Acceleration waves in the nonlinear micromorphic continuum. (October 2018)

• Record Type: Journal Article
• Authors: Eremeyev, Victor A.; Lebedev, Leonid P.; Cloud, Michael J.
• Is Part Of: Mechanics research communications. Volume 93(2018)
• Page Start: 70
• Page End: 74
• Publication Date: 2018-10
• Subjects: Acceleration wave -- Micromorphic continuum -- Discontinuities -- Ellipticity; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2017.07.004
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: Acceleration waves in the nonlinear micromorphic medium are studied. The formulas for the acoustic tensors are derived. For the relaxed micromorphic continuum, the strong ellipticity condition is violated. Abstract: Within the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for the micromorphic medium and formulate the conditions for existence of acceleration waves. As examples we consider these conditions for the linear micromorphic medium and for the relaxed micromorphic model.