Abstract
We consider a mathematical model of dynamics of small elastic perturbations in an inhomogeneously deformed rigid body, where for the determining parameters of a local state we take the tensor characteristics of a given actual (strained) configuration (the Cauchy stress tensor and the Hencky or Almansi or Figner strain measure). An iteration algorithm is developed to solve the Cauchy problem stated in the framework of this model for a system of hyperbolic equations with variable coefficients that describes the propagation of elastic pulses in an inhomogeneous deformed continuum. In the case of two-dimensional stress fields, we obtain acoustoelasticity integral relations between the probing pulse parameters and the initial strain (stress) distribution in the direction of pulse propagation in the strained body. We also consider an example of application of the obtained integral relations in the inverse acoustic tomography problem for residual strains in a strip.
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Original Russian Text © O.L. Kravchishin, V.F. Chekurin, 2009, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2009, No. 5, pp. 150–163.
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Kravchishin, O.Z., Chekurin, V.F. Acoustoelasticity model of inhomogeneously deformed bodies. Mech. Solids 44, 781–791 (2009). https://doi.org/10.3103/S0025654409050161
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DOI: https://doi.org/10.3103/S0025654409050161