Analysis of a dilatation in a non-linearly elastic sphere

• Main Author: Zhang, Qingxian
• Other Authors: Wu Mao See
• Format: Final Year Project
• Language: English
• Published: 2009
• Subjects: DRNTU::Engineering::Materials::Biomaterials; DRNTU::Engineering::Materials::Mechanical strength of materials
• Online Access: http://hdl.handle.net/10356/16185
• Institution: Nanyang Technological University

A 2nd order non-linear elastic material has been successfully modeled as a 2-layered spherical shell bonded to a rigid core. Based on this model, the mechanical state described by 5 elastic parameters, λ, μ, l, m, and n is investigated. These parameters can be numerically manipulated to give desired properties for various functions. An application requiring minimal swelling of the bio-gel can be optimised by making the l and n values positive, while decreasing µ, l, m and n. On the other hand, an application requiring maximum swelling can be optimised by increasing λ and µ, while decreasing l and m. A spherical gel with no core has been found to be radially and tangentially stress free in both its linear and non-linear capacities. Its displacement, independent of the elastic parameters, is a function of only the thermal properties and radial position. This is compared to the case of a spherical shell bonded to a rigid core, which has non-zero stresses. This implies that the presence of a rigid core act as a constraint to the material.