基于SMP破坏准则的土体弹塑性动力本构模型

利用土体的塑性流动理论,提出了用于描述饱和砂土动力反应性质的弹塑性本构模型。土体总的变形由三部分组成:即弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变。土体在初始加载与卸载和重新加载阶段性质的差别通过采用不同的模型参数加以反映。该模型能够较为准确地描述饱和砂土在单调加载和循环加载条件下的反应性质。     

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

Two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate (time)-dependent inelastic behavior of structural metals in the absence of recovery and aging. The structure of the model is close to the unified theories but contains essential differences. The properties of the model are delineated by analytical means and numerical experiments.It is shown that the model reproduces almost elastic regions upon initial loading and in the unloading regions of the hysteresis loop. Under loading, unloading and reloading in strain control the model simulated the experimentally observed sharp transition from nearly elastic to inelastic behavior. These properties are essential for modeling mean stress effects in tension-tension strain cycling. When a formulation akin to existing unified theories is adopted the almost elastic regions reduce to points and the transition upon reloading is very gradual.For different formulations the behavior under sudden increases/decreases of the strain rate by two orders of magnitude is simulated by numerical experiments and differences are noted.The model presently represents cyclically neutral behavior and contains three constants and two positive, decreasing functions. It is described how these constants and functions can be determined from tests involving monotonic loading with strain rate changes and relaxation periods.     

Constitutive equation of plastic deformation of a zn-al alloy under tension-tension strain controlled cyclic loading

A constitutive equation of plastic deformation under tension-tension, strain controlled cyclic loading condition was derived from the transition state theory of rate processes. It was considered that the rate of plastic flow during the (tension-tension) cyclic deformation is controlled by a system of two consecutive energy barriers and that the material structural characteristics remain constant during cyclic deformation. The study revealed that within the stress, time, and temperature range, where the backward activations over the energy barriers are negligibly small, tension-tension, strain controlled cyclic deformation is essentially a stress relaxation process. The theory described well the cyclic deformation behavior of a near eutectoid ZnAl alloy. The constitutive parameters determined from the analysis of stress relaxation and tension-tension, strain controlled cyclic loading experimental results were identical. Consequently, it was recommended that stress relaxation can be used to determine the material structural characteristics which can then be used to predict the tension-tension, strain controlled cyclic deformation behavior of the alloy, using the constitutive equation derived in this report.     

Transient growth of a micro-void in an infinite medium under thermal load with modified Zerilli–Armstrong model

In this paper, the transient growth of a spherical micro-void under remote thermal load in an infinite medium is investigated. After developing the governing equations in the problem domain, the coupled nonlinear set of equations is solved through a numerical scheme. It is shown that a small cavity can grow rapidly as the temperature increases in a remote distance and may damage the material containing preexisting micro-voids. Conducting a transient thermal analysis simultaneously with a structural one reveals that the material may experience a peak in the radial stress distribution, which is five times larger compared to the steady-state one, and shows the importance of employing a time-dependent approach in this problem. Furthermore, utilizing a sensible yield criterion, i.e., the modified Zerilli–Armstrong model, discloses that there is a large discrepancy in the results assuming perfectly plastic constitutive model. It is verified that the obtained results do not violate the proportional loading conditions that is the basis for development of the governing formulation in this work. The monotonic alteration of the plastic strain components versus time proves that we do not encounter any elastic unloading during the void growth, which is a basic assumption in the present work. Some numerical examples are also presented to investigate the features of the presented model.     

Constitutive equations optimized for determining strengths of metallic alloys

We investigate compatibilities of three constitutive equations, the Hollomon, the Swift, and the Voce equations for determination of yield and ultimate tensile strengths based on tensile true stress–strain curves of 27 metal alloys including those with power-law type and linear-type strain-hardening. We analyze each constitutive equation in terms of yield strength determined by the intercept of the linear elastic loading curve and plastic flow curve and ultimate tensile strength evaluated by the concept of instability in tension. We found that the describing plastic flow is very sensitive in determination of the yield strength and tensile strength from parameters of constitutive equation. Voce equation gives estimate yield strength and tensile strength better than Hollomon and Swift equations.     

A new boundary element technique without domain integrals for elastoplastic solids

A simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements, namely, to use the Green's functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions, respectively. In this way, domain integrals are completely avoided in the boundary integral equations. Though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation, the elastoplastic analysis reduces, in essence, to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations (the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law). Numerical examples, using J₂‐flow theory with linear hardening, demonstrate that the proposed method retains all the advantages related to boundary element formulations, is stable and performs well. The method presented is for simplicity developed for the associative flow rule; however, a full derivation of Green's function and boundary integral equations is also given for the general case of non‐associative flow rule. It is shown that in the non‐associative case, a domain integral unavoidably arises in the formulation. Copyright © 2005 John Wiley & Sons, Ltd.     

