论文信息 - Evaluating the volume of a hidden inclusion in an elastic body

Evaluating the volume of a hidden inclusion in an elastic body

We show by numerical simulations a procedure for the evaluation of the size (area or volume) of an elastic inclusion in an elastic body by means of work data measurements collected from the exterior. In this paper we focus especially on the case when the unknown inclusion is harder than the surrounding material. The computations are performed both in a 2-D and in a 3-D setting.

[1] Avner Friedman,et al. Identification of the conductivity coefficient in an elliptic equation , 1987 .

[2] Victor Isakov,et al. On uniqueness of recovery of a discontinuous conductivity coefficient , 1988 .

[3] Emilio Turco,et al. Numerical size estimates of inclusions in elastic bodies , 2005 .

[4] A. Love. A treatise on the mathematical theory of elasticity , 1892 .

[5] Antonino Morassi,et al. Detecting an Inclusion in an Elastic Body by Boundary Measurements , 2004, SIAM Rev..

[6] Luca Rondi,et al. Examples of exponential instability for inverse inclusion and scattering problems , 2003 .

[7] Masaru Ikehata,et al. Size estimation of inclusion , 1998 .

[8] Victor Isakov,et al. Local uniqueness in the inverse conductivity problem with one measurement , 1995 .

[9] M. Gurtin. The Linear Theory of Elasticity , 1973 .

[10] V. Isakov. Appendix -- Function Spaces , 2017 .

[11] N. Muskhelishvili. Some basic problems of the mathematical theory of elasticity , 1953 .

[12] Avner Friedman,et al. Detection of mines by electric measurements , 1987 .

[13] M. Aristodemo. A high-continuity finite element model for two-dimensional elastic problems , 1985 .

[14] Avner Friedman,et al. On the Uniqueness in the Inverse Conductivity Problem with One Measurement , 1988 .

[15] Generic uniqueness and size estimates in the inverse conductivity problem with one measurement , 1999 .