Mechanical & Materials Engineering, Department of


First Advisor

Mehrdad Negahban

Date of this Version



Zhong Chen, Optimal Grading for Strength and Functionality of Parts Made of Interpenetrating Polymer Networks: Load Capacity Enhancement ,2016


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Engineering, Under the Supervision of Professor Mehrdad Negahban, Lincoln, Nebraska: December, 2016


Uniform parts with stress concentrations or singularities are prone to failure under relatively small loads, which motivates researchers to seek methods to enhance the strength of these parts. This dissertation studies the optimization of material grading to design parts made of functionally graded interpenetrating polymer networks (FG-IPNs) to improve their load capacity.

An acrylate/epoxy IPN with variations of elastic Young’s modulus, Poisson’s ratio, and ultimate stress at failure is used for optimization of a plate with stress concentration. The grading is optimized by attaching the finite element method (FEM) solver to a general purpose bound-constrained optimizer. Two examples, a plate with a hole and a bent bracket, show more than 100% improvement in the part’s load capacity when compared to the uniform IPNs.

Parts with stress singularities are studied using a PMMA/PU IPN system. For this system, we have the elastic modulus and the critical stress intensity factor KIC as a function of the concentration of the components. A material mesh is utilized to control the grading near the crack tip and uniform material is assumed outside the tip area. The displacement correlation technique (DCT) is used to calculate stress intensity factors and the maximum hoop stress criterion is selected as the fracture criterion. Parts with edge cracks, interior cracks and interacting cracks under tension are considered. For the PMMA/PU IPN system, improvements in load capacity in the order of one hundred percent were commonly obtained through grading the region around the crack tip, compared to both optimal uniform plates, and plates with simple toughening of the region around the crack.

In addition, in FEM modelling of FGM part with graded elements, the polynomial interpolations used in such elements can be prone to oscillations that can result in regions of negative elastic modulus, even with only positive nodal values of elastic moduli. The result of these negative modulus regions, even if the region is small, can be unexpected singularities in the solution. To avoid this potential problem, conditions for robust higher order materially graded elements were developed.

Advisor: Mehrdad Negahban