Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport

Overview

Nonhomogeneous Semi-Infinite Body
Forward Problem

Authors: G Rozza & AT Patera
in collaboration with DBP Huynh, NC Nguyen, & (previously) MA Grepl


Engineering Motivation

This problem considers the transient evolution of the temperature field near the surface of a Fiber-Reinforced-Polymer (FRP) concrete wall. The FRP is affixed or retrofitted to concrete or masonry surfaces to strengthen or rehabilitate the (infra)structure. Unfortunately, the FRP is susceptible to delamination: the formation of cracks at the FRP-concrete interface which can jeopardize integrity [MA Starnes, Development of Technical Basis for Using Infrared Thermography for Nondestructive Evaluation of Fiber Reinforced Polymer Composites Bonded to Concrete, Ph.D. Thesis, MIT, September 2002]. These cracks are the focus of this problem. From the engineering point of view, the inverse version of this problem illustrates the application of transient conduction to real-time nondestructive evaluation — in this case, crack detection.

Physical Principles

From the physical point of view, this problem illustrates (i) the basic timescales associated with transient conduction, and (ii) the dependence of temperature field evolution on material properties and geometric inhomogeneities.

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