Simulation of the tensile loading of a cylindrical gel

• Main Author: Mohammad Yasin Abdul Majeed.
• Other Authors: School of Mechanical and Aerospace Engineering
• Format: Final Year Project
• Language: English
• Published: 2013
• Subjects: DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics
• Online Access: http://hdl.handle.net/10356/54108
• Institution: Nanyang Technological University

This project serves to highlight the goal of obtaining the theoretical deformation response of a cylindrical soft gel derived when subjected to a tensile load. This is achieved with the aid of higher-order non-elastic models for simulations. The use of the computational software, Mathematica and Matlab will assist in creating simulations of the gel in order to study the complex material behaviour through characterizing elastic constants: λ, μ, l, m and n. λ and μ are called the 2nd order elastic constants while l, m and n are termed 3rd order elastic constants. λ and μ which are the 2nd order elastic constants have been found to be the Lame’s parameters. μ that represents shear modulus is the measure of rigidity. Through simulation, it is shown that as μ, the rigidity of the specimen increases the overall relative extension in z-direction reduces at a decreasing rate. This can be attributed to the increase in the rigidity of the material. λ which is the first Lame’s parameter, is also shown through simulation to contribute to the drop in relative extension. This is dependent on both rigidity and compressibility. The additional component of compressibility in λ accounts for a more pronounced drop in relative extension compared to that of μ constant as compressibility shares an inverse relationship with λ. Next the relationship between the three 3rd order elastic constants: l, m and n were studied. Prior to that, a physically possible range for the elastic constants were obtained as hydrogels have no evidence of undergoing negative strain and hence a negative Poisson’s ratio. A suitable range set amounted to a positive range set for λ & μ and negative to positive range set for l, m and n. The relationship studies showed that as the values of l,m and n were increased to a very large value, there was noticed to be an inverse relationship with some of the other elastic constants: λ, l, m, n. Both linear and non-linear second order deformation theories were studied in this report but the bulk of the focus fell on the latter. The range of values for the constants: λ and μ for which the linear theory coincided with the non-linear one was observed through graphical analysis of different combination of changes to the other elastic constants. This yielded an extensive range of correspondence for both λ and μ and is shown in the report.