※Abaqus材料属性定义部分翻译《User-defined mechanical material behavior》

ABAQUS/Standard 用户材料子程序实例－Johnson-Cook 金属本构模型卢剑锋 庄茁* 张帆清华大学工程力学系 北京 100084摘要：用户材料子程序是ABAQUS 提供给用户定义自己的材料属性的Fortran 程序接口，使用户能使用ABAQUS 材料库中没有定义的材料模型。

ABAQUS 中自有的Johnson-Cook 模型只能应用于显式ABAQUS/Explicit 程序中，而我们希望能在隐式ABAQUS/Standard 程序中更精确的实现本构积分，而且应用Johnson-Cook 模型的修正形式。

这就需要通过ABAQUS/Standard 的用户材料子程序UMAT 编程实现。

在UMAT 编程中使用了率相关塑性理论以及完全隐式的应力更新算法。

1 Johnson-Cook 强化模型简介Johnson-Cook （JC ）模型用来模拟高应变率下的金属材料。

JC 强化模型表示为三项的乘积，分别反映了应变硬化，应变率硬化和温度软化。

这里使用JC 模型的修正形式：()()*01ln 11n m A B C T εσεε =+++−&& 并使参考应变率01ε=&，这样公式中的A 即为材料的静态屈服应力。

公式中包含,,,,A B n C m 五个参数，需要通过实验来确定。

2 ABAQUS 用户材料子程序用户材料子程序（User-defined Material Mechanical Behavior ，简称UMAT ）通过与ABAQUS 主求解程序的接口实现与ABAQUS 的数据交流。

在输入文件中，使用关键字“*USER MATERIAL”表示定义用户材料属性。

子程序概况与接口UMAT 子程序具有强大的功能，使用UMAT 子程序：(1) 可以定义材料的本构关系，使用ABAQUS 材料库中没有包含的材料进行计算，扩充程序功能。

(2)几乎可以用于力学行为分析的任何分析过程，几乎可以把用户材料属性赋予ABAQUS中的任何单元；(3)必须在UMAT中提供材料本构模型的雅可比（Jacobian）矩阵，即应力增量对应变增量的变化率。

