Dechun Lu: Professor Dechun Lu earned his PhD degree in 2006 from Beihang University and then worked as a teacher at the College of Architecture and Civil Engineering of Beijing University of Technology up to now. Prof. Lu is the leader of the Beijing Academic Innovation Team and the winner of the National Science Fund for Distinguished Young Scholars. His expertise spans multi-physical geotechnical engineering, computational geotechnical mechanics, urban underground engineering, and intelligent geotechnical engineering. He has published more than 100 academic papers in internationally renowned journals, such as Géotechnique, Journal of the Mechanics and Physics of Solids, Computer Methods in Applied Mechanics and Engineering, and Computers and Geotechnics. Prof. Lu has undertaken more than 10 national-funded projects in China, including 5 key projects. These projects have received over 30 million RMB in government funding. Prof. Lu has received numerous honors and awards, such as the Second Prize of the State Science and Technology Progress Award, the Second Prize of the State Natural Science Award, and the 15th Science and Technology Award for Chinese Youth.Xin Zhou: Dr. Xin Zhou earned his PhD degree in 2022 from the Beijing University of Technology. He subsequently joined the Department of Civil Engineering at Tsinghua University as a Postdoctoral Fellow. His work focuses on constitutive modeling of geomaterials, numerical methods of elastoplastic problems, and nonlocal methods. Over the past five years, he has published more than 20 papers in prestigious international journals. Dr. Zhou has led projects funded by the Youth Program of the National Natural Science Foundation of China and the Postdoctoral Research Foundation of China, among others. In recognition of his academic contributions, Dr. Zhou was selected for the 9th Young Elite Scientist Sponsorship Program by CAST and received the First Prize of the Natural Science Award (4/5) from the Chinese Society for Rock Mechanics & Engineering in 2023.Jingyu Liang: Dr. Jingyu Liang earned his PhD degree in 2020 from the Beijing University of Technology. Subsequently, he commenced his postdoctoral research at the Beijing University of Civil Engineering and Architecture, where he was subsequently promoted to the position of research associate in 2023. He has been involved in 5 national and provincial fund projects. Additionally, He has published more than·20 academic papers in renowned journals. Dr. Liang has been recognized for his contributions with awards, such as the “Excellent Doctoral Dissertation Award” (1/1) and the “Natural Science Prize” (5/5) from the Chinese Society for Rock Mechanics & Engineering. His primary research interests encompass geotechnical plasticity, urban underground engineering, frozen soil mechanics, and freezing method construction.Xiuli Du: Professor Xiuli Du is an academician of the Chinese Academy of Engineering. He earned his PhD degree from the Institute of Engineering Mechanics, China Earthquake Administration, in 1990. In 1996, he was exceptionally promoted to professor. In 2001, he joined the Beijing University of Technology as a faculty member up to now. Prof. Du has long been dedicated to research and practical work in earthquake-resistant engineering. He has authored over 400 research papers published in high-impact journals, both domestically and internationally. Prof. Du has led and completed five major national projects. His achievements have been recognized with five Second Prize of the State Science and Technology Progress Award.

• Introduction.- Non-orthogonal plastic theory in unsteady environments.- Non-orthogonal elastoplastic model for soil in the steady environment.- Non-orthogonal elastoplastic model for soil in the unsteady water environment.- Non orthogonal plastic damage model of concrete.- Non-orthogonal elastoplastic model for concrete in the variable strain rate environment.- Unconstrained stress update algorithm for elastoplastic models.- Stress update algorithm based on numerical optimization methods.- Stress update algorithm based on numerical differentiation methods.- Stress update algorithm based on integral nonlocal method.

Dechun Lu: Professor Dechun Lu earned his PhD degree in 2006 from Beihang University and then worked as a teacher at the College of Architecture and Civil Engineering of Beijing University of Technology up to now. Prof. Lu is the leader of the Beijing Academic Innovation Team and the winner of the National Science Fund for Distinguished Young Scholars. His expertise spans multi-physical geotechnical engineering, computational geotechnical mechanics, urban underground engineering, and intelligent geotechnical engineering. He has published more than 100 academic papers in internationally renowned journals, such as Géotechnique, Journal of the Mechanics and Physics of Solids, Computer Methods in Applied Mechanics and Engineering, and Computers and Geotechnics. Prof. Lu has undertaken more than 10 national-funded projects in China, including 5 key projects. These projects have received over 30 million RMB in government funding. Prof. Lu has received numerous honors and awards, such as the Second Prize of the State Science and Technology Progress Award, the Second Prize of the State Natural Science Award, and the 15th Science and Technology Award for Chinese Youth.Xin Zhou: Dr. Xin Zhou earned his PhD degree in 2022 from the Beijing University of Technology. He subsequently joined the Department of Civil Engineering at Tsinghua University as a Postdoctoral Fellow. His work focuses on constitutive modeling of geomaterials, numerical methods of elastoplastic problems, and nonlocal methods. Over the past five years, he has published more than 20 papers in prestigious international journals. Dr. Zhou has led projects funded by the Youth Program of the National Natural Science Foundation of China and the Postdoctoral Research Foundation of China, among others. In recognition of his academic contributions, Dr. Zhou was selected for the 9th Young Elite Scientist Sponsorship Program by CAST and received the First Prize of the Natural Science Award (4/5) from the Chinese Society for Rock Mechanics & Engineering in 2023.Jingyu Liang: Dr. Jingyu Liang earned his PhD degree in 2020 from the Beijing University of Technology. Subsequently, he commenced his postdoctoral research at the Beijing University of Civil Engineering and Architecture, where he was subsequently promoted to the position of research associate in 2023. He has been involved in 5 national and provincial fund projects. Additionally, He has published more than·20 academic papers in renowned journals. Dr. Liang has been recognized for his contributions with awards, such as the “Excellent Doctoral Dissertation Award” (1/1) and the “Natural Science Prize” (5/5) from the Chinese Society for Rock Mechanics & Engineering. His primary research interests encompass geotechnical plasticity, urban underground engineering, frozen soil mechanics, and freezing method construction.Xiuli Du: Professor Xiuli Du is an academician of the Chinese Academy of Engineering. He earned his PhD degree from the Institute of Engineering Mechanics, China Earthquake Administration, in 1990. In 1996, he was exceptionally promoted to professor. In 2001, he joined the Beijing University of Technology as a faculty member up to now. Prof. Du has long been dedicated to research and practical work in earthquake-resistant engineering. He has authored over 400 research papers published in high-impact journals, both domestically and internationally. Prof. Du has led and completed five major national projects. His achievements have been recognized with five Second Prize of the State Science and Technology Progress Award.

