Theoretical Analysis Of Strain Localization Based On Unified Strength Theory

The formation of shear band and the theory of progressive failure of soils are key topicsfocused greatly both in solid mechanics and geomechanics around the world. Softeningproperties of soil is the structurally reflection of localized deformation. Strain localizationbifurcation theory predicts to reveal the failure mechanism of rock and soil materials providedstrong basis. The unified strength theory which has be widely used in various engineeringfields has a unified mechanical model, a unified theory and a unified mathematical expression,that can be applicable to more than one kind of material and establishing the relationshipamong different theories. But unified strength theory that has be used in the shear bandformation mechanism, non-coaxiality constitutive model and strain localization bifurcationdiscriminant is still lack of intensive study, and have not considered the effects of mixedhardening model in three-dimensional stress space when in the study of strain localization inthe past. In this paper, the unified strength theory and the mixed hardening model are used tostudy the stress strain relationship and bifurcation point position of strain localization, and theangle of shear band. The main contents in this dissertation can be summarized as follows:(1) We deduce the unified strength theory when compressive stress is positive, the yieldfunction, the plastic potential function and the constitutive equation. Based on the revisedEuler integral, the constitutive equation of rate type integral program to simulate and verifydense sand true triaxial test and the clay plane strain tests was prepared, we obtain that when bis right value, the predicted results is closer to the experimental results than the existingliterature. For the dense sand and the clay, we can choose the strength theory when b=1andb=0.9to predict the relations of stress and strain.(2) In three-dimensional stress space, considering the effect of the third stress invarianton the non-coaxality of plastic deformation, based on the non-coaxial mixed hardening modeland non-coaxial elastoplastic constitutive model, the criterion of deformation localizationbifurcation in the true triaxial state and the shear band angle were deduced, then verify theresults by degradation. At the same time, combining with the basic steps of the revised Euler integral to simulate and comparing with existing results and test data, we verified thepreliminary rationality of the obtained bifurcation point criterion.(3) Based on the unified strength theory and the mixed hardening rule, the new loadingfunction, the plastic potential function, non-coaxiality constitutive model, strain localizationbifurcation point criterion and the angle of shear band were established, then the dense sandtrue triaxial test and the clay plane strain tests were simulated and verified. We concluded thatthe introduction of non-coaxiality does not change the stress-strain relationship of soilproperties, For the dense sand and the clay, we can choose the strength theory when b=1andb=0.9to predict the bifurcation point and the angle of shear band.