A higher order phase field approach for crack propagation in brittle and quasi brittle structures

t Angela Watson Acknowledgments Support and assistance were invaluable throughout my dissertation writing I would first like to acknowledge the Flemish Government funding the project under the financial support of the VLIR-UOS TEAM Project (VN2017TEA454A103) This project could not have reached its goal without this funding In addition, I am very grateful to the H2020 MSCARISE-project BESTOFRAC (734370), which has afforded me the opportunity to visit research institutions in order to further my scientific knowledge I would like to give my special regards to Professor Magd Abdel Wahab It is greatly appreciated that his excellent conceptualization and advice helped lead to exceptional results in this project In appreciation of Professor Nguyen Xuan Hung's valuable guidance and for the unconditional and enthusiastic support throughout my doctoral journey, I would like to express my deepest gratitude I would like to express my gratitude to my brothers, Dr Le Thanh Cuong, Dr Vu Huu Truong, and Dr Tran Minh Trang, who accompanied me in completing this dissertation To my colleagues at Laboratory Soete, I would like to say a heartfelt "thank you" for their friendship, assistance, and support During our group discussion, I received constructive suggestions, professional opinions, and opinions from others that helped improve my research quality Finally, I would like to express my enormous gratitude to my wife and my family for everything that has been done for me This Ph.D journey would not have been possible without their encouragement and unconditional supports Khuong Duy Nguyen Ghent, 12 December 2021 5.3 Suggestions for Further Research 160 when using the phase-field model Therefore, a three-dimensional ductile failure would be considered by using the fourth-order phasefield formulation for more practical problems • This study has not considered crack propagation depending on time as a dynamic crack problem Hence, the study would be expanded into dynamic crack problems • The VUKIMS algorithm is limited to a local refinement mesh approach This study has not considered an adaptive mesh for computing Therefore, an adaptive mesh for IGA would be developed to integrate with the phase-field theory for crack propagation in three-dimensional problems • More general softening laws by using different optimal characteristic functions should be proposed for the concrete structures • This dissertation studied only the benchmark problems or the simple geometry problems So, the following studies should apply the proposed approach to the practical problems, including the interlocking concrete blocks of embankments and breakwaters • The phase-field model should develop for geotechnical engineering failure problems to exploit damage on soils • In addition, because Vietnam is in a tropical area, extreme climate events, including temperature and moisture factors, would impact Vietnamese life The thermal and moisture factors also impact much on the constructions in Vietnam 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[134] D.-C Feng, J.-Y Wu, Phase-field regularized cohesive zone model (CZM) and size effect of concrete, Engineering Fracture Mechanics, 197 (2018) 66-79 ... the phase- field theory recently became the most popular approach in modelling crack propagation in solid mechanics Its main idea is to use a scalar auxiliary variable, namely a phase- field variable,... isogeometric analysis for crack propagation in brittle and quasi -brittle materials • Chapter presents a brief background for the phase- field model and isogeometric analysis approach The phase- field. .. brittle and quasi -brittle materials 1.2 Purpose statement In computational solid mechanics, the accurate prediction of crack formation and propagation remains a crucial challenge applicable in