Dr. X. R. Wu (Xue-Ren Wu) obtained his Ph.D. in 1983 from the Royal Institute of Technology (KTH), Stockholm, Sweden. He is Professor at Beijing Institute of Aeronautical materials, where he was technical director for 14 years and senior advisor for 10 years. He was Co-chief Scientist of the Sino-American first aerospace cooperative research program (fatigue and fracture mechanics) between Chinese Aeronautical Establishment (CAE) and National Aeronautics and Space Administration (NASA, USA) from 1987 to 1994. He has promoted China's involvement in international research activities on fatigue life prediction methods for small cracks. He was Chairman of the 7th International Fatigue Congress (FATIGUE'99) in Beijing. Professor Wu has received many awards, including China's National Natural Science Award (1993), Kwang-Hua Science and Technology Foundation Award (1994), the IUMRS first Somiya Award for International Cooperation (2000) jointly with Dr. J C Newman (NASA Langley Research Center), and a number of Technology Progress Awards at the national and ministerial level in China. He published (by Pergamon Press, Oxford England, 1991) the world first weight function book "Weight Functions and Stress Intensity Factor Solutions" co-authored with Professor A J Carlsson. The book has been well received and extensively used by the international fracture mechanics community. He has authored/co-authored over 200 papers and edited several books in the technical literature.

Dr. W. Xu is an associate professor at Shanghai Jiao Tong University. He got his Ph.D. in 2012 from Shanghai Jiao Tong University, Shanghai, China. From 2012 to 2015, he was a postdoctoral research fellow at the Aerospace Engineering Department in the University of Michigan, Ann Arbor, USA. His research interests are mainly focused on fracture mechanics and composite material mechanics. His research was fund by NSFC, AVIC, and the Shanghai Sailing Program for outstanding young talent in science and technology by the Shanghai Municipality. He is the author of more than 50 journal papers.

Part I Theoretical Background of Fracture Mechanics Weight Function Methods.- Standardized Analytical Weight Function Method Based on Crack Opening Displacements.- Analysis and Discussions of Weight Function Methods Based on Multiple Reference Load Cases.- Accuracy Verifications of Various Weight Functions and Method Assessments.- Part II Weight Functions and Stress Intensity factors for Various Crack Geometries.- Center Crack(s) in Single Connected Domain.- Edge Crack(s) in Single Connected Domain.- Edge Crack(s) in Multiple Connected Domain.- Weight Function Method and Applications to Orthotropic Composite Material.- Weight Function Method and Fracture Analysis for Plates with Multiple Cracks.- Analytical Weight Functions and Mixed Mode Stress Intensity Factors for Mode II Cracks.- Weigh Functions for Three-dimensional Crack Problems.- Part III Various Engineering Applications of Weight Function Methods.- Weigh Function Analysis of Crack Problems with Thermal/Residual Stresses.- Computation of Crack Opening Displacements/Areas with Weigh Function Methods.- Analysis of Bridging, Cohesive Model and Crack Opening Stress with Weigh Function Methods.- Weigh Functions and Stress Intensity Factors for Complex Crack Geometry.- Application of Weigh Function Methods to Multiple Site Damage Analysis.- Determination of Un-cracked Stresses Using Inverse Weight Function Method.- Appendix.