A stability analysis of the uniaxial viscoplasticity theory based on overstress

In the development of a viscoplasticity theory without a yield surface and without a loading and unloading condition, the properties of a uniaxial constitutive model consisting of two coupled nonlinear differential equations are examined. The critical points of the system of differential equations are evaluated for monotonic loading, creep and relaxation conditions and are shown to be stable. The conditions necessary for the elimination of stable but oscillatory solutions are given. Also given are the asymptotic solutions valid near the critical points. The analytical predictions are confirmed by numerical results.     

On the theory of plasticity with smooth surfaces of loading

The well-known theories of plastic yield with smooth surfaces of loading are developed and generalized on the basis of a model of a nonlinear anisotropically hardened medium based on the concept of slip. Unlike the commonly used procedure of application ofa priori known laws of hardening (variation of the surface of loading in the process of plastic deformation), we suggest a method for the experimental evaluation of a universal function of the material appearing in the constitutive equations for arbitrary complex loading processes including elastic unloading and plastic deformation in the direction opposite to the initial one. The constitutive equations are relatively simple and, hence, can easily be used for the statement and solution of boundary-value problems in the theory of plastic yield. Dnepropetrovsk State University, Dnepropetrovsk. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 6, pp. 63–70, November–December, 1997.     

Constitutive equation of a non-simple elastic plastic material

Summary The mechanical response predicted by the constitutive equation of a non-simple elastic material is considered in relation to the total strain behaviour of an elastic-plastic solid extensively deformed in the range of plastic strain. Both loading and unloading are considered in relation to the range of total elastic-plastic strain. In the absence of appropriate experimental studies, comparison of the predictions of the proposed constitutive equation of a non-simple elastic material, when applied to the work-hardening behaviour of the material, has been restricted to a study of the characteristic stress-strain behaviour of a strain hardening material. This has centred on the correlation of stress-strain curves characteristic of the mechanical response of a material tested in simple compression, simple torsion and pure shear with the object of obtaining a universal stress-strain curve.With 1 Figure     

An analysis procedure for plane strain contained plastic deformation problems

An analysis procedure for the plane strain contained plastic deformation problem is proposed. It is shown that, when piecewise-linear elastic–plastic laws are adopted, the plane strain problem can be formulated in terms of exactly the same variables appearing in a plane stress problem, even if the transverse stress and plastic strain components do not vanish in general. The two problems are governed by the same equilibrium and compatibility equations and the only difference is in the elastic–plastic material constitutive laws, in complete analogy with the linear elastic case. The problem is discretized by using a compatible finite element model on which basic elastic-plastic constitutive laws for an element in plane strain conditions can be obtained. When the assemblage is performed, the resulting set of governing relations presents a mathematical structure which enable, for solution, techniques efficiently used for truss and frame problems. Some solutions for axisymmetric tubes subjected to pressure and temperature gradients are illustrated.     

A plastic shakedown constitutive curve based on uniaxial ratcheting behavior of 304 stainless steel at room temperature

On the basis of the Bauschinger effect, a relationship between the elastic space defined in this study and the accumulated plastic strain is measured in uniaxial ratcheting tests of 304 stainless steel at room temperature. According to this relationship, a new model of uniaxial ratcheting is established and used to simulate uniaxial ratcheting behavior. The results of simulation agree well with the experimental results. These results demonstrate that the relationship between the elastic space and the accumulated plastic strain plays an important role in uniaxial ratcheting simulation. Furthermore, by taking into account the interaction of ratcheting and viscoplasticity, the relationships among elastic space, accumulated plastic strain and loading cases are discussed. It can be seen that, when the stress ratio R of valley stress versus peak stress is not less than zero, the accumulated plastic strain is a function of the peak stress. So, a constitutive curve is obtained to describe the stable states of plastic shakedown for 304 stainless steel material under the stress ratio R ≥ 0. It can be used to determine the accumulated plastic strain of engineering structures under cyclic loading only by an elastic–plastic analysis.     

混凝土坝地震动力损伤分析

基于塑性损伤本构理论,将损伤变量作为内变量,在Drucker-Prager本构模型中引入损伤变量,考虑材料损伤引起的材料劲度的退化,基于非关联流动法则计算材料的塑性应变,根据材料的有效塑性应变计算损伤量,考虑到张开裂缝闭合时材料弹性劲度的恢复,推导了考虑塑性损伤的混凝土动态本构关系,并给出了内变量的计算步骤和动力方程的迭代格式。最后利用建立的动态本构模型对Koyna重力坝进行了非线性地震响应时程分析,并给出了关键时刻坝体最大受拉损伤分布,结果表明在坝颈和坝基处出现了较大的损伤,坝颈处的损伤最终形成由下游向上游的开裂破坏,这与该坝的实际震害较为一致。     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.     

