Theses and Dissertations

Issuing Body

Mississippi State University


Horstemeyer, Mark F.

Committee Member

Bammann, Douglas J.

Committee Member

Marin, Estban B.

Committee Member

Steele, W. Glenn

Committee Member

Hammi, Youssef

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


any experiments demonstrate that isotropic ductile materials used in engineering applications develop anisotropic damage and shows significant variation in elongation to failure. This anisotropic damage is manifest by material microstructural heterogeneities and morphological changes during deformation. The variation in elongation to the failure could be attributed to the uncertainties in the material microstructure and loading conditions. To study this deformation induced anisotropy arising from the initial material heterogeneities, we first performed uncertainty analysis using current form on an internal state variable plasticity and isotropic damage model (Bammann, 1984; Horstemeyer, 2001) to quantify the effect due to variations in material microstructure and loading conditions on elongation to failure. We extend the current isotropic damage form of theory into an anisotropic damage form for ductile material in which material heterogeneities are introduced based on damage distribution functions converted into a damage tensor of second rank. The outcome of this research is a physically motivated, uncertainty-based, anisotropic damage constitutive model that links microstructural features to mechanical properties. This was accomplished by pursuing three sub goals: (1) develop and quantify uncertainty related to material heterogeneities, (2) develop a methodology related to a higher order tensorial rank of damage for void nucleation and void growth, and (3) integrate thermodynamically constrained damage with a rate dependent plasticity constitutive material model. Later, we also proposed a new ISV theory that physically and strongly couples deformation due to damage-related internal defects to metal plasticity.



Finite-strain||Elastic-plastic||Thermodynamics||Void Growth||Anisotropic Damage||Material Length Scale||Model Verification and Validation||Internal State Variable||Uncertainty||Kinematics||Void Nucleation