Formulation of the Second Gradient Elastodynamic Problem in Interaction with a Flow of Defects
DOI:
https://doi.org/10.70567/mc.v41i1.1Palavras-chave:
Cauchy problem, Second gradient ElastodynamicsResumo
In the following work, the problem of initial and edge conditions for elastodynamic systems dependent on certain characteristic lengths identified as microscales, or in general multiple scales, is formulated. A problem of initial values is constructed, which, unlike the classic Cauchy problem, is now extended with new initial conditions coming from the so-called micro-inertia terms, that is, in the formulation of multiple scales it is not possible to fail to consider the high-order corrections of gradients, which produce initial conditions defined on surfaces, characterized by lengths ls. Using a variation of the divergence theorem and the third Green Lagrange representation theorem, solutions associated with the propagation of elastic waves in micro-structured media are constructed.
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