1.1.41 UMATUser subroutine to define a material's mechanical behavior.Product: Abaqus/StandardWarning: The use of this subroutine generally requires considerable expertise. Y ou arecautioned that the implementation of any realistic constitutive model requires extensivedevelopment and testing. Initial testing on a single-element model with prescribedtraction loading is strongly recommended.References“User-defined mechanical material behavior,” Section 26.7.1 of the Abaqus Analysis User's Guide“User-defined thermal material behavior,” Section 26.7.2 of the Abaqus Analysis User's Guide*USER MA TERIAL“S D V I N I,” Section 4.1.11 of the Abaqus V erification Guide“U M A T and U H Y P E R,” Section 4.1.21 of the Abaqus V erification GuideOv erv iewUser subroutine U M A T:can be used to define the mechanical constitutive behavior of a material;will be called at all material calculation points of elements for which the material definition includes auser-defined material behavior;can be used with any procedure that includes mechanical behavior;can use solution-dependent state variables;must update the stresses and solution-dependent state variables to their values at the end of theincrement for which it is called;must provide the material Jacobian matrix, , for the mechanical constitutive model;can be used in conjunction with user subroutine U S D F L D to redefine any field variables before they are passed in; andis described further in “User-defined mechanical material behavior,” Section 26.7.1 of the AbaqusAnalysis User's Guide.Storage of stress and strain componentsIn the stress and strain arrays and in the matrices D D S D D E, D D S D D T, and D R P L D E, direct components are stored first, followed by shear components. There are N D I direct and N S H R engineering shear components. The order of the components is defined in “Conventions,” Section 1.2.2 of the Abaqus Analysis User's Guide. Since the number of active stress and strain components varies between element types, the routine must be coded toprovide for all element types with which it will be used.Defining local orientationsIf a local orientation (“Orientations,” Section 2.2.5 of the Abaqus Analysis User's Guide) is used at the same point as user subroutine U M A T, the stress and strain components will be in the local orientation; and, in the case of finite-strain analysis, the basis system in which stress and strain components are stored rotates with the material.StabilityY ou should ensure that the integration scheme coded in this routine is stable—no direct provision is made to include a stability limit in the time stepping scheme based on the calculations in U M A T.Convergence rateD D S D DE and—for coupled temperature-displacement and coupled thermal-electrical-structural analyses—D D S D D T, D R P L D E, and D R P L D T must be defined accurately if rapid convergence of the overall Newton scheme is to be achieved. In most cases the accuracy of this definition is the most important factor governing the convergence rate. Since nonsymmetric equation solution is as much as four times as expensive as the corresponding symmetric system, if the constitutive Jacobian (D D S D D E) is only slightly nonsymmetric (for example, a frictional material with a small friction angle), it may be less expensive computationally to use a symmetric approximation and accept a slower convergence rate.An incorrect definition of the material Jacobian affects only the convergence rate; the results (if obtained) are unaffected.Special considerations for various element typesThere are several special considerations that need to be noted.A v ailability of deformation gradientThe deformation gradient is available for solid (continuum) elements, membranes, and finite-strain shells(S3/S3R, S4, S4R, SAXs, and SAXAs). It is not available for beams or small-strain shells. It is stored as a 3× 3 matrix with component equivalence D F G R D0(I,J). For fully integrated first-order isoparametric elements (4-node quadrilaterals in two dimensions and 8-node hexahedra in three dimensions) the selectively reduced integration technique is used (also known as the technique). Thus, a modified deformation gradientis passed into user subroutine U M A T. For more details, see “Solid isoparametric quadrilaterals and hexahedra,”Section 3.2.4 of the Abaqus Theory Guide.Beams and shells that calculate transv erse shear energyIf user subroutine U M A T is used to describe the material of beams or shells that calculate transverse shear energy, you must specify the transverse shear stiffness as part of the beam or shell section definition to define the transverse shear behavior. See “Shell section behavior,” Section 29.6.4 of the Abaqus Analysis User's Guide, and “Choosing a beam element,” Section 29.3.3 of the Abaqus Analysis User's Guide, for informationon specifying this stiffness.Open-section beam elementsWhen user subroutine U M A T is used to describe the material response of beams with open sections (for example, an I-section), the torsional stiffness is obtained aswhere J is the torsional constant, A is the section area, k is a shear factor, and is the user-specified transverse shear stiffness (see “Transverse shear stiffness definition” in “Choosing a beam element,” Section29.3.3 of the Abaqus Analysis User's Guide).E lements w ith hourglassing modesIf this capability is used to describe the material of elements with hourglassing modes, you must define the hourglass stiffness factor for hourglass control based on the total stiffness approach as part of the element section definition. The hourglass stiffness factor is not required for enhanced hourglass control, but you can define a scaling factor for the stiffness associated with the drill degree of freedom (rotation about the surface normal). See “Section controls,” Section 27.1.4 of the Abaqus Analysis User's Guide, for information on specifying the stiffness factor.Pipe-soil interaction elementsThe constitutive behavior of the pipe-soil interaction elements (see “Pipe-soil interaction elements,” Section 32.12.1 of the Abaqus Analysis User's Guide) is defined by the force per unit length caused by relative displacement between two edges of the element. The relative-displacements are available as “strains” (S T R A N and D S T R A N). The corresponding forces per unit length must be defined in the S T R E S S array. The Jacobian matrix defines the variation of force per unit length with respect to relative displacement.For two-dimensional elements two in-plane components of “stress” and “strain” exist (N T E N S=N D I=2, andN S H R=0). For three-dimensional elements three components of “stress” and “strain” exist (N T E N S=N D I=3, and N S H R=0).Large volume changes with geometric nonlinearityIf the material model allows large volume changes and geometric nonlinearity is considered, the exact definition of the consistent Jacobian should be used to ensure rapid convergence. These conditions are most commonly encountered when considering either large elastic strains or pressure-dependent plasticity. In the former case, total-form constitutive equations relating the Cauchy stress to the deformation gradient are commonly used; in the latter case, rate-form constitutive laws are generally used.For total-form constitutive laws, the exact consistent Jacobian is defined through the variation in Kirchhoff stress:Here, J is the determinant of the deformation gradient, is the Cauchy stress, is the virtual rate of deformation, and is the virtual spin tensor, defined asFor rate-form constitutive laws, the exact consistent Jacobian is given byUse with incompressible elastic materialsFor user-defined incompressible elastic materials, user subroutine U H Y P E R should be used rather than user subroutine U M A T. In U M A T incompressible materials must be modeled via a penalty method; that is, you must ensure that a finite bulk modulus is used. The bulk modulus should be large enough to model incompressibility sufficiently but small enough to avoid loss of precision. As a general guideline, the bulk modulus should be about – times the shear modulus. The tangent bulk modulus can be calculated fromIf a hybrid element is used with user subroutine U M A T, Abaqus/Standard will replace the pressure stress calculated from your definition of S T R E S S with that derived from the Lagrange multiplier and will modify the Jacobian appropriately.For incompressible pressure-sensitive materials the element choice is particularly important