Numerical modeling and simulation of shape memory allows using the mesh-free method

• Main Author: Ren, Ji
• Other Authors: School of Mechanical and Production Engineering
• Format: Theses and Dissertations
• Published: 2008
• Subjects: DRNTU::Engineering::Materials::Metallic materials::Alloys
• Online Access: http://hdl.handle.net/10356/6323
• Institution: Nanyang Technological University

This thesis represents the first instance in which the capability of mesh-free methods for the modeling of shape memory alloys (SMAs) is explored. Being a relatively recent computational tool, mesh-free source codes are not easily available compared with the easy access to various finite element source codes. Consequently, many efforts in this thesis have been dedicated to the development of mesh-free methods. The emphasis here is on the moving least squares approximation (MLS), and detailed derivation of MLS approximation is described, whereby an efficient approach for obtaining the MLS shape functions and their derivatives is introduced. The determination of the domain of influence (DOI) of a node and the choice of weight functions are examined and discussed. For discrete consistency, which is not easily satisfied in smooth particle hydrodynamics (SPH), an alternative derivation of the MLS shape functions is introduced by applying the consistency condition directly.