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1 [CT133]

[CT133]

[00861] Using elastic waves to measure mechanical stress

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In principle, elastic waves could be used to assess the stress in a material, as the higher the stress, the faster the wave will propagate. However, the speed also depends on material parameters, which is why there are no robust (non-invasive) measurement techniques. In this talk we show how to overcome these challenges by using universal relationships between stress and wave speeds. This has led to robust measurements with either bulk waves [2] or surface waves [3]. Universal relationships in continuum mechanics are those that hold for any type of material, or constitutive choice [1]. To measure stress, it would be ideal to have a relationship between the wave speed and the stress that holds for any elastic material. However, there is only one such universal relationship: $\rho v_{12}^2 - \rho v_{21}^2 = \sigma_{11} - \sigma_{22}$, where $\sigma_{ij}$ are the components of the Cauchy stress tensor, and $v_{12} (v_{21})$ is the speed of a shear wave propagating in the $x_1 (x_2)$ direction that is polarised in the $x_2 (x_1)$ direction. Inspired by this identity we propose, and experimentally validate, several new ultrasonic methods. [1] Truesdell, Clifford, and Walter Noll. "The non-linear field theories of mechanics." The non-linear field theories of mechanics. Springer, Berlin, Heidelberg, 1992. 1-579. [2] Li, Guo-Yang, Artur L. Gower, and Michel Destrade. "An ultrasonic method to measure stress without calibration: The angled shear wave method." The Journal of the Acoustical Society of America 148.6 (2020): 3963-3970. [3] Li, Guo-Yang, et al. "Non-destructive mapping of stress and strain in soft thin films through sound waves." Communications Physics 5.1 (2022): 1-7.
Classification : 74J05, 74B10, 74B15, 74J25
Author(s) :
- Art Gower (University of Sheffield)
- Michel Destrade (University of Galway)
- Guo-yang Li (Harvard Medical School and Wellman Center for Photomedicine)

[02071] Wave propagation in nonlocal diffusive materials

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : The nonlocal elasticity theory is applied to study the propagation of plane wave and Rayleigh-type surface wave in transversely isotropic diffusive materials. The time-harmonic solutions of two-dimensional motion equations are obtained and a velocity equation for homogeneous plane wave is derived. The two-dimensional equations are also solved to deduce a Rayleigh characteristic equation. Some special cases of velocity equation of plane waves and characteristic equation of the Rayleigh waves in absence of nonlocality and diffusion are also derived. The effects of nonlocality and material parameters on the speeds of plane and Rayleigh waves are illustrated graphically
Classification : 74J05, 74J10, 74J15
Author(s) :
- Baljeet Singh (Post Graduate Government College, Sector 11, Chandigarh)

[00002] Propagation of Lamb wave in the plate of microstretch thermoelastic diffusion materials

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : The present study investigates the effect of three thermoelastic theories on the propagation of Lamb wave in a linearly isotropic microstretch diffusion plate subject to stress free thermally insulated/impermeable and isothermal/isoconcentrated boundary conditions. The secular equations of the Lamb wave are obtained for both symmetric and anti-symmetric modes of vibration. The phase velocities and attenuation coefficients are computed numerically for a particular model and these results are compared for the three theories: Coupled Thermoelasticity theory, Lord-Shulman theory and Green-Lindsay theory. The velocity curves and the attenuation coefficients are illustrated graphically. It is observed that there are three modes of velocity and attenuation for each symmetric and anti-symmetric vibration. We have noticed that the velocity of the corresponding Lamb wave increases from first to third mode of symmetric vibration in both thermally insulated/impermeable and isothermal/isoconcentrated plates. At short wavelength, the secular equation of symmetric mode of vibration reduces to that of Rayleigh surface wave for both the plates. Some special cases are also deduced from the present formulation.
Classification : 74J15, 74B15, 80A17, 80A10
Author(s) :
- Sarat Singh Sanasam (Mizoram University)
- Sanjay Debnath (Mizoram University)

[00208] Love wave along the interface with triangular irregularity

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Propagation of the love wave is studied along the irregular interface between the porous layer and the elastic half-space. The porous layer is assumed to be saturated by two immiscible fluids. The irregularity at the interface is considered in the form of a triangular pit embedded in the half-space. The elastic half-space is considered to be initially stressed under the effect of gravity. A complex transcendental and implicit relation between the frequency and the phase speed of the Love wave is derived in the form of a dispersion relation. A numerical study is conducted to observe the effect of material parameters and irregularity on the behavior of the Love wave. A significant impact of the triangular pit, porosity, and frequency is observed on the phase speed of the propagating Love wave and depicted graphically.
Classification : 74J15
Author(s) :
- Ashish Arora (I. K. Gujral Punjab Technical University)

[00841] Destabilization of interfacial elastic waves due to friction

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Elasticity theory permits several interfacial wave solutions. In antiplane elasticity, the well-known Love wave occurs in bonded contact of an elastic layer on a dissimilar elastic half-space. A new interfacial elastic wave solution, namely the antiplane slip wave, which occurs in slipping contact of a layer on a half-space or on another layer will be discussed. It is shown that the interfacial elastic waves are often destabilized when frictional slipping occurs.
Classification : 74J15, 74M10, 74R10, 74B05
Author(s) :
- Ranjith Kunnath (Mahindra University)