Wave Processes in Solids with Microstructure

Erofeyev, Vladimir I.

doi:10.1142/9789812794505

Cited by 46 publications

(55 citation statements)

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“…For a theoretical description of the nonlinear dynamical effects in composite materials, a number of higher-order continuum models mainly focused on reduction of heterogeneous objects to the homogeneous ones were proposed, For detailed reviews of the subject, we refer to Ting [2], Engelbrecht and Braun [3], Erofeev [4], Cattani and Rushchitsky [5], and Rushchitsky [6]. The mentioned homogeneous models are widely employed in infinite spaces, which gives a possibility of application of wide palette of methods offered by modern Nonlinear Physics (inverse scattering transforms, theory of solitons, library of integrated nonlinear equations, etc., see Bhatnagar [7], Porubov [8], Samsonov [9] for more details).…”

Section: Introductionmentioning

confidence: 99%

Influence of geometric and physical nonlinearities on the internal resonances of a finite continuous rod with a microstructure

Andrianov

Awrejcewicz

Danishevskyy

et al. 2017

Journal of Sound and Vibration

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Abstract. In this work, nonlinear longitudinal vibrations of a finite composite rod are studied including geometric and physical nonlinearities. An original boundary value problem for a heterogeneous rod yielded by the macroscopic approximation obtained earlier by the higher-order asymptotic homogenization method is used. The effects of internal resonances and modes coupling are predicted, validated and analyzed. The defined novel continuous problem governed by PDEs is solved using space-discretization and the method of multiple time scales. We are aimed at understanding and analyzing how the presence of the microstructure influences the processes of mode interaction. It is shown that, depending on a scaling relation between the amplitude of the vibrations and the size of the unit cell, different scenarios of the modes coupling can be realized.Additionally to the asymptotic solution, numerical simulation of the modes coupling is performed by means of the Runge-Kutta fourth-order method. The obtained numerical and analytical results demonstrate good qualitative agreement.

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Section: Introductionmentioning

confidence: 99%

Influence of geometric and physical nonlinearities on the internal resonances of a finite continuous rod with a microstructure

Andrianov

Awrejcewicz

Danishevskyy

et al. 2017

Journal of Sound and Vibration

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“…The Earth's interior is modeled as an elasto-plastic continuum and elastoplastic waves [9,10], that describe elastic longitudinal and plastic shear distortion solitons. We apply similar method in order to determine the solitons propagating along the fault SRF.…”

Section: : the San Ramón Fault Scarp Chile (Wat-west Andean Thrust)mentioning

confidence: 99%

A Seismic Channel Model: The San Ramon Fault

Torres-Silva¹,

Cabezas²

2016

IJAERS

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“…Besides nonlocal models in elasticity, Bazant and Jirasek (2002) review models in nonlocal plasticity and damage, including cohesive zone models for fracture. Analytical results are possible for special cases for nonlocal models and some are presented in, for example, the monographs by Kunin (1982), and by Erofeyev (2003) which discusses wave processes in solids with microstructure. One of the factors that have delayed the widespread adoption of nonlocal formulations by industry has been the difficulty of correlating them to existing constitutive models that have performed well under certain strain rates and thermal ranges.…”

Section: Nonlocal Modelsmentioning

confidence: 99%