Inverse determination of spatially varying material coefficients in solid objects

Abstract

Material properties such as thermal conductivity, magnetic permeability, electric permittivity, modulus of elasticity, Poisson's ratio, thermal expansion coefficient, etc. can vary spatially throughout a given solid object as it is the case in functionally graded materials. Finding this spatial variation is an inverse problem that requires boundary values of the field quantity such as temperature, magnetic field potential or electric field potential and its derivatives normal to the boundaries. In this paper, we solve the direct problem of predicting the spatial distribution of the field variable based on its measured boundary values and on the assumed spatial distribution of the diffusion coefficient using radial basis functions, the finite volume method and the finite element method, whose accuracies are verified against analytical solutions. Minimization of the sum of normalized least-squares differences between the calculated and measured values of the field quantity at the boundaries then leads to the correct parameters in the analytic model for the spatial distribution of the spatially varying material property.

Inverse Determination of Spatially Varying Heat Capacity and Thermal Conductivity in Arbitrary 2d Objects

“…Here, (9) where s q is the boundary heat flux. The test functions become zero at the boundary nodes where Dirichlet condition is specified leading to the first term on the right side of Eq.…”

“…In this approach, the initial distribution of material properties is assumed and iteratively updated (by varying the values of the parameters) until the scaled sum of squares of differences is below a specific threshold. This inverse parameter identification concept was previously used to estimate a single spatially varying material property [8][9][10] based on solutions of steady state equation (1). It is here extended to simultaneously determining two spatially varying material properties: heat capacity and thermal conductivity.…”

Determination of thermal conductivity of inhomogeneous orthotropic materials from temperature measurements

“…The use of inverse analysis for the estimation of thermal conductivity by utilizing steady [2] or transient temperature measurements taken within the medium and/or its boundary has numerous practical applications. The simultaneous determination of the thermal conductivity and heat capacity depending on space or temperature has been studied using the direct integration and Levenberg-Marquardt methods in [3,4], respectively.…”