when using user subroutine U M A T. In particular, first-order wedge elements should be avoided. For these elements the technique is not used to alter the deformation gradient that is passed into user subroutine U M A T, which increases the risk of volumetric locking.Increments for which only the Jacobian can be definedAbaqus/Standard passes zero strain increments into user subroutine U M A T to start the first increment of all the steps and all increments of steps for which you have suppressed extrapolation (see “Defining an analysis,”Section 6.1.2 of the Abaqus Analysis User's Guide). In this case you can define only the Jacobian (D D S D D E).Utility routinesSeveral utility routines may help in coding user subroutine U M A T. Their functions include determining stress invariants for a stress tensor and calculating principal values and directions for stress or strain tensors. These utility routines are discussed in detail in “Obtaining stress invariants, principal stress/strain values and directions, and rotating tensors in an Abaqus/Standard analysis,” Section 2.1.11.U ser subroutine interfaceS U B R O U T I N E U M A T(S T R E S S,S T A T E V,D D S D D E,S S E,S P D,S C D,1R P L,D D S D D T,D R P L D E,D R P L D T,2S T R A N,D S T R A N,T I M E,D T I M E,T E M P,D T E M P,P R E D E F,D P R E D,C M N A M E,3N D I,N S H R,N T E N S,N S T A T V,P R O P S,N P R O P S,C O O R D S,D R O T,P N E W D T,4C E L E N T,D F G R D0,D F G R D1,N O E L,N P T,L A Y E R,K S P T,K S T E P,K I N C)CI N C L U D E'A B A_P A R A M.I N C'C H A R A C T E R*80C M N A M ED I ME N S I O N S T R E S S(N T E N S),S T A T E V(N S T A T V),1D D S D D E(N T E N S,N T E N S),D D S D D T(N T E N S),D R P L D E(N T E N S),2S T R A N(N T E N S),D S T R A N(N T E N S),T I M E(2),P R E D E F(1),D P R E D(1),3P R O P S(N P R O P S),C O O R D S(3),D R O T(3,3),D F G R D0(3,3),D F G R D1(3,3)user coding to define D D S D D E,S T R E S S,S T A T E V,S S E,S P D,S C Dand, if necessary,R P L,D D S D D T,D R P L D E,D R P L D T,P N E W D TR E T U R NE N DV ariables to be definedIn all situationsD D S D D E(N TE N S,N T E N S)Jacobian matrix of the constitutive model, , where are the stress increments and are the strain increments. D D S D D E(I,J) defines the change in the I th stress component at the end of the time increment caused by an infinitesimal perturbation of the J th component of the strain increment array.Unless you invoke the unsymmetric equation solution capability for the user-defined material,Abaqus/Standard will use only the symmetric part of D D S D D E. The symmetric part of the matrix iscalculated by taking one half the sum of the matrix and its transpose.S T R E S S(N T E N S)This array is passed in as the stress tensor at the beginning of the increment and must be updated in this routine to be the stress tensor at the end of the increment. If you specified initial stresses (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1 of the Abaqus Analysis User's Guide), this array will contain the initial stresses at the start of the analysis. The size of this array depends on the value of N T E N S as defined below. In finite-strain problems the stress tensor has already been rotated to account for rigid body motion in the increment before U M A T is called, so that only the corotational part of the stress integration should be done in U M A T. The measure of stress used is “true” (Cauchy) stress.S T A T E V(N S T A T V)An array containing the solution-dependent state variables. These are passed in as the values at thebeginning of the increment unless they are updated in user subroutines U S D F L D or U E X P A N, in which case the updated values are passed in. In all cases S T A T E V must be returned as the values at the end of the increment. The size of the array is defined as described in “Allocating space” in “User subroutines:overview,” Section 18.1.1 of the Abaqus Analysis User's Guide.In finite-strain problems any vector-valued or tensor-valued state variables must be rotated to account for rigid body motion of the material, in addition to any update in the values associated with constitutivebehavior. The rotation increment matrix, D R O T, is provided for this purpose.S S E,S P D,S C DSpecific elastic strain energy, plastic dissipation, and “creep” dissipation, respectively. These are passed in as the values at the start of the increment and should be updated to the corresponding specific energy values at the end of the increment. They have no effect on the solution, except that they are used forenergy output.Only in a fully coupled thermal-stress or a coupled thermal-electrical-structural analysisR P LV olumetric heat generation per unit time at the end of the increment caused by mechanical working of the material.D D S D D T(N TE N S)V ariation of the stress increments with respect to the temperature.D R P L D E(N TE N S)V ariation of R P L with respect to the strain increments.D R P L D TV ariation of R P L with respect to the temperature.Only in a geostatic stress procedure or a coupled pore fluid diffusion/stress analysis for pore pressure cohesive elementsR P LR P L is used to indicate whether or not a cohesive element is open to the tangential flow of pore fluid. Set R P L equal to 0 if there is no tangential flow; otherwise, assign a nonzero value to R P L if an element is open.Once opened, a cohesive element will remain open to the fluid flow.V ariable that can be updatedP N E W D TRatio of suggested new time increment to the time increment being used (D T I M E, see discussion later in this section). This variable allows you to provide input to the automatic time incrementation algorithms in Abaqus/Standard (if automatic time incrementation is chosen). For a quasi-static procedure the automatic time stepping that Abaqus/Standard uses, which is based on techniques for integrating standard creep laws (see “Quasi-static analysis,” Section 6.2.5 of the Abaqus Analysis User's Guide), cannot becontrolled from within the U M A T subroutine.P N E W D T is set to a large value before each call to U M A T.If P N E W D T is redefined to be less than 1.0, Abaqus/Standard must abandon the time increment andattempt it again with a smaller time increment. The suggested new time increment provided to theautomatic time integration algorithms is P N E W D T × D T I M E, where the P N E W D T used is the minimum value for all calls to user subroutines that allow redefinition of P N E W D T for this iteration.If P N E W D T is given a value that is greater than 1.0 for all calls to user subroutines for this iteration and the increment converges in this iteration, Abaqus/Standard may increase the time increment. The suggestednew time increment provided to the automatic time integration algorithms is P N E W D T × D T I M E, where the P N E W D T used is the minimum value for all calls to user subroutines for this iteration.If automatic time incrementation is not selected in the analysis procedure, values of P N E W D T that aregreater than 1.0 will be ignored and values of P N E W D T that are less than 1.0 will cause the job to terminate. V ariables passed in for informationS T R A N(N T E N S)An array containing the total strains at the beginning of the increment. If thermal expansion is included in the same material definition, the strains passed into U M A T are the mechanical strains only (that is, thethermal strains computed based upon the thermal expansion coefficient have been subtracted from the total strains). These strains are available for output as the “elastic” strains.In finite-strain problems the strain components have been rotated to account for rigid body motion in the increment before U M A T is called and are approximations to logarithmic strain.D S T R A N(N TE N S)Array of strain increments. If thermal expansion is included in the same material definition, these are the mechanical strain increments (the total strain increments minus the thermal strain increments).T I M E(1)V alue of step time at the beginning of the current increment or frequency.T I M E(2)V alue of total time at the beginning of the current increment.D T I M ETime increment.T E M PTemperature at the start of the increment.D TE M PIncrement of temperature.P R E D E FArray of interpolated values of predefined field variables at this point at the start of the increment, based on the values read in at the nodes.D P RE DArray of increments of predefined field variables.C M N A M EUser-defined material name, left