On Constraints for Displacement Gradients in Elastic Materials

2017

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Nonlinear plane longitudinal elastic waves with different profiles are studied using the Murnaghan model. The novelty is that the waves are analyzed using the same approximate method and the solutions of the nonlinear wave equations are similar in form. The distortion of the initial wave profile described by cosinusoidal, Gaussian, and Whittaker functions is described theoretically and numerically. About 80 variants of initial parameters are studied numerically: three analytical representations of the initial profile, three materials (aluminum, copper, steel), three wave lengths, three initial maximum amplitudes. For each variant, four (cosine) and five (Gauss, Whittaker) two-dimensional graphs of wave shape versus traveled distance are plotted to demonstrate the distortion of the wave profile

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Section: Approximate Approach To the Analysis Of The Evolution Of Thementioning

confidence: 99%

Numerical Analysis of the Evolution of Plane Longitudinal Nonlinear Elastic Waves with Different Initial Profiles

Yurchuk

2017

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“…Apply further to the nonlinear equations ( 36) - (38) the procedure of analysis of the state of uniaxial tension that is used in the linear theory of elasticity as applied to equations (39). Sub traction of equation (38) from equation (37) gives the formula…”

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confidence: 99%

Nonlinearity of Elastic Deformations and Moderateness of Strains as a Factor Explaining the Auxeticity of Materials*

2019

A theoretical attempt is proposed to explain of auxeticity of elastic materials by use of nonlinear models of elastic deformations for wide range of strain values up to moderate level. The analytical expressions are obtained that corresponds to three kinds of universal deformations (simple shear, uniaxial tension, omniaxial tension) within the framework of three well-known in the nonlinear theory of elasticity models -two-constant Neo-Hookean model, three-constant Mooney-Rivlin model, five-constant Murnaghan model. A most interesting novelty consists in that the sample from elastic material is deformed as the conventional material for small values of strains whereas as the auxetic with increasing to moderate values of strains.

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An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials

Yurchuk

2016