adina土的模型(双语).doc

3.9 Geotechnical material models 地质材料模型3.9.1 Curve description material model曲线描述的材料模型 The curve description model can be employed with the 2-D solid (plane strain and axisymmetric) and 3-D solid elements. 曲线描述的材料模型可以用于二维实体（平面应变及轴对称的）和三维实体单元 The curve description model can be used with the small displacement and large displacement formulations. In all cases, small strains are assumed. When used with the small displacement formulation, a materially-nonlinear-only formulation is employed, and when used with the large displacement formulation, a TL formulation is employed.曲线描述的材料模型可以用于大变形和小变形分析。在任何情况下都假设为小应变。当用于小应变分析时，使用材料非线性分析；当使用大应变分析时使用的是TL分析。The curve description model is a simple incremental stress strain law used to represent the response of geological materials. The model describes the instantaneous bulk and shear moduli as piecewise linear functions of the current volume strain, as shown in Fig. 3.9-1. An explicit yield condition is not used and whether the material is loading or unloading is determined by the history of the volume strain only.曲线 描述模型是单值的应力应变规律，通常用来表示地质材料。模型用实时体积的分段线性函数描述了材料的瞬态体积和剪切模量，如图3.9.1所示。不需要直接的屈服条件并且是否受荷取仅仅取决于材料体积应变得历史。 To present the governing constitutive relations, lettotal strains (the left superscript t always refers to time t) 总应变（左上标t表示时间t）incremental strains 应变增量mean strain (negative in compression) 平均应变（忽略压缩）= incremental mean strain 平均应变增量= deviatoric strains 偏应变incremental deviatoric strains 偏应变增量total stresses (negative in compression) 全应力= incremental stresses 应力增量= mean stress 平均应力= incremental mean stress 平均应力增量minimum mean stress ever reached 曾经达到的最小平均应力deviatoric stresses 偏应力 = incremental deviatoric stresses 偏应力增量shear and bulk moduli 剪切及体积模量The incremental stress-strain relations using the curve description model are then使用曲线描述的应力-应变增量关系是：23The instantaneous bulk and shear moduli, tK and tG, are functions of the loading condition, and the volumetric strainis defined as瞬时体积及剪切模量和是荷载条件的函数，并且体积应变定义如下：where is the volumetric strain (three times the mean strain and taken positive in compression) due to the gravity pressure and is the mean strain at time t. Defining emin as the minimum mean strain ever reached during the solution, we have that the material is loading if， and the material is unloading if i.e.,式中是有重力引起的体积应变（3倍的平均应变并且压缩为正），是t时刻的平均应变，定义为求解过程中达到的最小平均应变，如果材料为受荷的，如果材料为不受荷的。例如：及 Note that the loading conditions for both the bulk and the shear moduli are determined by the history of only. The values of tKLD, tKUN, and tGLD are obtained using the curves in Fig. 3.9-1, and the modulus注意体积和剪切模量的荷载条件仅仅是由得历史绝定的。、及的值是通过图3.9.1的曲线获得，系数The incremental solution at time t is obtained using the equationst时刻增加的结果通过下面的公式得到： 及To obtain and , we check whether the loading or unloading conditions are active by comparing the current volumetric strains and previous volumetric strains. To start the procedure at time 0, loading conditions are assumed. It should be noted that the stresses at time are calculated using the material moduli pertaining to time t.为获得和 ，我们通过比较当时的和以前的体积应变来检查受荷和非受荷状况是否起作用。在时刻0开始程序，假定为受荷状况。可以注意到时刻的应力是通过t时刻的材料模量计算出来的。