justified. Some internal material models are given names starting with the “ABQ_” character string. To avoid conflict, you should not use “ABQ_” as the leading string for C M N A M E. N D INumber of direct stress components at this point.N S H RNumber of engineering shear stress components at this point.N T E N SSize of the stress or strain component array (N D I + N S H R).N S T A T VNumber of solution-dependent state variables that are associated with this material type (defined asdescribed in “Allocating space” in “User subroutines: overview,” Section 18.1.1 of the Abaqus Analysis User's Guide).P R O P S(N P R O P S)User-specified array of material constants associated with this user material.N P R O P SUser-defined number of material constants associated with this user material.C O O RD SAn array containing the coordinates of this point. These are the current coordinates if geometricnonlinearity is accounted for during the step (see “Defining an analysis,” Section 6.1.2 of the Abaqus Analysis User's Guide); otherwise, the array contains the original coordinates of the point.D R O T(3,3)Rotation increment matrix. This matrix represents the increment of rigid body rotation of the basis system in which the components of stress (S T R E S S) and strain (S T R A N) are stored. It is provided so that vector-or tensor-valued state variables can be rotated appropriately in this subroutine: stress and straincomponents are already rotated by this amount before U M A T is called. This matrix is passed in as a unit matrix for small-displacement analysis and for large-displacement analysis if the basis system for thematerial point rotates with the material (as in a shell element or when a local orientation is used).C E L E N TCharacteristic element length, which is a typical length of a line across an element for a first-order element;it is half of the same typical length for a second-order element. For beams and trusses it is a characteristic length along the element axis. For membranes and shells it is a characteristic length in the referencesurface. For axisymmetric elements it is a characteristic length in the plane only. For cohesiveelements it is equal to the constitutive thickness.D F G R D0(3,3)Array containing the deformation gradient at the beginning of the increment. If a local orientation is defined at the material point, the deformation gradient components are expressed in the local coordinate system defined by the orientation at the beginning of the increment. For a discussion regarding the availability of the deformation gradient for various element types, see “Availability of deformation gradient.”D F G R D1(3,3)Array containing the deformation gradient at the end of the increment. If a local orientation is defined at the material point, the deformation gradient components are expressed in the local coordinate system defined by the orientation. This array is set to the identity matrix if nonlinear geometric effects are not included in the step definition associated with this increment. For a discussion regarding the availability of thedeformation gradient for various element types, see “Availability of deformation gradient.”N O E LElement number.N P TIntegration point number.L A Y E RLayer number (for composite shells and layered solids).K S P TSection point number within the current layer.K S T E PStep number.K I N CIncrement number.Example: Using more than one user-defined mechanical material modelTo use more than one user-defined mechanical material model, the variable C M N A M E can be tested for different material names inside user subroutine U M A T as illustrated below:I F(C M N A M E(1:4).E Q.'M A T1')T H E NC A L L U M A T_M A T1(argument_list)E L S E I F(C M N A M E(1:4).E Q.'M A T2')T H E NC A L L U M A T_M A T2(argument_list)E N D I FU M A T_M A T1 and U M A T_M A T2 are the actual user material subroutines containing the constitutive material models for each material M A T1 and M A T2, respectively. Subroutine U M A T merely acts as a directory here. The argument list may be the same as that used in subroutine U M A T.Example: Simple linear viscoelastic materialAs a simple example of the coding of user subroutine U M A T, consider the linear, viscoelastic model shown in Figure 1.1.41–1. Although this is not a very useful model for real materials, it serves to illustrate how to code the routine.Figure 1.1.41–1 Simple linear viscoelastic model.The behavior of the one-dimensional model shown in the figure iswhere and are the time rates of change of stress and strain. This can be generalized for small straining of an isotropic solid asandwhereand , , , , and are material constants ( and are the Lamé constants).A simple, stable integration operator for this equation is the central difference operator:where f is some function, is its value at the beginning of the increment, is the change in the function over the increment, and is the time increment.Applying this to the rate constitutive equations above givesandso that the Jacobian matrix has the termsandThe total change in specific energy in an increment for this material iswhile the change in specific elastic strain energy iswhere D is the elasticity matrix:No state variables are needed for this material, so the allocation of space for them is not necessary. In a morerealistic case a set of parallel models of this type might be used, and the stress components in each model might be stored as state variables.For our simple case a user material definition can be used to read in the five constants in the order , , , , and so thatThe routine can then be coded as follows:S U B R O U T I N E U M A T(S T R E S S,S T A T E V,D D S D D E,S S E,S P D,S C D,1R P L,D D S D D T,D R P L D E,D R P L D T,2S T R A N,D S T R A N,T I M E,D T I M E,T E M P,D T E M P,P R E D E F,D P R E D,C M N A M E,3N D I,N S H R,N T E N S,N S T A T V,P R O P S,N P R O P S,C O O R D S,D R O T,P N E W D T,4C E L E N T,D F G R D0,D F G R D1,N O E L,N P T,L A Y E R,K S P T,K S T E P,K I N C)CI N C L U D E'A B A_P A R A M.I N C'CC H A R A C T E R*80C M N A M ED I ME N S I O N S T R E S S(N T E N S),S T A T E V(N S T A T V),1D D S D D E(N T E N S,N T E N S),2D D S D D T(N T E N S),D R P L D E(N T E N S),3S T R A N(N T E N S),D S T R A N(N T E N S),T I M E(2),P R E D E F(1),D P R E D(1),4P R O P S(N P R O P S),C O O R D S(3),D R O T(3,3),D F G R D0(3,3),D F G R D1(3,3)D I ME N S I O N D S T R E S(6),D(3,3)CC E V A L U A T E N E W S T R E S S T E N S O RCE V=0.D E V=0.D O K1=1,N D IE V=E V+S T R A N(K1)D E V=D E V+D S T R A N(K1)E N D D OCT E R M1=.5*D T I M E+P R O P S(5)T E R M1I=1./T E R M1T E R M2=(.5*D T I M E*P R O P S(1)+P R O P S(3))*T E R M1I*D E VT E R M3=(D T I M E*P R O P S(2)+2.*P R O P S(4))*T E R M1ICD O K1=1,N D ID S T RE S(K1)=T E R M2+T E R M3*D S T R A N(K1)1+D T I M E*T E R M1I*(P R O P S(1)*E V2+2.*P R O P S(2)*S T R A N(K1)-S T R E S S(K1))S T R E S S(K1)=S T R E S S(K1)+D S T R E S(K1)E N D D OCT E R M2=(.5*D T I M E*P R O P S(2)+P R O P S(4))*T E R M1II1=N D ID O K1=1,N S H RI1=I1+1D S T RE S(I1)=T E R M2*D S T R A N(I1)+1D T I M E*T E R M1I*(P R O P S(2)*S T R A N(I1)-S T R E S S(I1)) S T R E S S(I1)=S T R E S S(I1)+D S T R E S(I1)E N D D OCC C R E A T E N E W J A C O B I A NCT E R M2=(D T I M E*(.5*P R O P S(1)+P R O P S(2))+P R O P S(3)+12.*P R O P S(4))*T E R M1IT E R M3=(.5*D T I M E*P R O P S(1)+P R O P S(3))*T E R M1ID O K1=1,N TE N SD O K2=1,N TE N SD D S D D E(K2,K1)=0.E N D D OE N D D OCD O K1=1,N D ID D S D D E(K1,K1)=TE R M2E N D D OCD O K1=2,N D IN2=K1–1D O K2=1,N2D D S D D E(K2,K1)=TE R M3D D S D D E(K1,K2)=TE R M3E N D D OE N D D OT E R M2=(.5*D T I M E*P R O P S(2)+P R O P S(4))*T E R M1II1=N D ID O K1=1,N S H RI1=I1+1D D S D D E(I1,I1)=TE R M2E N D D OCC T O T A L C H A N G E I N S P E C I F I C E N E R G YCT D E=0.D O K1=1,N TE N ST D E=T D E+(S T R E S S(K1)-.5*D S T R E S(K1))*D S T R A N(K1)E N D D OCC C H A N G E I N S P E C I F I C E L A S T I C S T R A I N E N E R G YCT E R M1=P R O P S(1)+2.*P R O P S(2)D O K1=1,N D ID(K1,K1)=T E R M1E N D D OD O K1=2,N D IN2=K1-1D O K2=1,N2D(K1,K2)=P R O P S(1)D(K2,K1)=P R O P S(1)E N D D OE N D D OD E E=0.D O K1=1,N D IT E R M1=0.T E R M2=0.D O K2=1,N D IT E R M1=T E R M1+D(K1,K2)*S T R A N(K2)T E R M2=T E R M2+D(K1,K2)*D S T R A N(K2)E N D D OD E E=D E E+(T E R M1+.5*T E R M2)*D S T R A N(K1)E N D D OI1=N D ID O K1=1,N S H RI1=I1+1D E E=D E E+P R O P S(2)*(S T R A N(I1)+.5*D S T R A N(I1))*D S T R A N(I1)E N D D OS S E=S S E+D E ES C D=S C D+T D E– D E ER E T U R NE N D。

