This book is to provide the basic concepts and formulations related to the theory of elasticity, including the strain and stress tensors, the constitutive law, the principal strains and principal stresses, the plain stress and plain strain problems, etc. The theory of elasticity is an important basic subject for engineering students and serves as the basis for many advanced engineering courses, such as finite element method, the elastic-plastic mechanics, the continuum mechanics, etc. Therefore, understanding the basic concepts, the relevant formulations and mathematical preliminaries are important and crucial for students to understand the subsequent mechanics courses.

Dr. Yongtao Lyu is an Associate Professor in the School of Mechanics and Aerospace Engineering at Dalian University of Technology, China. He received his Bachelor’s and Master’s degrees in Engineering from Huazhong University of Science and Technology (2001–2007), and his Ph.D. in Mechanical Engineering from Cardiff University, UK (2007–2010). Following his doctoral studies, he conducted postdoctoral research at the Institute of Biomechanics, Hamburg University of Technology, Germany (2010–2013), and later worked as a Senior Research Associate at the Insigneo Institute for in silico Medicine, University of Sheffield, UK (2013–2015). He joined Dalian University of Technology as a faculty member in late 2015. Dr. Lyu's research focuses on the mechanical behavior of biomaterials, computational modeling of human body systems, and the bionic design of bone scaffolds. He has published over 50 SCI-indexed papers in leading journals in the field of biomechanics.

Dr. Yonggang Zheng is a Full Professor and Vice Dean of the School of Mechanics and Aerospace Engineering at Dalian University of Technology, China. He received both his Bachelor’s and Ph.D. degrees from Dalian University of Technology. He has since held various academic positions at the same institution, including Lecturer, Associate Professor, and Professor. His research interests include computational soft matter mechanics, computational nanomechanics and biomechanics, and impact dynamics. Professor Zheng has authored over 130 SCI-indexed papers in top-tier journals in computational and solid mechanics (such as CMAME, IJNME, ACS Nano, APL, etc.). He is the recipient of numerous prestigious awards, including the “Young Talents” award under China’s National Ten Thousand Talents Program and the New Century Excellent Talents Program of the Ministry of Education.