Tseng N.T., Lee G.C.

Based on the existence of a yield surface and a memory surface which represents the maximum stress state the material ever experienced, a plasticity model is proposed to describe the inelastic behavior of metal. By choosing the initial locations and sizes of these two surfaces based on the internal structure and the loading history of materials, theoretical results have been obtained. These results compare well with available experimental observations on cyclic creep, cyclic stress relaxation and other transitory phenomena of strain softening materials under generalized cyclic loading conditions. The inelastic behavior of annealed copper subjected to nonproportional strain paths can also be predicted by the proposed model.

Yang B., Dafalias Y.F., Herrmann L.R.

A macroscopic plasticity constitutive model employing the concept of a contracting Bounding Surface is formulated for plain concrete. The concrete strength fc is the only necessary input material constant. The model is used to predict the stress‐strain relations for uniaxial, biaxial, and triaxial compression states for both monotonic and cyclic loading conditions including post‐failure states for different strength concretes. The results are successfully compared with available experimental data.

Mróz Z., Norris V.A., Zienkiewicz O.C.

This Paper extends the previous work (Mróz, Norris and Zienkiewicz, 1978a) where an anisotropic hardening model for soils was proposed, taking into account both isotropic hardening due to porosity changes and anisotropy effects induced by the initial consolidation process. The analysis is restricted to the case of triaxial state for which two principal stresses are equal. The incremental relations are derived and applied to study the drained and undrained material behaviour after isotropic and anisotropic K0 consolidation of clays. The material response under cyclic loading is also discussed. The predicted inelastic behaviour is compared with available experimental results for kaolin and Weald clays for which the material parameters are also identified. Further improvements of the model are indicated, Cette étude prolonge le travail antérieur (Mróz, 1978a) réalisé par Norris et Zienkiewicz dans lequel un modèle anisotrope de durcissement pour sols était proposé, tenant compte du durcissement isotrope par suite de changements de porosité ainsi que les effets induits par le procédé de consolidation instantanée. L'analyse est limitée au cas de l'étreinte triaxiale dans laquelle deux contraintes principales sont égales. Les relations incrémentales sont dérivées et appliquées à l'étude du comportement de la matière drainée et non drainée après la consolidation K0 isotrope et anisotrope des argiles. Le comportement de la matière sous chargement cyclique est aussi examiné. Le comportement non élastique prédit, est comparé aux résultats expérimentaux obtenus sur le kaolin et les argiles de Weald pour lesquels les paramètres de matière sont aussi identifiés. D'autres améliorations du modèle sont indiquées.

Fardis M.N., Alibe B., Tassoulas J.L.

A simple time-independent, mathematical model is proposed for the monotonic and cyclic behavior of concrete under multiaxial stress conditions. An essential feature of the model is a bounding surface in stress space, which is a function of ϵ\N\dm\da\dx = the maximum strain experienced by the material to the present time. The “yield” surface degenerates into the current stress point. Strain increments dϵ\N\di\dj are considered completely plastic and are computed by superposition of: (1) An isotropic component, proportional to the hydrostatic stress increment; and (2) deviatoric and isotropic components, proportional to the octahedral shear stress increment. The plastic modulus for calculation of the latter strain components is a function of: (1) The distance of the stress point from the bounding surface, measured along the direction of the stress increment dσ\N\di\dj; and (2) ϵ\N\dm\da\dx. This functional dependence of the plastic modulus and the fact that the bounding surface shrinks as ϵ\N\dm\da\dx increases allow realistic modeling of the nonlinear unloading and reloading behavior of concrete.

McVay M., Taesiri Y.

The influence of stress path on the stress-strain behavior of a Florida sand subject to repetitive moving wheel loads is investigated in the laboratory with conventional triaxial equipment. A conventional resilient modulus test with only cyclic varying compressive loads and a moving wheel stress path involving both extension and compressive loads determined from an elastic solution were examined at different initial confining pressures. The tests showed that excursions of applied extension loading followed by compression loading resulted in anisotropic material behavior. This, in turn, influenced both the cyclic permanent strain (rutting) build-up as well as the resilient (distortion) behavior of the material for initial confining pressures below approximately 40 psi (276 kPa). It was concluded that, in order to model both the distortion and rutting characteristics of a sand, improved constitutive relationships over the simple linear elastic theory are warranted. A bounding surface plasticity model was subsequently developed based upon both the plastic shear dilation and volumetric behavior of the sand. The predicted model response agreed both qualitatively and quantitatively for the tests investigated.

