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General approach to the development of mathematical models of nondestructive stress testing. II. Physical model and equations of local relation between stresses and their initial distribution

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Within the framework of a physical model of free strain, we propose a method for reducing nonlinear equations of state of a deformable body to equations that characterize the local influence of initial stresses on the current state of the body. The method is based on the constructive mathematical formulation of the principle of initial independence of the strained state and the general theorem on the elasticity potential.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    I. B. Prokopovych

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  1. I. B. Prokopovych
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 4, pp. 87–95, October–December, 2010.

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Prokopovych, I.B. General approach to the development of mathematical models of nondestructive stress testing. II. Physical model and equations of local relation between stresses and their initial distribution. J Math Sci 181, 401–410 (2012). https://doi.org/10.1007/s10958-012-0693-7

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