美国 ABAQUS 软件公司北京代表处华贸中心 2 号写字楼，707-709 室 中国，北京 100016 电话：(8610) 6536 2345 传真：(8610) 6598 9050ABAQUS模块简介ABAQUS 有两个主分析模块——ABAQUS/Standard 和 ABAQUS/Explicit，ABAQUS 也包含一个具 有交互作用的图形模块——ABAQUS/CAE,他提供了 ABAQUS 图形界面的交互作用工具。

ABAQUS/CAE（前后处理） ABAQUS/CAE 是 ABAQUS 有限元分析的前后处理模块，也是建模、分析和仿真的人机交互平台。

该模块根据结构的几何图形生成网格，将材料和截面的特性被分配到网格上，并施加载荷和边界条件。

该模块可以进一步将生成的模型投入到后台的分析模块运行，对运行情况进行监测，并对计算结果进行 后处理。

ABAQUS/CAE 的后处理支持 ABAQUS 分析模块的所有功能，并且对计算结果的描述和解释提 供了范围很广的选择，除了通常的云图，等值线和动画显示之外，还可以用列表，曲线等其他常用工具 的来完成工程显示。

该模块的许多独特功能与特点，例如 CAD 建模方式、参数化建模、适应设计者要求 的数据管理系统等极大的方便了 ABAQUS 的使用者。

ABAQUS/Standard（通用程序） ABAQUS/Standard 是一个通用分析模块，它能够求解广泛的线性和非线性问题，包括结构的静态、 动态、 热和电反应等。

