This thesis presents a method to correct for non-positive-definiteness in linear viscoelastic material functions. Viscoelastic material functions for anisotropic materials need to be interconverted in a matrix coefficient prony series form, with a requirement of positive definiteness. Fitting is usually done as a uniaxial prony series, resulting in scalar coefficients. When these uniaxial coefficients are placed in a coefficient matrix, the required positive definiteness cannot be guaranteed. For those matrices that do not meet this requirement, finding the nearest symmetric semi-positive definite form of the matrix results in a viable prony series matrix coefficient with the required positive definiteness. These corrected prony series coefficients allow for material functions to be interconverted with minimal changes to experimental data.
Bachelor Science in Aerospace Engineering (B.S.A.E.)
College of Engineering and Computer Science
Mechanical and Aerospace Engineering
Rehberg, Christopher D., "Ensuring Positive Definiteness in Linear Viscoelastic Material Functions Based on Prony Series" (2020). Honors Undergraduate Theses. 749.