Abstract
The basic principles of structural modeling for the construction of mathematical models of microstructured media (generalized continua) are given. Here, microstructure means not the smallness of absolute values, but the smallness of some medium scale with respect to other scales, and the particles are considered to be non-deformable and homogeneous, without their own internal structure, presenting realistic materials. A nonlinear dynamically consistent model of a gradient-elastic medium has been elaborated by the method of structural modeling and using the continualization method involving nonlocality of coupling between the displacements of the lattice sites and the obtained continuum. The formation of spatially localized nonlinear strain waves in such media has been investigated.
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The research was carried out under the financial support of the Russian Foundation for Basic Research (projects NN 18-29-10073-mk and 19-08-00965-a).
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Erofeev, V.I., Leontyeva, A.V., Malkhanov, A.O., Pavlov, I.S. (2019). Structural Modeling of Nonlinear Localized Strain Waves in Generalized Continua. In: Altenbach, H., Müller, W., Abali, B. (eds) Higher Gradient Materials and Related Generalized Continua. Advanced Structured Materials, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-030-30406-5_4
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