An important additional analysis option is that the material can weaken under loading conditions if tensile stresses exceed preassigned values. Since the curve description model has been developed primarily for the analysis of geological materials, the material weakening is assumed to occur once the principal tensile stresses due to the applied loading exceed the in-situ gravity pressure p (taken positive). The gravity pressure p is calculated as where hi are the element interpolation functions and pi is the pressure at the element nodes. The nodal pressure pi is calculated as ,where is the material density and Zi the nodal Z coordinate, which coincides with the vertical direction. The material weakening can be included using a tension cut-off model or a cracking model.一个重要的附加分析选项是在荷载状态下如果拉应力超过许可值材料会被削弱。由于曲线描述的模型主要为地质材料的分析而发展起来的，假定一旦由效用荷载导致的主要拉应力超过in-situ自重压力p（取正）那么材料的削弱就会发生。自重压力p通过公式计算得到。式中hi是单元的插值函数，pi是单元结点的压力。结点压力pi通过计算：式中使材料的密度；Zi 为结点Z的坐标，与垂直方向一致。使用tension cut-off模式或cracking模式可以包含材料的削弱。In both modes of behavior (tension cut-off and cracking) the principal stresses due to the external loading are calculated and compared with the in-situ gravity pressure. Once the principal tensile stress is equal to the in-situ gravity pressure, the material is treated as being orthotropic, with the modulus corresponding to the direction of the principal tensile stress being multiplied by a stiffness reduction factor (an input parameter). Another factor, also an input parameter, is applied to reduce the shear stiffness.在这两种模式(tension cut-off and cracking)由外部荷载引起的主应力都将被计算出来，并且与初始重力相比较。一旦主要张应力等于初始重力，材料被认为是正交的，同时与主要张应力方向相应的系数通过刚度衰减系数（一个输入参数）被增加。另一个系数（也是一个输入参数）被用来减小剪切刚度。In the tension cut-off mode, the normal and shear stiffnesses corresponding to the direction of the maximum principal tensile stress are reduced, but the stresses are fully retained. The model therefore simulates elastic-plastic flow of the material. 在tension cut-off模式中，与最大主要张应力方向相同的法向剪切刚度减小，但是应力被全部保留下来。模型可以用来模拟材料的弹塑性流On the other hand, in the cracking mode the stiffnesses are reduced, and in addition the normal and shear stresses due to external loads and corresponding to the direction of stiffness reduction are released. The reduction of stiffness together with the stress release models a crack, i.e., a tensile failure plane, that forms at right angles to the direction of the maximum principal tensile stress.另一方面，在cracking模式中刚度被减小，另外由外荷载引起的法向剪应力及与刚度减小的方向相应的法向剪应力被释放。刚度的减小及应力的释放共同作用来模拟一个裂纹，例如，一个拉伸断裂面， In subsequent load steps, tension cut-off or cracking only in the direction already determined and/or other(s) perpendicular to it may be active, i.e., no change in the tension cut-off or cracking direction is considered. The tension cut-off or cracking mode is considered to be inactive provided the strain normal to the crack (in the direction of tension cut-off) becomes both negative and less than the strain at which the failure occurred initially; otherwise it remains active. Fig. 3.9-2 illustrates the tension cut-off and cracking options. 在随后的荷载步中，tension cut-off 或 cracking仅仅在已经确定的方向和其余与它正交的方向是活动的，例如，在tension cut-off 或 cracking中不考虑任何变化。如果裂纹的法向应变（在tension cut-off方向）变为负数和小于破坏最初发生时的应变，那么tension cut-off 或 cracking模式被认为是不活动的；否则被认为是活动的。图3.9.2说明了tension cut-off 和 cracking选项。Note that the Z direction should be the vertical direction and that the ground level is assumed to be at Z = 0 in the calculation of the in-situ gravity pressure.注意Z方向应该为垂直方向，并且在计算初始地压力时水准平面假定为在Z=0。The in-situ gravity pressure is evaluated using the input for material density which corresponds to the weight per unit volume. This is different than the mass density which is used in the element mass matrix calculation.初始地压力通过输入的相应于单位体积的重量的材料密度来计算求得，这与用单元的质量矩阵计算的质量密度不同的。