Speaker: Srinivasan Gopalakrishnan, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom link : A link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  Wave Propagation, Non-local waveguides, Karmer-Kronig Relatins, Bon-based Peridynamics

Abstract: Traditionally, in solid mechanics, classical continuum theories (CCT) of elasticity have been an important tool in the examinations of behavior of solids under external loads. However, due to absence of length scale information in the theory, CCT has been found to be inadequate in examining phenomena such as shear band formations, damage evolution, etc., in solids. Further, with advent of novel solid materials, such as, composites and metamaterials, which necessarily involve microscale structure, a need has arisen to generate knowledge for behavior of solids with microstructure. To address these aspects, generalization or reformulation of continuum elasticity theories has been proposed in the solid mechanics literature. Concepts put forth included: augmenting material particles with additional internal degrees of freedom, augmenting constitutive equation with higher gradients of strain or with atomic potential type interactions, etc. The former type of generalization involves Mindlin type solid, and the later type involves, what now known in the literature as, nonlocal continuum solid. In practice, given a new theory, it is customary to apply the theory to various initial-boundary value problems (IVBPs) for examination of its predictability of experimentally observable characteristics of solids. The IVBPs typically include static, buckling, bending, vibration and wave propagation analyses. Although there exists abundant literature on most of the IVBPs, however, wave motion analyses are few and requires further investigations. In this thesis, nonlocal continuum theories of elasticity are critically examined with respect to wave motion characteristics.

In the first part of the talk, the framework of wave motion spectral analysis is elucidated, on classical theories of elasticity. It involves a Fourier frequency analysis examining frequency spectrum behavior of wavenumber, group speeds and frequency response function. This data is further utilized within the Kramer-Kronig (K-K) relations analysis framework, which is developed for the elasticity theories, to examine the agreement/disagreement of a theory to the principle of primitive causality.

In the second part of the talk, the above framework is applied to nonlocal strain/stress gradients and integral nonlocal elasticity theories. It is observed that, all the theories show at least one of the unphysical wave motion characteristics. The unphysical characteristics include infinitesimally small or zero group speeds, infinitely large group speeds, negative group speeds and absence of wave attenuation. It is noted that, a theory shows agreement to primitive causality due to existence of wave dispersion as well as attenuation. Relation between boundary conditions and physically justifiable wave motion phenomena is also examined.

Biography: Prof. Gopalakrishnan received his BS degree from Bangalore University, master’s degree in engineering Mechanics from Indian Institute of Technology, Madras, Chennai and Ph.D from School of Aeronautics and Astronautics from Purdue University, USA in the year December 1992. After his Ph.D., he was a Postdoctoral Fellow in the Department of Mechanical Engineering at Georgia Institute of Technology. In the year November 1997, he joined the Department of Aerospace Engineering at Indian Institute of Science Bangalore, where currently he is a Senior Professor. His main areas of interest are Wave Propagation in complex media, Computational Material Science, Computational Mechanics, Smart Structures, Structural Health Monitoring, MEMS and Nano Composite Structures.

Prof. Gopalakrishnan has extensively published his work on many top international journals. He has a total of 245international journal papers, 9 graduate level textbooks, two undergraduate books, 15 book chapters, and 180 international conference papers. He has an h-index of 56 in Google scholar with nearly 12,000 citations, which is highest in India for any researchers in Aerospace domain. He is in the editorial board of 5 international journals and is the Editor-in-chief of ISSS Journal for Micro and Smart Systems and Associate editor for Smart Materials and Structures and Structural Health Monitoring international journals. Prof. Gopalakrishnan is decorated with many awards and honors, which include, International Structural Health Monitoring person of the year awards 2016 instituted by SAGE Publications, Fellow of Indian National Academy of Engineering, Fellow of Indian Academy of Sciences, Associate Fellows AIAA, Distinguished Alumnus Award, Indian Institute of Technology, Madras, Chennai, Satish Dhawan Young Scientist Award by Government of Karnataka, Biren Roy Trust award of Aeronautical society of India, Alumni Award of excellence in research at IISc in the year 2013 and the Royal Academy of Engineering, UK Distinguished visiting Fellowship. He was elected Fellow of Institute of Mechanical Engineers, UK in the year 2020. Prof. Gopalakrishnan figures in the Stanford list of top 2% of scientist in the world for four consecutive years. This year he will receive the ASME Founders Medal for his outstanding contributions to Structural health Monitoring and NDE. He has guided 32 Ph.D’s, 7 M.Tech (Research) and 23 M.Tech students and has attracted funding of over 5 Million US dollars in research funding.

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