SEMINAR:Recent Advances in the Unified Mechanics Theory...

Guest: Cemal Başaran, University at Buffalo

Title: Recent Advances in the Unified Mechanics Theory

Date/Time: 22 May 2024, 13.40

Location: FENS G035

Abstract: Newton’s three universal laws of motion do not account for dissipation, or degradation.  However, the laws of thermodynamics govern dissipation and degradation evolution. The unified mechanic's theory unifies Newton's universal laws of motion and the second law of thermodynamics at the ab-initio level. Therefore, the degradation, and dissipation are included directly in the governing partial differential equation. Moreover, in the Lagrangian equation the derivative of displacements (or velocity) with respect to entropy is no longer zero, as in classical Newtonian continuum mechanics.  However, to be able to unify these two sets of independent laws the Newtonian space-time coordinate system must be modified.  Therefore, a new linearly independent fifth axis is introduced. The new axis is called the Thermodynamic State Index (TSI) axis, which can have coordinate values between zero and one.  When the entropy generation rate is maximum TSI coordinate is zero. When the entropy generation rate is minimum the TSI coordinate approaches one.  The coordinate on the TSI axis is determined by Boltzmann's formulation of the second law of thermodynamics.  Therefore, the entropy generation rate must be calculated at each time increment at each material point from the thermodynamic fundamental equation of a material.  The thermodynamic fundamental equation must be derived analytically from the fundamental principles of physical chemistry accounting for all entropy-generating micro-mechanisms active for the chosen failure definition. Analytical derivation of the thermodynamic fundamental equation does not require any testing for curve fitting an empirical degradation function and dissipation potential. As a result, when the unified mechanics theory is used, there is no need for an empirical dissipation potential, an empirical degradation evolution function, or empirical curve-fitting parameters to determine failure evolution.  Degradation and dissipation evolution are defined along the TSI axis according to the second law of thermodynamics as formulated by Boltzmann.  Recent developments with applications in corrosion, hydrogen embrittlement, and ultra-high cycle fatigue will be presented.

Bio: Dr. Cemal Basaran is a Professor in the Dept. of Civil, Structural, and Environmental Engineering at the University at Buffalo, The State University of New York. Adjunct Prof. in the Dept. of Applied Mechanics at the Indian Institute of Technology Madras, and Research Professor in the Dept. of Applied Mechanics at the Cracow University of Technology, Poland. He specializes in computational and theoretical mechanics.  He has authored more than 160 peer-reviewed journal publications, a textbook on the Unified Mechanics Theory, and several book chapters.  His research focuses on the development of the Unified Mechanics Theory, in engineering applications.  Some of his awards include the US Navy ONR Young Investigator Award, and the  American Society of Mechanical Engineers (ASME) EEPD, Excellence in Mechanics Award. He is a Fellow of the ASME.  He has been serving on the editorial board of many peer-reviewed international journals. He has been the primary dissertation advisor to 25 Ph.D. students.  His research has been funded by the US National Science Foundation, US Navy, US Department of Defense, State of New York, and many industrial sponsors including but not limited to Intel, Motorola, Northrop Grumman, Raytheon, Delphi, DuPont, Texas Instruments, Micron, Tyco Electronics, Analog Devices, and many others. He serves as a research proposal reviewer to many national and international research funding agencies around the globe including but not limited to the UK, EU, France, China, Hong Kong, Saudi Arabia, Germany, Ireland, Austria, Netherlands, and many other countries. 

References 

1-Cemal Basaran, Introduction to Unified Mechanics Theory with Applications, Springer-Nature Switzerland AG, 2nd edition, 2023.