3.9.2 Drucker-Prager material model 德鲁克普拉格模型The Drucker-Prager model is based on 德鲁克普拉格模型基于：The Drucker-Prager yield condition (see p. 604, ref. KJB) 德鲁克普拉格屈服准则 An associated flow rule using the Drucker-Prager and cap yield functions A perfectly-plastic Drucker-Prager yield behavior 德鲁克普拉格产生行为的完美的塑性体Tension cut-off Cap hardeningThe Drucker-Prager model can be used with the 2-D solid and 3-D solid elements.德鲁克普拉格模型可以被用于2维和3维实体单元中。The Drucker-Prager model can be used with the small displacement/small strain, large displacement/small strain and large displacement/large strain formulations. When used with the small displacement/small strain formulation, a materially-nonlinear-only formulation is employed,德鲁克普拉格模型可用于小位移/小应变，大位移/小应变和大位移/大应变的表达中。当使用小位移/小应变表达时，需要使用一个材料的非线性表达。when used with the large displacement/small strain formulation, a TL formulation is employed and when used with the large displacement/large strain formulation, the ULH formulation isemployed.当用于大位移/小应变表达时，要使用一个TL表达；当用于大位移/大应变表达时，要使用一个ULH表达。Fig. 3.9-3 summarizes some important features of the Drucker- Prager model (with tension cut-off and cap hardening). The Drucker-Prager yield function is given by:图3.9.3概述了德鲁克普拉格模型的一些重要特性（with tension cut-off and cap hardening). 德鲁克普拉格屈服准则通过下式给出：where , k are material property parameters, is the first stress invariant at time t, is the second deviatoric stress invariant at time t.式中, k是材料的特性参数， 是t时刻的应力第一不变量，是t时刻的偏应力第二不变量。The cap yield function depends on the shape of the cap. For a plane cap:where is a function of the volumetric plastic strain:式中是体积塑性应变的一个函数：where is the cap initial position and W and D are material constants.上面的是cap的初始位置，W和D是材料的常数。For an elliptical cap:对一个椭圆capwhere is the vertical semi-axis of the ellipse (AH), R is the cap ratio (AC/AH) and is equal to OA. The dependence of on the volumetric plastic strain is as for the plane cap. In the case of tension cut-off, T is the maximum value that can take.式中 是椭圆的垂直半轴（AH），R是cap率（AC/AH），等于OA。 在tension cut-off状况下，T是所取得最大值。We note that:我们注意到Unlike for the von Mises model, the Drucker-Prager yield function cannot be used with hardening (the material is always assumed to be elastic perfectly-plastic, except for cap hardening).不象von Mises模型，德鲁克普拉格屈服准则不能用来硬化（除了cap hardening以外，材料总是假定为弹性的纯塑性的）If approaches zero (minimum value of is taken to be ), the initial position of the cap is moved far to the right in Figure 3.9-3 and is not reached in the analysis, and the position of the tension cut-off T is moved far to the left and is also not reached in the analysis, then the Drucker-Prager yield condition approaches the von Mises elastic-perfectly-plastic yield condition.如果接近于0(的最小值为)，的初始位置被移动到远离图形3.9.3的右边分析不能达到的地方，tension cut-off T的位置移到远离左边并且分析不能达到的地方，因而德鲁克普拉格屈服条件接近Mises的弹性纯塑性屈服条件。 In the case of Drucker-Prager yielding, the dilatency (volume expansion of the material in shear) is governed by the magnitude of (for the von Mises yield condition = 0 and there is no dilatency). 在德鲁克普拉格屈服的情况下，膨胀量（材料剪切中的体积膨胀）通过的值来确定（Mises屈服条件0并且没有膨胀量)。 Cap yielding leads to an increase of compressive plastic volumetric strain. If the plane cap is used, there is no change of deviatoric plastic strains, while if the elliptical cap is used, the deviatoric components of the plastic strain change during the cap yielding. Fig. 3.9-4 shows the relation between the cap position and the volumetric strainCap屈服导致有压缩的塑性体积应变得增加。如果使用平面cap，没有deviatoric塑性应变的改变，that is, the constraint that exists between these two quantities. We note that the cap movement corresponds to a hardening and that the volumetric plastic strain is constrained to be smaller than the input parameter W in absolute value.