Nondestructive Evaluation of Porous Materials

We report here on the use of the heat equation to simulate a thermal interrogation method for detecting damage in a heterogeneous porous material. We first use probability schemes to randomly generate pores in a sample material; then we simulate flash heating of the compartment along one of its boundaries. Temperature data along the source and back boundaries are recorded and then analyzed to distinguish differences between the undamaged and damaged materials. These results suggest that it is possible to detect damage of a certain size within a porous medium using thermal interrogation.;We discuss a mathematical model for the flash heat experiment in homogeneous isotropic media. We then use this model to investigate the use of homogenization techniques in approximating models for interrogation via flash-heating in porous materials. We represent porous materials as both randomly perforated domains and periodically perforated domains.;In this effort, we investigate the behavior of a model derived from homogenization theory as the model solution in parameter estimation procedures for simulated data. We consider data simulated from a model on a perforated domain with isotropic flow and data simulated from a model on a homogeneous domain with anisotropic flow. We consider both ordinary and generalized least squares parameter estimation procedures.;We then use these methodologies along with a method of maps to detect damage using a hypothesis test. Finally, we consider using the homogenization approximation to characterize elliptical damage.