Henryk K. Stolarski, Associate Fellow

Numerical Analysis of Linear Elasticity Problems With Injectivity Constraints; Investigation of Factors Related to Surface-Initiated Cracks in Flexible Pavements

This team was involved in two areas of research during this period. The first involves solving a problem that occurs with existing linear elasticity solutions for some engineering problems, and that violates one of the basic principles related to deformation of real materials—injectivity. Violation of injectivity leads to a paradoxical situation in which two or more, originally distinct, parts of the deforming body occupy the same physical space after deformation. Although this violation usually occurs in an extremely small region(s), Fosdick and Carfagni have recently shown that this still has very significant influence on the results in the entire domain of analysis.

To rectify this pathological situation, additional local (or differential) injectivity constraints have to be appended to the usual governing equations of the problem. Due to the nonlinear nature of the constraints, a numerical solution procedure is needed, since analytical solutions are not possible, except for very few, simple, one-dimensional problems. In this work, a finite element model will be developed to solve some of these problems with the injectivity constraints. The constraints will be enforced using Lagrange multipliers. This model will describe a minimization problem with unilateral, non-linear, local constraints, and will lead to a large, highly nonlinear system of equations, which will be solved iteratively.

The second research area concerned surface initiated cracking on roads. Construction and maintenance of pavement structures (roads) require enormous resources and funds. Thus, even small advances in construction practices of roads translate into substantial savings. The researchers are trying to achieve those savings by a better understanding of mechanisms leading to road deterioration, especially why longitudinal cracking occurs.

In contrast with purely thermal cracking, which typically runs transversely to the road, surface-initiated cracking extends along the road. The phenomenon is not well understood and it is not accounted for in current design procedures. Understanding this relatively new phenomenon would likely lead to improvements extending life of the pavement. Given the costs involved, even small extensions of that life would imply significant monetary savings.

The research is based on the hypothesis (supported by some observations) that tire-road interactions may lead to surface tensile stresses which, compared to the tensile strength of the material involved, is high enough to initiate surface cracking. The team investigated the problem with numerical simulations. The abaqus computer program was used to analyze the pavement stress and strain levels in the vicinity of the pavement-tire contact area. The team conducted three-dimensional calculations, changing parameters such as layout of the road layers and their material properties, to determine whether an optimal design exists that minimizes likelihood of cracking.

Research Group and Collaborators

Shongtao Dai, Minnesota Department of Transportation, Maplewood, Minnesota
Andrew Drescher, Faculty Collaborator
Jill Holewinski, Graduate Student Researcher
Khalid Obeidat, Graduate Student Researcher
See-Chew Soon, Graduate Student Researcher
Zourab Tchomakhidze, Research Associate
Julie M. Vandenbossche, Graduate Student Researcher