对于通常同时发生作用的几何、 材料和接触非线形采用自动控制技术处理。

ABAQUS 拥有 CAE 工业领域最为广泛的材料模型，它可以模拟绝大部分工程材料的线形和非线形行为，而且任何 一种材料都可以和任何一种单元或复合材料的层一起用于任何合适的分析类型。

ABAQUS/Explicit（显示分析） ABAQUS/Explicit 是利用对事件变化的显示积分求解动态有限元方程。

OverviewUser subroutine USDFLD:主要目的是改变材料点上的场变量，从而改变材料的属性。

•allows you to define field variables at a material point as functions of time or of any of the available material point quantities listed in the Output Variable Identifiers table(“ABAQUS/Standard output variable identifiers,” Section 4.2.1) except the user-definedoutput variables UVARM and UVARM n;允许你在一个材料点上定义场变量作为时间的函数，或是任何可用的材料点变量（在输出变量标识符表中列出的那些，但是不包括用户自己定义的UVARM and UVARM n中的那些输出变量）的函数。

•can be used to introduce solution-dependent material properties since such properties can easily be defined as functions of field variables;可以被用于引入与解有关的材料属性，因为这种属性可以很容易的被定义为场变量的函数。

•will be called at all material points of elements for which the material definition includes user-defined field variables;将被调用在所有的单元材料点上，因为材料定义包括用户定义的场变量。

•must call utility routine GETVRM to access material point data;必须调用应用程序GETVRM来得到材料点数据。

节选-ABAQUS帮助文档翻译 reference to: user manual 18.62008-10-10 12:5918.6 理解自适应网格（adaptive meshing）自适应网格可以通过移动独立的材料网格(allowing the mesh to move independently of the material),让你在整个分析过程中即使发生大变形，也能保持高质量的网格。

通常自适应网格只移动节点，网格的拓扑并不改变。

注意：通常自适应网格多用在Dynamic （动态分析），Explicit and Dynamic（显示动态分析）, Temp-disp, Explicit 中。

定义模型中某个区域采用自适应网格的设置：other-->Adaptive Mesh Domain 自适应网格的选项控制设置:Other--〉Adaptive Mesh Controls 通常，在每一个step中只能有一个自适应网格区域。

21.2.1 ABAQUS/Standard defines contact between two bodies in terms of two surfaces that may interact; these surfaces are called a “contact pair.”ABAQUS/Standard defines “self-contact,” which is available only in two-dimensional analysis, in terms of a single surface. [if gte vml 1]><![endif][if !vml][endif]Figure 21.2.1–1 Contact and interaction discretization. 从the first surface (the “slave” surface)的节点向the second surface (the “master” surface)做垂线，寻找最近的垂线的垂足，The interaction is then discretized between the point on the master surface and the slave node. Strict master-slave contact 在这种关系下，主面的节点可以穿入从面（副面），但副面不可以穿入主面。

abaqus关键字翻译接触相关的keyword：*Contact：开始定义通用的接触(该选项表明通用接触定义的开始。

每个step只能用一次，通用接触定义的不同方面可以通过下面的一些选项指定。

)产品：explicit可选参数：OP：设置OP=MOD(默认)，更改已存的通用接触定义。

设置OP=NEW删除以前定义的接触并定义新的。

----------------------------*Contact Clearance：定义接触间隙属性(该选项用来创建接触间隙属性定义。

接触间隙属性将通过*Contact clearance assignment选项控制任何接触交互。

)产品：explicit必须参数：Name:定义属性名可选参数：Adjust：设置adjust=yes(默认)，是通过调整节点坐标而无需创建约束来解决间隙问题。

adjust=yes只能用在第一个step定义间隙。

设置adjust=no则存储接触偏移以使间隙能被满足而不需调整节点坐标。

Clearance：设置该参数等于一个数值是为整个从节点集定义初始间隙或等于节点分布的名字。

对于实体单元表面上的从节点，间隙值必须是非负的。

默认是Search above：设置该参数等于表面上的距离加上指定的间隙值将作为搜索从节点的距离。

对于实体单元，默认距离是与从节点关联的单元尺寸的1/10。

对结构单元，默认是从节点相关的厚度。

Search below：设置该参数等于表面下的距离设置该参数等于表面上的距离加上指定的间隙值将作为搜索从节点的距离。

对于实体单元，默认距离是与从节点关联的单元尺寸的1/10。

对结构单元，默认是从节点相关的厚度。

------------------------*Contact clearance assignment：在一般接触区域的表面间施加接触间隙(该选项用来在接触面间定义初始接触间隙，并控制初始接触过盈如何解决。

