Mathematical Solutions for Elastodynamic Problems

Date: 15/03/2025

Time: 6 – 7 PM (IST)

Speaker Name: Dr. Pulkit Kumar

Registration Form Link: https://forms.gle/KXmJG16ToCGHrpdC9 

YouTube Live Link:  https://youtube.com/live/pQaXkGetm80?feature=share

Speaker Email: pulkitkumar.maths@gmail.com

Speaker Affiliation: Research Scientist II, Center for Nondestructive Evaluation (CNDE), Iowa State University Ames, Iowa, USA

Mode: Online

Abstract:

The study of crack propagation and wave diffraction in materials is essential for understanding structural integrity and failure mechanisms. This webinar will present analytical solutions for two critical phenomena: crack propagation in anisotropic materials and the diffraction of plane waves by a rigid strip. In the first part, the focus will be on crack propagation in monoclinic crystalline layers, where the interaction between elastic waves and cracks is studied under mechanical point loading. The formulation of this model involves coupled singular integral equations, from which the stress intensity factor (SIF) at the crack tip is derived. The effects of crack length, punch pressure, and anisotropy are explored through numerical simulations, revealing how these parameters influence crack behavior and structural stability. In the second part of this presentation, we will discuss the diffraction of magnetoelastic plane waves by a rigid strip in a reinforced infinite medium. The analytical model is solved using integral equations, yields closed-form expressions for vertical displacement and normal stress. The dependence of diffraction patterns on parameters such as magnetoelastic coupling, wave number, and material anisotropy is examined, providing insights into wave behavior in different material media. This presentation will highlight the challenges and contributions of these studies, showcasing their relevance in the fields of solid mechanics, fracture analysis, and non-destructive evaluation (NDE) techniques.