Theses and Dissertations

Issuing Body

Mississippi State University


Bammann, Douglas J.

Committee Member

Horstemeyer, Mark F.

Committee Member

Hammi, Youssef

Committee Member

Lacy, Thomas E.

Date of Degree


Document Type

Dissertation - Open Access


Mechanical Engineering

Degree Name

Doctor of Philosophy


James Worth Bagley College of Engineering


Department of Mechanical Engineering


The objective of this work is to develop an evolution equation for the ductile growth of a spherical void in a highly strain rate and temperature dependent material. The material considered in this work is stainless steel 304L at 982 °C. The material is characterized by a physically-based internal state variable model derived within consistent kinematics and thermodynamics — Evolving Microstructure Model for Inelasticity. Through this formulation, the degradation of the elastic moduli due to damage has been naturally acquired. An elastoviscoplasticity user material subroutine has also been developed and implemented into a commercially available finite element software ABAQUS. The subroutine utilizes a return mapping algorithm, where a purely elastic trial state (elastic predictor) is followed by a plastic corrector phase (return mapping). A conditionally stable fully-implicit scheme, derived from the backward Euler integration method, has been employed to calculate the values of the internal state variables in the elastoviscoplasticity integration routine. A repeating unit cell problem is set up by introducing a spherical void inside a matrix material that simulates a periodic array of voids in a component. Using finite element analysis, a database is generated by recording the responses of the unit cell under various combinations of loading conditions, porosity, and state variables. Functional forms of the void growth equations are constructed by utilizing normalization techniques to collapse all the data into master curves. The evolution equations are converted to a form consistent with the continuum damage variable in the complete thermal-elastic-plastic-damage version of the physically-based internal state variable model.



return mapping algorithm||finite element analysis||finite strain||plasticity||internal state variable||damage||void growth