An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule

Predicting the unloading and/or cyclic deformation behavior of polymers is a challenge for most nonlinear viscoelastic constitutive models. Experimental data of an epoxy polymer under uniaxial loading/unloading and two other types of cyclic loadings are used to assess the predictive capabilities of three types of nonlinear viscoelastic models. A general loading/unloading criterion and a switching rule, proposed recently by the authors, are further modified and incorporated into each of the three models. For each model, predictions by both the original formulations and that incorporating the proposed loading/unloading rule are compared with the test data. It is clearly shown that such a rule is essential to correctly simulate the unloading and cyclic loading behavior of polymers. By introducing such a rule to constitutive models, the quantitative predictions can be improved, to various degrees of success, with respect to cyclic deformation features such as ratcheting under cyclic loading with a mean stress and stress relaxation under cyclic straining with a mean strain.     

An integration scheme for Prandtl-Reuss elastoplastic constitutive equations

We investigate the Generalized Midpoint Rule for the time integration of elastoplastic constitutive equations for pressure-independent yield criteria. The incremental equations are divided into one scalar hydrostatic pressure/dilation rate equation, and a stress deviator/strain rate deviator tensorial equation, the solution of which reduces to one single scalar equation in the plastic multiplier. The existence and uniqueness of an incremental solution is discussed. The pressure/deviator decomposition is the basis for reduced integration of the pressure term in the Principle of Virtual Work, in order to avoid locking and spurious pressure oscillations. It is also shown that an optimal choice of the parameter of the Midpoint Rule can be computed by reference to the analytical solution of the equations assuming no work hardening. A benchmark test shows that this choice allows increased time steps. This formulation is applied to two classical problems: bulging of a tube under internal pressure and tension test on a notched specimen, and a comparison with the analytical solution is performed. Finally, the hypothesis which sustains these formulations of elastoplasticity (constant strain rate during an increment) is discussed with reference to elastic unloading and residual stress computation.     

On the Elastic and Plastic Strain Decomposition in Granular Materials

An impressive number of constitutive relations have been developed in the past few decades. With respect to the class of elastoplastic phenomenological models, elastic and plastic strain decomposition is generally stated as a basic assumption, so as to treat the elastic (i.e., recoverable) and plastic (i.e., unrecoverable) parts of the strains separately. For incrementally nonlinear relations, this decomposition is not possible. In the first part of this paper a detailed discussion of elastic and plastic decomposition is presented. Then the paper expands the debate on this crucial point by addressing the question of defining elastic (or plastic) deformation specifically for granular materials, considering two complementary approaches. An incrementally nonlinear model is used first and then a multi-scale approach is considered to examine the compatibility of this partition from a micromechanical point of view, with the usual definition of both elastic and plastic incremental strains. Finally, micro-structural considerations show that only a fraction of the elastic strain energy can be recovered, whatever the unloading path, after an incremental loading path inducing both elastic and plastic mechanisms.     

Constitutive equation for a class of non-simple elastic materials

Summary Initial yield is the upper limit of the purely elastic deformation behaviour of an elasticplastic solid. Thus the choice of the constitutive equation describing the purely elastic deformation behaviour determines the initial yield function. The constitutive equation of a simple elastic material is only compatible with von Mises yield criterion, a conclusion which applies also to the classical infinitesimal theory. A more general form of constitutive equation for an elastic material is formulated by way of the concept of a stress loading function, the proposed constitutive equation being quadratic in the stress. The two loading coefficients associated with the stress loading function are assumed to be deriveable from a generalised isotropic yield criterion which is now assumed to hold over the entire range of deformation, and in this context is referred to as the stress intensity function. The proposed constitutive equation has the same representation in terms of the left Cauchy-Green deformation tensor as that for a simple elastic material. Using the Cayley-Hamilton theorem, this representation is rearranged and expressed in terms of a measure of finite strain which is defined to be one quarter of the difference between the left Cauchy-Green deformation tensor and its inverse. In this way the strain properties of the proposed constitutive equation are formulated by way of the concept of a strain response function. The three response coefficients associated with the strain response function are assumed to be deriveable from a generalised, isotropic, strain intensity function. The predictions of the proposed constitutive equation are considered in the context of the combined stressing of a thin sheet of incompressible material. In this way, it is shown that the proposed constitutive equation is not limited in the same way as the constitutive equation of a simple elastic material.