Implementation of the Constitutive Equations of the Gurson Material Model in Finite Element Code

• Main Author: Darayi, Mohsen
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2018
• Subjects: Engineering; Mechanical engineering
• ISBN: 9780355972719; 0355972719

Engineering structures inevitably contain microstructural defects such as voids and crack-like flaws due to the process of manufacturing and operation. This physical existence requires the engineers to apprehend the material state concerning damage caused by the manufacturing process. In the analysis of material behavior, the understanding of when the ductile fracture occurs is essential. Ductile fracture is due to gradual change in the material during plastic deformation, and it is characterized by mostly void growth, nucleation and their coalescence that lead to a crack. This study focuses on a well-known micromechanical model for ductile fracture, the Gurson model which can predict void growth. The constitutive framework introduced by Gurson that takes into account the effects of micro-voids on plastic flow is presented, and derivations followed to develop the numerical implementation. The system of equations obtained by the derivations is solved based on a semi-implicit time integration scheme that calculates the consistent tangent matrix, which is a variation of the Newton-Raphson method. A finite element formulation using the principle of virtual work is described in details, and the implementation procedure into a Matlab code is explained. Then, the finite element code that implements the Gurson material model is verified by the built-in Gurson material model in ABAQUS. Finally, a brief comparison between the original Gurson model, the modified Gurson presented by Tvergaard, and the J2 flow theory of plasticity material model is presented.