Nonlinear waves and solitons in complex solids

Author:

Pastrone Franco1,Enghelbrecht Jüri2

Affiliation:

1. Department of Mathematics, University of Turin, Turin, Italy

2. Centre for Nonlinear Studies, Institute of Cybernetics, Tallinn Technical University, Tallinn, Estonia

Abstract

The problem of the propagation of nonlinear waves in complex solids, namely bodies with different internal microstructures, is analyzed. In the first part, we make use of a general model of microstructured solids as introduced by Engelbrechet and Pastrone ( Acc Sc Torino Mem Sc Fis 2011; 35: 23–36) and study two particular relevant models: one-dimensional solid with hierarchical microstructure and with concurrent microstructures. As expected, the hierarchical microstructure leads, with a particular but meaningful choice of the strain energy function, to a sixth-order partial differential equation (PDE) with a characteristic hierarchical structure. Hence, the case of two concurrent microstructures, as introduced by Berezovski, Engelbrecht and Berezovski ( Acta Mech 2011; 220(1–4): 349–363), is studied and again for suitable explicit forms of the energy function we can obtain a fourth-order PDE and actually prove the possibility of propagation of solitary and cnoidal waves.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Soliton Propagation in Solids: Advances and Applications;Encyclopedia of Complexity and Systems Science Series;2022

2. Soliton Propagation in Solids: Advances and Applications;Encyclopedia of Complexity and Systems Science;2019-11-20

3. Emergence of Solitonic Structures in Hierarchical Korteweg–de Vries Systems;Applied Wave Mathematics II;2019

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