)-------------*Contact controls：为接触指定额外的控制(该选项用来为接触模型提供额外的控制选项。

Static ['stætɪk]静力Dynamic [daɪ'næmɪk]动力Explicit[ɪk'splɪsɪt]∙显示adj. 明确的；清楚的；直率的；详述的∙Time period ~ ['pɪrɪəd]n. 周期，期间；时期；月经；课时；（语法学）句点，句号时间长度Nlgeom 几何非线性Include adiabatic heating effects∙~（adiabatic[,ædɪə'bætɪk]adj. [物] 绝热的；隔热的）['hitɪŋ]~包括绝热效应Incrementation∙(increment['ɪŋkrɪm(ə)nt]n. [数] 增量；增加；增额；盈余)增量Automatic['ɔtə'mætɪk]自动Stable increment estimator∙['steɪb(ə)l]稳定~['estɪmeɪtə]n. [统计] 估计量；评价者稳定增量步数Unlimited[ʌn'lɪmɪtɪd]无限制的Use scaled mass and “throughoutstep”definitions∙(throughout[θrʊ'aʊt]整个，adv. 自始至终，到处；全部；prep. 贯穿，遍及∙definition [defɪ'nɪʃ(ə)n]n. 定义；[物] 清晰度；解说) 使用前一分析步的缩放系数和“整个分析步”定义Contact['kɑntækt]接触Tangential behavior[tæn'dʒenʃ(ə)l][bɪ'hevjɚ]切向行为Normal behavior['nɔrml]~法向行为Frictionless[f'rɪkʃnles]∙(friction['frɪkʃən]n. 摩擦，[力] 摩擦力)无摩擦∙Penalty['pen(ə)ltɪ]n. 罚款，罚金；处罚罚Friction formulation∙（formulation[fɔːmjʊ'leɪʃn]n. 构想，规划；公式化；简洁陈述）摩擦公式Directionality[daɪrɛkʃə'næləti]方向性Isotropic[,aɪsə'trɑpɪk]各向同性Anisotropic[,ænaɪsə'trɑpɪk]各向异性Use slip-rate-dependent data∙(rate[reɪt]n. 比率，率；速度；价格；等级∙Dependent[dɪ'pɛndənt]adj. 依靠的；从属的；取决于…的）使用基于滑动率的数据Use contact-pressure-dependent data 使用依赖接触压力的数据摩擦系数Friction coeff∙(coeff[kəuf]n. 多项式系数)Shear stress[ʃɪə]~剪应力Pressure-overclosure ~[əʊvək'ləʊʒər]压力过盈∙（closure ['kləʊʒə]n. 关闭；终止，结束∙vt. 使终止）约束执行方法Constraint enforcement method∙（enforcement [ɪn'forsmənt]n. 执行，实施；强制∙Method ['meθəd]n. 方法；条理；类函数∙adj. 使用体验派表演方法的)Allow separation after contact允许接触后分离∙（Allow[ə'laʊ]vt. 允许；给予；认可vi. 容许；考虑∙Separation [sepə'reɪʃ(ə)n]n. 分离，分开；间隔，距离；[法] 分居；缺口)Coupling['kʌplɪŋ]耦合接触领域Contact domain∙(domain [də(ʊ)'meɪn]n. 领域；域名；产业；地产)排除的表面对Excluded surface pairs∙（Exclude [ɪk'skluːd; ek-]vt. 排除；排斥；拒绝接纳；逐出）Exterior[ɪk'stɪərɪə; ek-]∙adj. 外部的；表面的；外在的∙n. 外部；表面；外型；外貌Segments['segm(ə)nt]∙vi. 分割n. 段；部分vt. 分割属性指派Attribute assignment∙(Attribute [ə'trɪbjut]n. 属性；特质∙vt. 归属；把…归于∙assignment[ə'saɪnmənt]n. 分配；任务；作业；功课)力学约束公式化Machanical constraint formulation（Machanical[məˈkænɪkl]adj. 机械的，机械学的; 呆板的; 体力的; 手工操作的;Kinematic contact method运动摩擦法∙（Kinematic[,kɪnə'mætɪk]adj. [力] 运动学上的，[力] 运动学的）有限滑移Finite sliding∙(Finite ['faɪnaɪt]adj. 有限的；限定的n. 有限之物∙Sliding ['slaɪdɪŋ]∙Clearance['klɪrəns]n. 清除；空隙过盈量∙Procedure[prə'sidʒɚ]n. 程序，手续；步骤步骤∙Frequency['frikwənsi]n. 频率；频繁频率∙Interval['ɪntəv(ə)l]n. 间隔；间距；幕间休息间隔场输出：S, Stress components and invariantsS,应力分量和不便量∙（component [kəm'ponənt]adj. 组成的，构成的∙n. 成分；组件；[电子] 元件∙invariant [ɪn'veərɪənt]adj. 不变的∙n. [数] 不变量；[计] 不变式PE,塑性应变分量PE, Plastic strain components∙(Plastic ['plæstɪk]adj. 塑料的；（外科）造型的；可塑的;n. 塑料制品；整形；可塑体PEEQ,等效塑性应变PEEQ, Equivalent plastic strain∙（Equivalent [ɪ'kwɪvələnt]adj. 等价的，相等的；同意义的∙n. 等价物，相等物PEMAG, Plastic strain magnitudePEMAG,塑性应变∙(magnitude ['mæɡnɪtud]n. 大小；量级；[地震] 震级；重要；光度LE,对数应变分量LE, Logarithmic strain components∙(Logarithmic [lɔɡə'rɪðmɪk]adj. 对数的位移、速度、加速度Displacement/Velocity/Acceleration∙（Velocity [və'lɑsəti]n. [力] 速率；迅速；周转率∙Acceleration [əkselə'reɪʃ(ə)n]n. 加速，促进；[物]加速度U，位移和转动U,Translation and rotations∙(rotation [rə(ʊ)'teɪʃ(ə)n]n. 旋转；循环，轮流UT,Translations UT,平移UR,Rotations UR，旋转作用力/反作用力Forces/Reactions∙(Reaction [rɪ'ækʃən]n. 反应，感应；反动，复古；反作用RF,Reaction forces and moments RF，反作用力和力矩CF,Concentrated forces and momentsCF，集中力和弯矩∙(Concentrate ['kɑnsn'tret]vi. 集中；浓缩；全神贯注；聚集∙vt.集中；浓缩∙n. 浓缩，精选；浓缩液CSTRESS, Contact stress CSTRESS,接触应力CDISP,接触位移CDISP, Contact displacements∙（Contact ['kɑntækt]n. 接触，联系∙vt.使接触∙vi. 联系，接触Evenly spaced time intervals均匀时间间隔∙(Evenly ['ivnli]adv. 均匀地；平衡地；平坦地；平等地∙Spaced [spest]adj. 隔开的；以规定距离排列的；间隔排列的∙v. 隔开；空出（space的过去分词）每x个时间单位Every x units of time∙(unit ['junɪt]n. 单位，单元；装置；[军] 部队；部件Concentrated force 集中力Moment 弯矩Pressure 压力Surface traction表面载荷∙(traction ['trækʃən]n. 牵引；[机][车辆] 牵引力∙Gravity['ɡrævəti]n. 重力，地心引力；严重性；庄严重力线性摄动Linear perturbation∙(perturbation [,pɜːtə'beɪʃ(ə)n]n. [数][天] 摄动；不安；扰乱∙Individually[ˌɪndɪˈvɪdʒuəli]adv. 个别地，单独地逐个对称/反对称/完全固定Symmetry/Antisymmetry/Encastre∙(Symmetry ['sɪmətri]n. 对称（性）；整齐，匀称Antisymmetry['æntɪsɪmɪtrɪ]n.反对称性Encastre[en'kɑ:stər]n. 端部固定∙Maintain[men'ten]∙vt. 维持；继续；维修；主张；供养Subsequent['sʌbsɪkwənt]∙adj. 后来的，随后的Active ['æktɪv]∙adj. 积极的；活跃的；主动的；有效的；现役的Applicable ['æplɪkəbl]∙adj. 可适用的；可应用的；合适的Allocation [,ælə'keʃən]∙n. 分配，配置；安置estimate['estɪmeɪt]估计∙vi. 估计，估价∙n. 估计，估价；判断，看法∙vt.估计，估量；判断，评价Parallelization[pærəlɪlaɪ'zeɪʃn]并行Use multiple processors运行多个处理器∙(multiple ['mʌltəpl]adj. 多重的；多样的；许多的∙n. 倍数；[电] 并联∙processor ['prɑsɛsɚ]n. [计] 处理器；处理程序；加工者精度∙Precision[prɪ'sɪʒ(ə)n]n. 精度，[数] 精密度；精确∙adj. 精密的，精确的提交∙Submit[səb'mɪt]vt.使服从；主张；呈递∙vi. 提交；服从监控∙Monitor['mɒnɪtə]n. 监视器；监听器；监控器；班长∙vt.监控边界条件：速度/角速度Velocity/Angular velocity∙（Velocity [və'lɑsəti]n. [力] 速率；迅速；周转率∙Angular ['æŋgjʊlə]adj. [生物] 有角的；生硬的，笨拙的；瘦削的Acceleration/Angular acceleration 加速度/角加速度可视化：Render['rendə]渲染风格Wireframe['waiəfreim]线框变形缩放系数Deformation scale factor∙(Deformation [,diːfɔː'meɪʃ(ə)n]n. 变形Uniform['junɪfɔrm]一致Nonumiform 不一致可见边Visible edges∙(Visible ['vɪzəbl]adj. 明显的；看得见的；现有的；可得到的∙n. 可见物；进出口贸易中的有形项目外部边Exterior edges∙(Exterior [ɪk'stɪərɪə; ek-]adj. 外部的；表面的；外在的∙n. 外部；表面；外型；外貌ODB display options:Refinement level细化精度∙(Refinement [rɪ'faɪnmənt]n. 精制；文雅；[化工][油气][冶] 提纯∙Level ['lev(ə)l]n. 水平；标准；水平面∙adj. 水平的；平坦的；同高的∙vi. 瞄准；拉平；变得平坦∙vt.使同等；对准；弄平∙Coarse[kɔrs]adj. 粗糙的；粗俗的；下等的稍粗极粗Extra coarse∙（Extra ['ekstrə]adv. 特别地，非常；另外∙n. 临时演员；号外；额外的事物；上等产品∙adj. 额外的，另外收费的；特大的中∙Medium['midɪəm]adj. 中间的，中等的；半生熟的∙n. 方法；媒体；媒介；中间物Fine 稍细Extra fine 极细辅助显示∙Idealizations[aɪ'dɪəlɪ'zeʃən]n. 理想化；理想化的事物考虑未激活的单元Account for deactivated elements∙(Account [ə'kaʊnt]n. 账户；解释；账目，账单；理由vi. 解释；导致；报账∙vt.认为；把…视为∙deactivate[di'æktə,vet]vt.使无效；使不活动；遣散；复员Mirror/Pattern镜像/图样∙(Pattern ['pæt(ə)n]n. 模式；图案；样品∙vt.模仿；以图案装饰∙vi. 形成图案Pattern 模式Pattern CSYS 阵列坐标系∙Rectangular[rek'tæŋgjʊlə]adj. 矩形的；成直角的直角Circular 圆形云图绘制选项：Contour type 云图类型Isosurface 等值表面离散∙Discrete[dɪ'skrit]adj. 离散的，不连续的∙n. 分立元件；独立部件Interval type 间隔类型Log 对数User-defined用户定义∙(defined [dɪ'faɪnd]adj. 有定义的，确定的；清晰的，轮廓分明的∙v. 使明确；给...下定义；使...的轮廓分明（define的过去分词）显示位置Show location∙（location [lə(ʊ)'keɪʃ(ə)n]n. 位置（形容词locational）；地点；外景拍摄场地动画Animation[ænɪ'meɪʃ(ə)n]∙n. 活泼，生气；激励；卡通片绘制Use limits from all frames使用所有桢的最大最小值∙(frame [freɪm]n. 框架；结构；[电影] 画面∙vt.设计；建造；陷害；使…适合∙vi. 有成功希望∙adj. 有木架的；有构架的Animate scale factor 动画缩放系数Animate harmonic动画：谐振∙(harmonic [hɑr'mɑnɪk]adj. 和声的；谐和的；音乐般的∙n. [物] 谐波；和声动画选项：Frame rate 帧频率显示帧计数Show frame counter∙(counter ['kaʊntə]n. 柜台；对立面；计数器；（某些棋盘游戏的）筹码∙vt.反击，还击；反向移动，对着干；反驳，回答∙vi. 逆向移动，对着干；反驳∙adj. 相反的∙adv. 反方向地；背道而驰地积分点Integration point∙(Integration [ɪntɪ'greɪʃ(ə)n]n. 集成；综合质心Centroid['sentrɒɪd]∙n. 图心单元结点Element nodal∙(nodal ['nodl]adj. 节的；结的；节似的唯一结点的Unique nodal∙(Unique [jʊ'nik]adj. 独特的，稀罕的；[数] 唯一的，独一无二的∙n. 独一无二的人或物网格：近似全局尺寸Approximate global size∙(Approximate [ə'prɑksɪmət]vt.近似；使…接近；粗略估计∙vi. 接近于；近似于∙adj. [数] 近似的；大概的Curvature control曲率控制∙(Curvature ['kɜːvətʃə]n. 弯曲，[数] 曲率Maximum deviation factor最大偏离因子∙（deviation [diːvɪ'eɪʃ(ə)n]n. 偏差；误差；背离By fraction of global size按占全局尺寸的比例∙(fraction['frækʃ(ə)n]n. 分数；部分；小部分；稍微By absolute value 按绝对值∙(absolute['æbsəlut]adj. 绝对的；完全的；专制的∙n. 绝对；绝对事Hex 六面体Hex-dominated六面体为主∙(dominated['dɔmineitid]adj. 占主导地位的；强势的；占统治地位的；[数] 受控的∙v. 控制，支配；处于支配地位（dominate的过去式Tet 四面体楔形Wedge[wedʒ]∙vt.楔入；挤进；楔住∙vi. 楔入；挤进∙n. 楔子；楔形物；导致分裂的东西技术Technique[tek'niːk]∙n. 技巧，技术；手法结构Structured['strʌktʃəd]∙adj. 有结构的；有组织的∙v. 组织；构成（structure的过去分词）；建造Medial axis 中性轴算法Appropriate [ə'prəʊprɪət]∙adj. 适当的∙vt.占用；拨出Linear 线性二次Quadratic[kwɑ'drætɪk]∙adj. [数] 二次的∙n. 二次方程式杂交公式Hybrid formulation∙（Hybrid['haɪbrɪd]n. 杂种，混血儿；混合物∙adj. 混合的；杂种的∙formulation[fɔːmjʊ'leɪʃn]n. 构想，规划；公式化；简洁陈述Reduced integration 减缩积分Incompatible modes 非协调模式Hourglass stiffness 沙漏刚度Viscosity 粘性Kinematic split 运动裂纹Second-order accuracy 二阶精度Distortion control 扭曲控制Hourglass control 沙漏控制Enhanced 增强Relax stiffness 松弛刚度Stiffness 刚度Viscous 粘性Combined 组合Element deletion 单元删除Max Degradation 最大下降Scaling factors 缩放系数Linear bulk viscosity 线性体积粘性Quadratic bulk viscosity 二次体积粘度优化：Freeze load regions 冻结载荷区域Freeze boundary condition regions 冻结边界条件区域Density update strategy 密度更新策略Conservative 保守Aggressive 激进Initial density 初始密度Maximun change per design cycle 每个设计循环的最大改变Convergence criteria 收敛准则首次设计循环作为评价标准First design cycle used to evaluatecriteriaCriteria to be fulfilled 要适应的准则Objective function delta criterion 目标函数delta准则Algorithm 算法Sensitivity-based 基于敏度Condition-based optimization 基于条件的优化Method 方法Material interpolation technique 材料内插技术Volume 体积Frozen area 冻结区域Member size 构件尺寸Memold control 脱模控制Rotational symmetry 轴对称Cyclic symmetry 循环对称Operator 运操作符Comparison operation 对比操作Previous iteration 前一次迭代Modify reference value by factor 按因子修改参考值Displacement by addition of material 有材料增加引起的位移Reduction 减少Total absolute displacement 总觉得位移Equivalent stress 等效应力任务区域内约束点的等效应力Equivalent stress of restricted pointsin task region载荷里的速度。