Dafalias Y.F.

A macroscopic formulation of large deformations elastoplasticity with tensorial structure variables is presented. The novel features are the effect of constitutive relations for the plastic spin and, to a lesser degree of importance, of elastically embedding the structure variables. The plastic spin constitutive relations are obtained for different kinds of initial and induced anisotropies on the basis of the representation theorems for isotropic second-order antisymmetric tensor-valued functions, and their role is illustrated by the analysis of several examples at large homogeneous deformations. In particular the analysis of simple shear with nonlinear kinematic hardening of the evanescent memory type provides, on the basis of the second Liapunov method for stability, conditions on the material constants for the occurrence or not of stress oscillations with monotonically increasing shear strain.

Bruhns O.T., M�ller R.

An internal variable theory of rate-independent plasticity is presented incorporating a combination of classical models of kinematic hardening as well as isotropic hardening. In addition to the yield surface a second “bounding surface” has been introduced to accommodate to problems with non-radial loading paths. The behaviour of this model unter uniaxial and complex loading has been tested and compared with experimental results and other theoretical predictions.

Valanis K.C., Lee C.

In this paper we presented a comprehensive review of recent developments of the endochronic theory of plasticity. The endochronic theory was first proposed by Valanis in 1971 with the aim of circumventing some of the difficulties associated with classical theories of plasticity, such as the concept of a yield surface and its motion in the stress space, criteria for unloading, hardening rules, etc. The theory is developed by using irreversible thermodynamics of internal variables. In the early version of the theory the intrinsic time was defined as a measure of length in strain space. This version is now called the simple endochronic theory. The derived constitutive equations have been applied with success to a number of problems of practical interest, e.g. cyclic response, cross hardening, cross ratcheting, etc. However, it has been shown by the first author that the simple theory leads to an unloading response which is not elastic at its onset. As a consequence infinitesimal hysteresis loops in the first quadrant of the stress-strain space are open, in disagreement with observed behavior in metals. Recently Valanis introduced a new intrinsic time scale which is a measure of length in the plastic strain space. As a result, a new model of endochronic theory has been developed which leads to closure of hysteresis loops in the small as well as the large. It is also shown that the new model predicts the existence of a yield surface. Hardening rules proposed in the classical theory of plasticity appear as special results. It is also shown that the constitutive equations derived from the new model are very powerful in their quantitative prediction of steady cyclic response under constant strain amplitude conditions. In the case of cyclic creep the theory predicts the dependence of cumulative axial creep on the plastic shear strain amplitude but that it overestimates the dependence of the latter on the number of cycles. At the present time we think that this difficulty cannot be overcome on the basis of an isotropic theory. This suggests a future area of investigation and application of the endochronic theory.

Hashiguchi K.

Constitutive equations of elastoplastic materials with anisotropic hardening and elastic-plastic transition are presented by introducing three similar surfaces, i.e., a loading surface on which a current stress exists, a subyield surface limiting a size of the loading surface and a distinct-yield surface representing a fully plastic state. The assumption of similarity of these surfaces leads the derived equations to remarkably simple forms. Also a more general rule of the kinematic hardening for the distinct-yield surface is incorporated into the constitutive equations. While they seem to be applicable to various materials, special constitutive equations of metals, for example, are derived from them and are compared with experimental data on a cyclic uniaxial loading of aluminum. A close correlation between theory and experiment is observed in this comparison.

Dafalias Y.F.

Dafalias Y.F.

The concept of the bounding surface in stress space is presented, and a novel unified formulation of the corresponding rate independent constitutive plastic relations is given. The salient feature of the bounding surface approach is that plastic deformation occurs for stress states within the surface at a rate which depends on the proximity between the current stress point and an “image” stress point on the bounding surface defined by a proper mapping rule. The material exhibits a memory of past loading history by means of plastic internal variables, and a projected “foresight” by means of the distance between actual and “image” stress points. Particular models and corresponding applications are presented within the general framework.

Hashiguchi K.