• Introduction.- Non-orthogonal plastic theory in unsteady environments.- Non-orthogonal elastoplastic model for soil in the steady environment.- Non-orthogonal elastoplastic model for soil in the unsteady water environment.- Non orthogonal plastic damage model of concrete.- Non-orthogonal elastoplastic model for concrete in the variable strain rate environment.- Unconstrained stress update algorithm for elastoplastic models.- Stress update algorithm based on numerical optimization methods.- Stress update algorithm based on numerical differentiation methods.- Stress update algorithm based on integral nonlocal method.

Dechun Lu: Professor Dechun Lu earned his PhD degree in 2006 from Beihang University and then worked as a teacher at the College of Architecture and Civil Engineering of Beijing University of Technology up to now. Prof. Lu is the leader of the Beijing Academic Innovation Team and the winner of the National Science Fund for Distinguished Young Scholars. His expertise spans multi-physical geotechnical engineering, computational geotechnical mechanics, urban underground engineering, and intelligent geotechnical engineering. He has published more than 100 academic papers in internationally renowned journals, such as Géotechnique, Journal of the Mechanics and Physics of Solids, Computer Methods in Applied Mechanics and Engineering, and Computers and Geotechnics. Prof. Lu has undertaken more than 10 national-funded projects in China, including 5 key projects. These projects have received over 30 million RMB in government funding. Prof. Lu has received numerous honors and awards, such as the Second Prize of the State Science and Technology Progress Award, the Second Prize of the State Natural Science Award, and the 15th Science and Technology Award for Chinese Youth.Xin Zhou: Dr. Xin Zhou earned his PhD degree in 2022 from the Beijing University of Technology. He subsequently joined the Department of Civil Engineering at Tsinghua University as a Postdoctoral Fellow. His work focuses on constitutive modeling of geomaterials, numerical methods of elastoplastic problems, and nonlocal methods. Over the past five years, he has published more than 20 papers in prestigious international journals. Dr. Zhou has led projects funded by the Youth Program of the National Natural Science Foundation of China and the Postdoctoral Research Foundation of China, among others. In recognition of his academic contributions, Dr. Zhou was selected for the 9th Young Elite Scientist Sponsorship Program by CAST and received the First Prize of the Natural Science Award (4/5) from the Chinese Society for Rock Mechanics & Engineering in 2023.Jingyu Liang: Dr. Jingyu Liang earned his PhD degree in 2020 from the Beijing University of Technology. Subsequently, he commenced his postdoctoral research at the Beijing University of Civil Engineering and Architecture, where he was subsequently promoted to the position of research associate in 2023. He has been involved in 5 national and provincial fund projects. Additionally, He has published more than·20 academic papers in renowned journals. Dr. Liang has been recognized for his contributions with awards, such as the “Excellent Doctoral Dissertation Award” (1/1) and the “Natural Science Prize” (5/5) from the Chinese Society for Rock Mechanics & Engineering. His primary research interests encompass geotechnical plasticity, urban underground engineering, frozen soil mechanics, and freezing method construction.Xiuli Du: Professor Xiuli Du is an academician of the Chinese Academy of Engineering. He earned his PhD degree from the Institute of Engineering Mechanics, China Earthquake Administration, in 1990. In 1996, he was exceptionally promoted to professor. In 2001, he joined the Beijing University of Technology as a faculty member up to now. Prof. Du has long been dedicated to research and practical work in earthquake-resistant engineering. He has authored over 400 research papers published in high-impact journals, both domestically and internationally. Prof. Du has led and completed five major national projects. His achievements have been recognized with five Second Prize of the State Science and Technology Progress Award.

• Introduction.- Non-orthogonal plastic theory in unsteady environments.- Non-orthogonal elastoplastic model for soil in the steady environment.- Non-orthogonal elastoplastic model for soil in the unsteady water environment.- Non orthogonal plastic damage model of concrete.- Non-orthogonal elastoplastic model for concrete in the variable strain rate environment.- Unconstrained stress update algorithm for elastoplastic models.- Stress update algorithm based on numerical optimization methods.- Stress update algorithm based on numerical differentiation methods.- Stress update algorithm based on integral nonlocal method.