总规则1、关键字必须以*号开头，且关键字前无空格2、**为注释行，它可以出现在文件中的任何地方3、当关键字后带有参数时，关键词后必须采用逗号隔开4、参数间都采用逗号隔开5、关键词可以采用简写的方式，只要程序能识别就可以了6、不需使用隔行符，如果参数比较多，一行放不下，可以另起一行，只要在上一行的末尾加逗号便可以*AMPLITUDE：定义幅值曲线这个选项允许任意的载荷、位移和其它指定变量的数值在一个分析步中随时间的变化(或者在ABAQUS/Standard分析中随着频率的变化)。

必需的参数：NAME：设置幅值曲线的名字可选参数：DEFINITION：设置definition=Tabular(默认)给出表格形式的幅值-时间(或幅值-频率)定义。

设置DEFINITION=EQUALL Y SPACED/PERIODIC/MODULATED/DECAY/SMOOTH STEP/SOLUTION DEPENDENT或BUBBLE来定义其他形式的幅值曲线。

INPUT：设置该参数等于替换输入文件名字。

TIME：设置TIME=STEP TIME(默认)则表示分析步时间或频率。

TIME=TOTAL TIME表示总时间。

V ALUE：设置V ALUE=RELATIVE(默认)，定义相对幅值。

V ALUE=ABSOLUTE表示绝对幅值，此时，数据行中载荷选项内的值将被省略，而且当温度是指定给已定义了温度TEMPERA TURE=GRADIENTS(默认)梁上或壳单元上的节点，不能使用ABSOLUTE。

对于DEFINITION=TABULAR的可选参数：SMOOTH：设置该参数等于DEFINITION=TABULAR的数据行第一行1、时间或频率2、第一点的幅值(绝对或相对)3、时间或频率4、第二点的幅值(绝对或相对) 等等基本形式：*Amplitude，name=Amp-10.，0.，0.2，1.5，0.4，2.，1.，1.*BEAM SECTION：当需要数值积分时定义梁截面*BOND：定义绑定和绑定属性*BOUNDARY：定义边界条件用来在节点定义边界条件或在子模型分析中指定被驱动的节点。

1、为何需要使用用户材料子程序（User-Defined Material, UMAT ）？很简单，当ABAQUS 没有提供我们需要的材料模型时。

所以，在决定自己定义一种新的材料模型之前，最好对ABAQUS 已经提供的模型心中有数，并且尽量使用现有的模型，因为这些模型已经经过详细的验证，并被广泛接受。

UMAT 子程序具有强大的功能，使用UMAT 子程序：(1)可以定义材料的本构关系，使用ABAQUS 材料库中没有包含的材料进行计算，扩充程序功能。

(2) 几乎可以用于力学行为分析的任何分析过程，几乎可以把用户材料属性赋予ABAQU S 中的任何单元。

(3) 必须在UMAT 中提供材料本构模型的雅可比（Jacobian ）矩阵，即应力增量对应变增量的变化率。

(4) 可以和用户子程序“USDFLD ”联合使用，通过“USDFLD ”重新定义单元每一物质点上传递到UMAT 中场变量的数值。

2、需要哪些基础知识？先看一下ABAQUS 手册（ABAQUS Analysis User's Manual ）里的一段话：Warning: The use of this option generally requires considerable expertise(一定的专业知识). The user is cautioned that the implementation （实现） of any realistic constitutive （基本） model requires extensive （广泛的） development and testing. Initial testing on a single eleme nt model with prescribed traction loading （指定拉伸载荷） is strongly recommended. 但这并不意味着非力学专业，或者力学基础知识不很丰富者就只能望洋兴叹，因为我们的任务不是开发一套完整的有限元软件，而只是提供一个描述材料力学性能的本构方程（Constitutive equation ）而已。

总规则1、关键字必须以*号开头，且关键字前无空格2、**为注释行，它可以出现在文件中的任何地方3、当关键字后带有参数时，关键词后必须采用逗号隔开4、参数间都采用逗号隔开5、关键词可以采用简写的方式，只要程序能识别就可以了6、不需使用隔行符，如果参数比较多，一行放不下，可以另起一行，只要在上一行的末尾加逗号便可以*AMPLITUDE：定义幅值曲线这个选项允许任意的载荷、位移和其它指定变量的数值在一个分析步中随时间的变化(或者在ABAQUS/Standard分析中随着频率的变化)。

必需的参数：NAME：设置幅值曲线的名字可选参数：DEFINITION：设置definition=Tabular(默认)给出表格形式的幅值-时间(或幅值-频率)定义。

设置DEFINITION=EQUALLY SPACED/PERIODIC/MODULATED/DECAY/SMOOTH STEP/SOLUTION DEPENDENT或BUBBLE来定义其他形式的幅值曲线。

INPUT：设置该参数等于替换输入文件名字。

TIME：设置TIME=STEP TIME(默认)则表示分析步时间或频率。

TIME=TOTAL TIME表示总时间。

VALUE：设置VALUE=RELATIVE(默认)，定义相对幅值。

VALUE=ABSOLUTE表示绝对幅值，此时，数据行中载荷选项内的值将被省略，而且当温度是指定给已定义了温度TEMPERATURE=GRADIENTS(默认)梁上或壳单元上的节点，不能使用ABSOLUTE。

对于DEFINITION=TABULAR的可选参数：SMOOTH：设置该参数等于DEFINITION=TABULAR的数据行第一行1、时间或频率2、第一点的幅值(绝对或相对)3、时间或频率4、第二点的幅值(绝对或相对) 等等基本形式：*Amplitude，name=Amp-10.，0.，0.2，1.5，0.4，2.，1.，1.*BEAM SECTION：当需要数值积分时定义梁截面*BOND：定义绑定和绑定属性*BOUNDARY：定义边界条件用来在节点定义边界条件或在子模型分析中指定被驱动的节点。