Estimating non-uniform constitutive law of an elastic rod and validation with simple benchtop experiments

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dc.contributor.advisor Palanthandalam-Madapusi, Harish Mishra, Sandeep kumar 2017-03-30T12:00:57Z 2017-03-30T12:00:57Z 2016
dc.identifier.citation Mishra, Sandeep kumar. (2016). Estimating non-uniform constitutive law of an elastic rod and validation with simple benchtop experiments, pp. 56. (Acc No: T00108) en_US
dc.description.abstract The mechanical behavior of materials at small length scales depend on not only the composition of the material but also the structure and arrangement of the atoms and molecules. In biolfilaments such as DNA, mechanical deformations play a major role in many of the biological process like gene-expression, thus modeling the deformations of filaments will have a direct impact in engineering biofilaments. Two opposing approaches to model these deformations are through Molecular Dynamics Approach or Continuum Approach. In molecular dynamics, ab-initio simulations taking into account the individual forces acting on each atoms and molecules are employed. While in the continuum approach, it is assumed that the filament can be approximated as a continuous material at the length scales of interest. However, for continuum modeling, one needs to extract out a bulk scale constitutive relationship from the atomic composition and arrangements. While this is not a challenge for macro-scale filaments, it can be a significant challenge for sub-micron scale filaments. In [Hinkle et al. (2012)] a methodology for estimating a constitutive law from bending and twisting deformations of a filament made up of a discrete lattice structure was developed. However, the method in [Hinkle et al. (2012)] addresses a case in which the constitutive law is uniform along the length of the filament. In this work, we extend that method to a case in which the constitutive law can be varying over the length of the filament. We further use a lab-scale experimental setup to apply and validate this method. The lab setup consists of an elastic rod that is cantilevered at one end and a follower load is applied at the free end. For the elastic rod, we use different variations of a typical 1-foot steel ruler, wherein one have slots made at half its length to imitate variations in constitutive law along the length. Note that while the Young's Modulus would remain uniform since the material is uniform, he bending stiffness relating internal bending moment and curvature and therefore the constitutive relationship of the rod will vary along the length. When the rod is loaded, a still image of the deformed shape (i.e. the static equilibrium shape) is captured with a camera, and the deformation profile and curvature along the length is extracted through image processing tools applied to this image. Further, these extracted variables are used in a Kirchoff elastic rod model formulation to solve for the internal bending moment and internal forces, and then a function fitting tool is used to fit a constitutive relationship. We consider multiple loading scenarios and by looking at the curvature, internal bending moment and internal force at a single location on the rod, can estimate the constitutive law at each cross section. By employing this approach, we demonstrate how constitutive laws that are varying along the length of the rod or filament can be estimated. en_US
dc.description.statementofresponsibility by Sandeep kumar mishra
dc.format.extent 56 p.; ill.; 30 cm+.
dc.language.iso en_US en_US
dc.publisher Indian Institute of Technology Gandhinagar en_US
dc.title Estimating non-uniform constitutive law of an elastic rod and validation with simple benchtop experiments en_US
dc.type Thesis en_US
dc.contributor.department Mechanical Engineering M.Tech.

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