也就是，两个量之间存在约束。我们注意到cap运动与一个hardening相应并且体积的塑性应变的绝对值被限制到小于输入参数W的绝对值In the case of vertex yielding (the stress state is represented by point H in Fig. 3.9-3), the plastic deformation corresponds to the Drucker-Prager and cap yielding. The vertex yielding leads to changes in volumetric and deviatoric plastic strains with the cap hardening behavior. Stress states beyond the tension cut-off value T (input to ADINA as a positive value) are not possible. When this limit is reached or exceeded, the program sets all the shear stress components equal to zero and the normal stress components all equal to. The elastic constitutive law is used for the stiffness matrix.应力状态不肯超过tension cut-off的值T（作为正值输入ADINA）。当达到或超过该极限系统将所有的剪应力设为0,并且所有的法向应力等于T/3。弹性临界剪应力准则用来确定刚度矩阵。3.9.3 Cam-clay material model The Cam-clay material model is a pressure-dependent plasticity model. It is based onCam-clay材料模型是依赖于压力的塑性模型。他基于：An associated flow rule using an elliptical yield function使用椭圆屈服函数的关联流动法则 The critical state line, which controls the failure of the material临界状态线控制了材料的破坏The consolidation behavior of clayey materials黏土状材料的固结特性 The Cam-clay model can be used with the 2-D solid and 3-D solid elements.Cam-clay可以被用于2维和3维实体单元 The Cam-clay model can be used with the small displacement and large displacement formulations. In all cases, small strains are assumed.Cam-clay模型可以用于小位移和大位移中。在所有的情况下都假定为小应变。When used with the small displacement formulation, a materially-nonlinear-only formulation is employed and when used ith the large displacement formulation, a TL formulation is employed.当用于小位移分析时，使用非线性材料模式；用于大位移分析时，使用TL模式。 The Cam-clay model is able to simulate the following mechanical behaviors for clayey materials, which are confirmed by lab tests and in-situ tests:Cam-clay模型可以用来模拟黏土材料的以下力学行为，这些通过实验室实验及in-situ试验证实： Strain hardening and softening under normal consolidation states or over consolidation states在正常固结状态或超固结状态下应变硬化和软化 Nonlinear dependence of the elastic volumetric strain on the hydrostatic pressure在静水压力作用下弹性体积应变为非线性An ultimate condition of perfect plasticity at which plastic shearing can continue indefinitely without changes in volume or effective stress在塑性体的最终状态，即使没有体积或有效应力的改变塑性剪切也可以不确定进行。 The Cam-clay yield function is given byCam-clay的屈服准则有如下式子给出where the mean stress and the distortional stress at time t are related to the first stress invariant and the second deviatoric stress invariant byand.M, a material constant, is the slope of the critical state line and , called the pre-consolidation pressure, is the diameter of the ellipsoid at time t along the axis p. All of the variables are shown in Fig. 3.9-5(a).式中t时刻的平均应力和扭转应力，通过和与第一应力不变量和偏应力第二不变量 联系起来。材料常数M，是临界状态线的斜率；称为预固结压力，是t时刻椭圆在p轴上的直径。图3.95(a)显示的所有的变量。The hardening rule is written as硬化准则写成:or, in rate form,或者以比值得格式where is the specific volume at time t andis the plastic specific volume rate at time t. , k and N are material constants, in which is the slope of the isotropic consolidation line, k is the slope of the over consolidation line and N is the specific volume at the isotropic consolidation state when is 1.0. N is related to , the specific volume at the critical state when is 1.0, by式中是t时刻的体积，是t时刻的塑性体积比。 k及 N 是材料的常数，其中二次固结线的斜率，k 是超固结线的斜率，N是二次固结状态下当等于1.0时的体积。