Ivan D. Breslavsky

Bio: Ivan D. Breslavsky is an academic researcher from McGill University. The author has contributed to research in topics: Hyperelastic material & Nonlinear system. The author has an hindex of 14, co-authored 31 publications receiving 441 citations. Previous affiliations of Ivan D. Breslavsky include National Technical University & National Academy of Sciences of Ukraine.

Physically and geometrically non-linear vibrations of thin rectangular plates

Abstract: Static deflection as well as free and forced large-amplitude vibrations of thin rectangular rubber plates under uniformly distributed pressure are investigated. Both physical, through a neo-Hookean constitutive law to describe the non-linear elastic deformation of the material, and geometrical non-linearities are accounted for. The deflections of a thin initially flat plate are described by the von Karman non-linear plate theory. A method for building a local model, which approximates the plate behavior around a deformed configuration, is proposed. This local model takes the form of a system of ordinary differential equations with quadratic and cubic non-linearities. The corresponding results are compared to the exact solution and are found to be accurate. Two models reflecting both physical and geometrical non-linearities and geometrical non-linearities only are compared. It is found that the sensitivity of the deflection to the physically induced non-linearities at moderate strains is significant.

Layer-specific hyperelastic and viscoelastic characterization of human descending thoracic aortas.

Abstract: A layer-specific hyperelastic and viscoelastic characterization of human descending thoracic aortas was experimentally performed Healthy aortas from twelve beating heart donors with an average age of 494 years, were received from Transplant Quebec Axial and circumferential strips were prepared from the specimens They were dissected into intima, media and adventitia layers Measurements of the opening angles were used to identify the circumferential residual stresses Uniaxial tensile tests on axial and circumferential strips, together with the Gasser-Ogden-Holzapfel material model, were used to characterize the hyperelastic behaviour of the three aortic layers for each donor Uniaxial harmonic excitations at different frequency, superimposed to initial stretch values, were used to characterize the viscoelastic behaviour The storage modulus and the loss tangent were obtained for each layer in both directions; comparison to intact aortic wall was also performed The generalized Maxwell model, within the framework of nonlinear viscoelasticity with internal variables, was used to obtain the constitutive material parameters Results showed a positive correlation (p

Anisotropic fractional viscoelastic constitutive models for human descending thoracic aortas.

Abstract: The generalized fractional Maxwell model, formulated for hyperelastic material within the framework of the nonlinear viscoelasticity with internal variables, is applied to identify viscoelastic constitutive equations from layer-specific experimental data obtained by uniaxial harmonic loading of ex-vivo human descending thoracic aortas. The constitutive parameters are identified by using a genetic algorithm for the optimal fitting of the experimental data. The accuracy of the fitted fractional model is compared to the fitted integer order model with the same number of Maxwell elements. The formulation of an original strain energy density function for anisotropic nonlinear viscoelasticity is introduced and constitutive parameters are obtained from the experiments.

Non-linear vibrations of shells: A literature review from 2003 to 2013

Abstract: The present literature review focuses on geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non-linear vibrations of shells subjected to normal and in-plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non-stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non-linear vibrations of shells and panels, including (i) fluid–structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced-order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non-linear normal modes and meshless methods are reviewed in depth.

Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials

Abstract: This book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales.

Nonlinear dynamic characterization of two-dimensional materials.

Abstract: Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator’s material properties has remained elusive. Here we show a method for determining the Young’s modulus of suspended 2D material membranes from their nonlinear dynamic response. To demonstrate the method, we perform measurements on graphene and MoS2 nanodrums electrostatically driven into the nonlinear regime at multiple driving forces. We show that a set of frequency response curves can be fitted using only the cubic spring constant as a fit parameter, which we then relate to the Young’s modulus of the material using membrane theory. The presented method is fast, contactless, and provides a platform for high-frequency characterization of the mechanical properties of 2D materials. The mechanical resonances of atomically thin membranes show nonlinear responses at driving forces in the picoNewton range. Here, the authors develop a contactless method to extract the Young’s modulus of 2D materials from the nonlinear dynamic response of these nanomechanical resonators.

Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems

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