The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the ...The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the sense of weak Hopf π-coalgebras.Let H be a finite type weak Hopf π-coalgebra,and A a weak right π-H-comodule algebra.It is constructed that a Morita context connects A#H＊ which is a weak smash product and the ring of coinvariants AcoH.This result is the generalization of that of Wang＇s in the paper ＂Morita contexts,π-Galois extensions for Hopf π-coalgebras＂ in 2006.Furthermore,the result is important for constructing weak π-Galois extensions.展开更多
A small strain unified hardening(SSUH) model is proposed in the present study to tackle the small strain behavior of clay. The model is an extension of the unified hardening(UH) model for overconsolidated(OC) clays ac...A small strain unified hardening(SSUH) model is proposed in the present study to tackle the small strain behavior of clay. The model is an extension of the unified hardening(UH) model for overconsolidated(OC) clays accounting for the small strain stiffness. The new features of the SSUH model over the UH model include:(a) a new elastic hysteretic stress-strain relationship to evaluate the stiffness degradation at small strains and to generate the hysteresis loop under cyclic loading condition;(b) a revised unified hardening parameter to enhance the plastic stiffness at small strains; and(c) a new overconsolidation parameter, which is crucial to make the UH model working with the elastic hysteretic stress-strain relationship effectively. With these enhancements, the SSUH model can describe a high initial stiffness and the highly nonlinear stress-strain relationship at small strains, in addition to the shear dilatancy and strain hardening/softening behaviors of OC clays at large strains. In comparison with the Modified Cam-clay(MCC) model, the proposed model needs two more small strain related parameters, which can be easily obtained from laboratory tests. Finally, some drained triaxial compression tests at large strains, drained triaxial compression/extension tests at small strains, an undrained compression test at small strains and a drained cyclic constant radial stress test are employed to validate the new model.展开更多
基金The Scientific Research Innovation Project for College Graduates in Jiangsu Province(No.CXLX_0094)
文摘The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the sense of weak Hopf π-coalgebras.Let H be a finite type weak Hopf π-coalgebra,and A a weak right π-H-comodule algebra.It is constructed that a Morita context connects A#H＊ which is a weak smash product and the ring of coinvariants AcoH.This result is the generalization of that of Wang＇s in the paper ＂Morita contexts,π-Galois extensions for Hopf π-coalgebras＂ in 2006.Furthermore,the result is important for constructing weak π-Galois extensions.
基金supported by the National Program on Key Basic Research Project of China(973 ProgramGrant No.2014CB047001)+2 种基金the National Natural Science Foundation of China(Grant Nos.1127203151179003 and 41372285)Beijing Natural Science Foundation(Grant No.8132042)
文摘A small strain unified hardening(SSUH) model is proposed in the present study to tackle the small strain behavior of clay. The model is an extension of the unified hardening(UH) model for overconsolidated(OC) clays accounting for the small strain stiffness. The new features of the SSUH model over the UH model include:(a) a new elastic hysteretic stress-strain relationship to evaluate the stiffness degradation at small strains and to generate the hysteresis loop under cyclic loading condition;(b) a revised unified hardening parameter to enhance the plastic stiffness at small strains; and(c) a new overconsolidation parameter, which is crucial to make the UH model working with the elastic hysteretic stress-strain relationship effectively. With these enhancements, the SSUH model can describe a high initial stiffness and the highly nonlinear stress-strain relationship at small strains, in addition to the shear dilatancy and strain hardening/softening behaviors of OC clays at large strains. In comparison with the Modified Cam-clay(MCC) model, the proposed model needs two more small strain related parameters, which can be easily obtained from laboratory tests. Finally, some drained triaxial compression tests at large strains, drained triaxial compression/extension tests at small strains, an undrained compression test at small strains and a drained cyclic constant radial stress test are employed to validate the new model.
