Abstract
The present chapter describes an averaging method for internal thermal and mechanical processes in ablative composites. The method is based on the assumption of a regularity in the internal structure of the ablative composite, and the concept of asymptotic expansion for partial differential equations with rapidly oscillating coefficients. This theory was formulated by Bakhvalov [1] and developed by Lions [10] and others for composites without phase transformations, and by Sanchez-Palencia [12] for porous media without phase transformations. For heterogeneous media with phase transformations the averaging method has been developed in works [2–7]. Four main types of boundary conditions on external surfaces of an ablative composite are considered. As a result of applying the methods of asymptotic averaging, a statement of problems for composites with ablative matrix and fibres is derived in terms of displacements and in terms of stresses.
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References
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Dimitrienko, Y.I. (2016). Mathematical Model of Ablative Composites. In: Thermomechanics of Composite Structures under High Temperatures. Solid Mechanics and Its Applications, vol 224. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7494-9_3
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DOI: https://doi.org/10.1007/978-94-017-7494-9_3
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