precision model experiments, scaling analyses, and computer simulations toward developing predictive understanding of the coiling process. Both cases of deposition onto static and moving substrates are considered. We construct phase diagrams for the possible coiling patterns and characterize them as a function of the geometric and material properties of the rod, as well as the height and relative speeds of deployment. The modes selected and their characteristic length scales are found to arise from a complex interplay between gravitational, bending, and twisting energies of the rod, coupled to the geometric nonlinearities intrinsic to the large deformations. We give particular emphasis to the first sinusoidal mode of instability, which we find to be consistent with a Hopf bifurcation, and analyze the meandering wavelength and amplitude. Throughout, we systematically vary natural curvature of the rod as a control parameter, which has a qualitative and quantitative effect on the pattern formation, above a critical value that we determine. The universality conferred by the prominent role of geometry in the deformation modes of the rod suggests using the gained understanding as design guidelines, in the original applications that motivated the study.

SUBMITTER: Jawed MK

PROVIDER: S-EPMC4205668 | biostudies-literature | 2014 Oct

REPOSITORIES: biostudies-literature

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Publications

Coiling of elastic rods on rigid substrates.

Jawed Mohammad K MK Da Fang F Joo Jungseock J Grinspun Eitan E Reis Pedro M PM

Proceedings of the National Academy of Sciences of the United States of America 20140929 41

We investigate the deployment of a thin elastic rod onto a rigid substrate and study the resulting coiling patterns. In our approach, we combine precision model experiments, scaling analyses, and computer simulations toward developing predictive understanding of the coiling process. Both cases of deposition onto static and moving substrates are considered. We construct phase diagrams for the possible coiling patterns and characterize them as a function of the geometric and material properties of ...[more]

PMID: 25267649

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Project description:The microstructure of trabecular bone is usually perceived as a collection of plate-like and rod-like trabeculae, which can be determined from the emerging high-resolution skeletal imaging modalities such as micro-computed tomography (?CT) or clinical high-resolution peripheral quantitative CT (HR-pQCT) using the individual trabecula segmentation (ITS) technique. It has been shown that the ITS-based plate and rod parameters are highly correlated with elastic modulus and yield strength of human trabecular bone. In the current study, plate-rod (PR) finite element (FE) models were constructed completely based on ITS-identified individual trabecular plates and rods. We hypothesized that PR FE can accurately and efficiently predict elastic modulus and yield strength of human trabecular bone. Human trabecular bone cores from proximal tibia (PT), femoral neck (FN) and greater trochanter (GT) were scanned by ?CT. Specimen-specific ITS-based PR FE models were generated for each ?CT image and corresponding voxel-based FE models were also generated in comparison. Both types of specimen-specific models were subjected to nonlinear FE analysis to predict the apparent elastic modulus and yield strength using the same trabecular bone tissue properties. Then, mechanical tests were performed to experimentally measure the apparent modulus and yield strength. Strong linear correlations for both elastic modulus (r(2) = 0.97) and yield strength (r(2) = 0.96) were found between the PR FE model predictions and experimental measures, suggesting that trabecular plate and rod morphology adequately captures three-dimensional (3D) microarchitecture of human trabecular bone. In addition, the PR FE model predictions in both elastic modulus and yield strength were highly correlated with the voxel-based FE models (r(2) = 0.99, r(2) = 0.98, respectively), resulted from the original 3D images without the PR segmentation. In conclusion, the ITS-based PR models predicted accurately both elastic modulus and yield strength determined experimentally across three distinct anatomic sites. Trabecular plates and rods accurately determine elastic modulus and yield strength of human trabecular bone.

Dataset Information

Coiling of elastic rods on rigid substrates.

Publications

Coiling of elastic rods on rigid substrates.

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