Modeling elastic wave propagation in heterogeneous materials (20/12/22)

Speaker and Affliation:

Mr Anubhav Roy
PhD candidate
Department of Engineering Science and Mechanics
The Pennsylvania State University, USA

About the Speaker:

Anubhav Roy is a PhD candidate in the Department of Engineering Science and Mechanics at The Pennsylvania State University. He has been pursuing research in theoretical and computational mechanics under the guidance of Dr. Christopher Kube at the Penn State Ultrasonics Lab (PennSUL). Anubhav graduated from the Department of Construction Engineering, Jadavpur University (Kolkata, India) in 2016 where he had gained computational research experience in static nondestructive evaluation (NDE) of 1D structures (beams and trusses). During his undergraduate studies in India, Anubhav had worked 1 as an intern in some of the most prestigious research groups in different institutes, namely, IIT Kharagpur (2014), IIT Bombay (2015) and IISc Bangalore (2015). He received Master of Science in Aerospace Engineering and Mechanics from the University of Alabama (UA) in 2018 where he got the Outstanding Graduate Resarch Assistant award in the same year. At UA, he worked on capturing nano-scale fracture mechanisms by coupling Hardy estimates-based atomistic J-integral with Molecular Dynamic (MD) simulations of isothermal (room temperature), uniaxial extention of defective Graphene sheets. Since joining Penn State, Anubhav has been involved in understanding mechanisms within the microstructure of polycrystalline materials. He received the Sabih and G¨uler Hayek graduate fellowship in Engineering Science and Mechanics in 2019 and 2020. Proposing a bottom-up research setup to facilitate an in situ, real time monitoring of structure-processing-properties of additively manufactured metals, Anubhav received the Best Poster Presentation award and a Travel Grant at the International Congress in Ultrasonics, organized at Belgium in 2019. Recently, in 2020 with Dr. Kube in collaboration with Sandia National Laboratory, he developed a computational tool “propSym” that can efficiently reduce material property tensors corresponding to general order (rank) across all crystal point groups. As a continuation of the collaboration, he was a part of Dr. Kube’s research to develop the large acoustoelasticity theory for anisotropic materials, introducing a coupling between finite initial deformation and finite amplitude waves highlighting the influence of residual stress. Currently, Anubhav is working on elastodynamic modelling of ultrasonic scattering and attenuation in complex polycrystalline microstructure. He is one of the five recipients of the 2022 ASNT (American Society for Nondestructive Testing) Fellowship Award.


20th December, 2022 (Tuesday), 11:00 AM (India Standard Time)


KPA Auditorium, Department of Materials Engineering


Scattering of waves is an interesting phenomenon that spans length scales of planets down to the nanoscale. A scattered wave field carries important information about the medium of propagation, and is useful for a variety of fields in geophysics, seismology, radiology, material science, to name a few. Elastic wave scattering is commonly used as a sensitive tool for nondestructive evaluation (NDE) and characterization of metallic microsctructure. Existing analytical models can predict ultrasonic propagation and grain boundary scattering in statistically homogeneous metals exhibiting spatially fluctuating mechanical properties. These models rely on two-point statistics that correspond to the first-order smoothing approximation (FOSA) of the mass-operator series present in the governing Dyson equation. The use of the Dyson equation in elastodynamics enables us to apply Feynman diagrams and its rules to the mass operator to readily recover solutions for the effective propagation properties including wave displacements, dissipation, and scattering behavior. FOSA-based prediction agrees well with finite element (FE) results over a wide range of metals for using ultrasonic frequencies within stochastic limit. However, recent studies indicate a discrepancy between the predictions starts to grow for strongly scattering polycrystals. For polycrystals comprising grains of high single-crystal anisotropy, the reported discrepancy is about 63% for Lithium, even for low frequencies in the Rayleigh limit. In our current model, the third-order smoothing approximation (TOSA) based estimates of attenuation and wavespeed are analytically incorporated imposing long wavelength (Rayleigh-limit) assumptions. One of our broader interests includes investigating formal linkages between elastodynamic and elastostatic homogenization theories, such that elastic wave techniques can be used to probe structure-property relationships important for characterizing material behavior.

This presentation will focus on the development of the analytical model. The current TOSA-based model improves the existing longitudinal attenuation estimates for strongly scattering polycrystals comprised of grains with high single crystal aniostropy, like Lithium or Nickel by about 17% or 7% respectively. Furthermore, improvements for incorporating the current model are observed to be pronounced for the cases corresponding to transverse incidence. The improvement motivates further investigation to provide improved estimates especially for microsturctures exhibiting high scattering. The four point statistics based current model is expected to effectively improve the existing elastodynamic estimates of such complex microstructures, such as, in multi-phase (including porous) or textured media, etc.. Beyond applications to NDE of complex materials, the derivation of the current mathematical model may inspire future work in improving estimates for application in other disciplines like electrodynamics and quantum field theories that involve first-order homogenization of the Dyson equation to quantify strong-fluctuation of properties along space.