Constitutive equations of elastoplastic materials with an elastic-plastic transition observed in the loading state after a first yield are presented by introducing a new parameter denoting the ratio of the size of a loading surface in the transitional state to that of a yield surface in the classical idealization which ignores the transitional state. These equations involve a reasonably simplified rule for the kinematic hardening. They would describe reasonably not only the hardening behavior but especially the softening behavior which requires our careful consideration about the elastic-plastic transition. From these equations, moreover, we derive plastic constitutive equations specifically of metals and granular media which exhibit very different plastic behaviors. Besides, brief discussions are provided concerning the existing constitutive equations describing the elastic-plastic transition.

Bažant Z.P.

Studied are second-order work inequalities for stability of plastic strain increments and fracturing stress decrements. It is found that the positiveness of the second-order work during small loading cycles does not necessarily require normality; it also allows non-normal plastic strains or fracturing relaxations which do no work, as well as non-normal ones which always do non-negative work. The latter ones include plastic strains and fracturing relaxations that are tangential to the loading surface. It is shown that the endochronic theory follows from Drucker's postulate by the same arguments as classical plasticity. The endochronic loading surface has the significance of separating the directions for which Drucker's postulate is satisfied from those for which it is not, whereas in classical plasticity it separates the stress increment directions for which the plastic strain increment vector points outside the loading surface from those for which it would point inward. The incremental linearity of classical plasticity is shown to be a tacitly implied hypothesis which does not follow from Drucker's postulate and the existence of the loading surface. Various incrementally nonlinear stress-strain relations satisfying Drucker's postulate, both such that do and do not obey normality, are demonstrated. Furthermore, it is found that for frictional materials there exists, in addition to Drucker's (or Il'yushin's) postulate, another inequality that also suffices for stability and reflects the fact that a release of elastic energy blocked by friction or by resistance to fracturing due to compression cannot cause instability. This enlarges the domain of all stable stress increment vectors from a halfspace to a reentrant wedge. The corresponding plastic strain increment vectors have no unique direction and occupy a fan, one boundary of which is the normal vector. Dependence of the second-order work in loading cycle upon the angle between the strain increment vector and the normal is useful for comparing various theories. For the incrementally linear vertex model one needs to introduce at the tangential direction a discontinuity in this dependence. Finally, some related questions of uniqueness or continuity of response are discussed, particularly for the case of a staircase path in strain space approaching a straight path as the number of stairs tends to infinity. For endochronic theory as well as some vertex models and for plasticity with a corner on the loading surface, the response to the staircase path in the limit does not approach the response to the straight path. Although this is not physically unreasonable, it is nevertheless possible to slightly adjust the definition of intrinsic time so that continuity (uniqueness) is achieved.

Christoffersen J., Hutchinson J.W.

A class of phenomenological flow theories of plasticity is proposed which models time-independent incremental behavior at a corner of the yield surface of a polycrystalline metal. The proposal is consistent with the physical theories of plasticity based on single crystal slip. Conditions for convexity, ensuring invertibility of the incremental relations, are derived. The simplest candidate, called J 2 corner theory, coincides with the J 2 deformation theory of plasticity for nearly proportional stress increments and incorporates a smooth transition to elastic unloading for increasingly non-proportional increments. The theory is applied to the bifurcation and imperfection-sensitivity analysis of necking in a thin sheet. For this example, like many others involving bifurcation in the plastic range, the corner theory appears to circumvent some of the difficulties associated with use of the standard phenomenological plasticity laws.

Phillips A., Lee C.

The concepts of yield surface and loading surface at room temperature and elevated temperature are discussed and experimental results on pure aluminum in support of these concepts are presented. Recommendations for future experimental research are presented.

Li L., Xu M., Lu H., Zhang Y., Guo Z.

Chen Z., Xiong Z., Chen X., Tian P., Niu J., Xie Z.

Xie W., Zhang Q., Ye G., Zhu W., Zhang F.

Zhang A., Dafalias Y.F., Wang D.

Ercolessi S., Fierro T., Santucci de Magistris F., Fabbrocino G.

Song X., Pashazad H.

Cheng X., Liu M., Li Q., Lu D., Du X.