N与有关，是等于1.0时的临界状态体积，由下式得到：The effective bulk modulus at time t can be expressed as t时刻的有效体积模量可以表示为The corresponding shear modulus at time t is obtained using， in which is the Poissons ratio (constant throughout the analysis).t时刻的相应的剪切模量通过得到，式中的是泊松比In an analysis using the Cam-clay model, ADINA requires either the initial stresses or an initial stiffness to be defined.使用Cam-clay模型的分析中，ADINA需要定义初始应力或者初始刚度 Initial stresses: The initial stresses are either directly input or elastically calculated before or at the first load step for any specified element group. They can be tiny isotropic compressive stresses (such as 5% of the gravity-induced stresses), or can be the full gravity-induced stresses.初始应力：初始应力或者直接输入或者任何单元群地初始应力在第一荷载步之前通过计算得到。它们可以是很小的二次压应力（例如5%的地应力），或者是全部包含的地压力。When the analysis starts with initial stresses, the initial size of the yield surface can either be directly input or computed from the initial stresses. If the initial stresses are induced by the full gravity load, the initial size of the yield surface (pre consolidation pressure) would be estimated by employing the input parameters OCR and KNULL, unless the initial size of the yield surface is specified in the Cam-clay model definition.当分析以初始应力开始的时候，初始屈服曲面的大小可以通过直接输入或者从初始应力计算获得。如果初始应力是由全部的重力引起的，初始屈服曲面的大小（预固结压力）将通过输入的参数OCR和KNULL进行估计的到，除非在Camclay模型定义的时候就指定了初始屈服曲面的大小。If the initial stresses are not directly input, they are calculated using the initial Youngs modulus and Poissons ratio using linear elastic analysis formulas.如果初始应力不是直接输入的，它们将通过初始弹性模量和泊松比使用线弹分析计算获得When the analysis starts with initial stresses, ADINA takes the true initial size of the yield surface as the greater of the specified initial size and the computed initial size.当分析以初始应力开始的时候，ADINA把真实的屈服曲面的大小作为较大的指定初始大小和计算得到的初始大小。Initial stiffness: The analysis can be performed with an initial stiffness, which is calculated using the initial Youngs modulus and Poissons ratio. In this case, the initial size of the yield surface must be directly specified.初始刚度：分析可以从初始刚度开始，初始刚度通过初始弹性模量和泊松比计算获得。在这种情况下，必须直接指定初始屈服曲面的大小。Parameter KNULL is defined as the coefficient of earth pressure at the normal consolidation state. Usually it is different than the coefficient of current earth pressure. KNULL is approximated by， where is the internal friction angle of the soil.参数KNULL被定义为在正常固结状态下的地压力地系数。通常它与当前地压力系数是不同的。KNULL通过估计，式中土壤的内摩擦角。The material constant M is computed based on. If triaxial compression tests are performed, M is given by. If triaxial extension tests are performed, M is given by材料常数M是基于计算获得的。如果进行三轴压缩试验，M可以通过给出。3.9.4 Mohr-Coulomb material model 莫尔库仑材料模型The Mohr-Coulomb model is based on 莫尔库仑模型基于_ A non-associated flow rule 非关联的流动法则_ A perfectly-plastic Mohr-Coulomb yield behavior 纯塑性莫尔库仑屈服条件_ Tension cut-offThe Mohr-Coulomb model can be used with the 2-D solid and 3-D solid elements.莫尔库仑模式可以用于2维和3维实体单元The Mohr-Coulomb model can be used with the small displacement and large displacement formulations. In all cases, small strains are assumed.莫尔库仑模型可用于小位移和大位移分析。在所有的情况中都假设为小应变。When used with the small displacement formulation, a materially-nonlinear-only formulation is employed and when used with the large displacement formulation, a TL formulation is employed.当用于小位移分析时，使用材料的非线性模式；当用于大位移分析时，使用TL模式The Mohr-Coulomb yield function is given by 莫尔库仑屈服准则通过下式给出and the corresponding potential function is written as 相应的势函数写成where 式中is the friction angle (a material constant), C is the cohesion (a material constant), is the dilatation angle (a material constant), is the first stress invariant at time t, is th