In the present paper we develop a mathematical basis to theoretically predict results of application to elastic materials containing huge arrays of linear cracks; we develop also reconstruction of an arbitrary curvilinear non-planar crack. The work is based on rigorous diffraction theories and allied inverse problems. The problem is first reduced to a system of basic boundary integral equations. Then the inverse reconstruction problem is formulated as a minimization problem for a certain strongly nonlinear functional. The proposed numerical algorithm is tested on some examples of complex-shaped cracks.

A New Algorithm for Reconstruction an Arbitrary Curvilinear non Planar Crack by the Inverse Diffraction Technique and US Method / Brigante, Michele. - ELETTRONICO. - 1:(2011), pp. 31-41. (Intervento presentato al convegno XX CONGRESSO AIMETA - ASSOCIAZIONE ITALIANA DI MECCANICA TEORICA E APPLICATA tenutosi a BOLOGNA nel 12-15 settembre 2011).

### A New Algorithm for Reconstruction an Arbitrary Curvilinear non Planar Crack by the Inverse Diffraction Technique and US Method

#### Abstract

In the present paper we develop a mathematical basis to theoretically predict results of application to elastic materials containing huge arrays of linear cracks; we develop also reconstruction of an arbitrary curvilinear non-planar crack. The work is based on rigorous diffraction theories and allied inverse problems. The problem is first reduced to a system of basic boundary integral equations. Then the inverse reconstruction problem is formulated as a minimization problem for a certain strongly nonlinear functional. The proposed numerical algorithm is tested on some examples of complex-shaped cracks.
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2011
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A New Algorithm for Reconstruction an Arbitrary Curvilinear non Planar Crack by the Inverse Diffraction Technique and US Method / Brigante, Michele. - ELETTRONICO. - 1:(2011), pp. 31-41. (Intervento presentato al convegno XX CONGRESSO AIMETA - ASSOCIAZIONE ITALIANA DI MECCANICA TEORICA E APPLICATA tenutosi a BOLOGNA nel 12-15 settembre 2011).
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11588/413253`
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