In the transitional waters of 30 to 90 m, jacket foundation has great application potential due to its advantages of light weight, high structural stiffness and good stability. In addition to the long-term normal wind and waves, the wind turbines will suffer from typhoons and waves in extreme bad weather. Currently, research on the dynamic response of jacket supported OWTs in clay under severe typhoons is very rare. The study develops a numerical method to calculate the dynamic response and fatigue damage of jacket supported OWTs under typhoon loads by incorporating a simplified single bounding surface model of clays. Through three-dimensional numerical analysis across various scenarios, this study investigates the dynamic response characteristics of jacket supported OWTs on clay soil. It also examines the impact of wind-wave coupling effects on the fatigue damage experienced by these structures. It was found that severe typhoons can lead to notable permanent tilting of the jacket foundation, thereby failing to meet the requirements of normal serviceability limits. The most critical nodes of the OWT are situated at the mudline of the pile foundations, followed closely by the bottom of the tower structure. The most significant fatigue damage occurs for wind-wave co-directional coupling loading along the orthogonal direction of the OWT. The research outcomes provide valuable guidance for enhancing the typhoon-resistant design of jacket supported OWTs.

Liang J., Ma C., Su Y., Lu D., Du X.

Monforte L., Rouainia M., Helm P., Najdi A., Glendinning S.

Linear geotechnical infrastructure undergoes seasonal volumetric changes due to climatic and hydrological cycles, leading to progressive failure of the soil mass and performance deterioration. The magnitude of the seasonal cycles of pore water pressure is expected to be increased by more extreme and frequent wet and dry events, leading to an accelerated deterioration process. Advanced constitutive models for unsaturated soils able to reproduce the observed behaviour are therefore required. A new advanced constitutive model for the hydro-mechanical behaviour of unsaturated soils is formulated and implemented within the framework of elasto-plasticity with internal variables. The effect of recent suction history is incorporated using a kinematic hardening constitutive model augmented by elements of bounding surface plasticity, initially developed for saturated soils, which is further extended to the unsaturated range through the inclusion of a loading collapse curve. The model permits the retention of information on recent stress history, allows prediction of irrecoverable stiffness and strength loss, and replicates the hysteretic response during cyclic loading. The model has been implemented in a constitutive driver using an implicit numerical scheme and its predictive capabilities are demonstrated by performing numerical simulations of a series of laboratory experiments involving complex sequences of isotropic loading, wetting, drying and shearing stages.

Cheng X., Xing J., Wang G., Lu D., Du X.

Wang L., Zhang T., Cheng X., Xu W., Shen Z., Rui S., Tian Y.

Yu J., Cao J., Chen Z., Zhu J., Zhang Y., Yu P.

The development of a constitutive model for soil–structure contact surfaces remains a pivotal area of research within the field of soil–structure interaction. Drawing from the Gudehus–Bauer sand hypoplasticity model, this paper employs a technique that reduces the stress tensor and strain rate tensor components to formulate a hypoplastic model tailored for sand–structure interfaces. To capture the influence of initial anisotropy, a deposition direction peak stress coefficient is incorporated; meanwhile, a friction parameter is introduced to address the surface roughness of the contact. Consequently, a comprehensive hypoplastic constitutive model is developed that takes into account both initial anisotropy and roughness. Comparative analysis with experimental data from soils on contact surfaces with diverse boundary conditions and levels of roughness indicates that the proposed model accurately forecasts shear test outcomes across various contact surfaces. Utilizing the finite element software ABAQUS 2021, an FRIC subroutine was developed, which, through simulating direct shear tests on sand–structure contact surfaces, has proven its efficacy in predicting the shear behavior of these interfaces.

Cheng X., Lu D., Wang P.

AbstractThe p-y method as a simplified analysis tool has been widely used to analyze the behavior of laterally loaded piles. This chapter develops a novel cyclic p-y elastoplastic model within the framework of the single-surface bounding surface theory. The model can capture the soil stiffness degradation during cyclic loading by incorporating the cumulative plastic displacement to an interpolation function of the elastoplastic resistance coefficient.

Cheng X., Lu D., Wang P.

AbstractA simple single bounding surface constitutive model is developed to predict the undrained behaviors of saturated clays under cyclic loads. The new model does not involve complex kinematic hardening rules, and it is only required to memorize important stress reverse events; therefore, the simplicity should be the largest advantage of the model. A new interpolation function of an elastoplastic shear modulus is proposed based on bounding surface theories.

Ng C.W., Zhang Q., Guo H., Ni J., Wang Y., Leung A.K., Zhou C.