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UMAT操作过程操作过程：1、CAE建模、定义边界条件、载荷条件2、定义UMATProperty>General>User material✧Mechanical Constants 中为用户输入到子程序中的参数。
这时只能在General栏中定义参数，如密度等，这时不能再在Mechanical中定义杨氏模量等，此时杨氏模量、泊松比等数就需要在Mechanical Constants中输入到子程序中。
✧定义剪切刚度Model>Edit Keywords 中直接输入到inp文件中。
“*Shell Section”后面添加*Transverse Shear5.31e8,5.31e8,0在定义剪切刚度时一定要注意，一定要按帮助文档中公式计算而得并不是任意取值。
对于正交各项异性壳单元其中t为层合板厚度。
Depvar 中的数字与Mechanical Constants栏中定义的参数数量相等。
3编辑.for后缀的子程序3.1 推导出本构关系建立刚度矩阵时最好是直接指定刚度阵的每一项的方法得到刚度阵。
3.2更新应力下面是各项同性弹性本构关系（刚度阵）及应力更新。
DO K1=1,NTENSDO K2=1,NTENSDDSDDE(K1,K2)=ZEROEND DOEND DODO K1=1,NDIDO K2=1,NDIDDSDDE(K2,K1)=EBULK3END DOEND DODO K1=1,NDIDO K2=1,NDIDDSDDE(K1,K1)=EG2END DOEND DODO K1=NDI+1,NTENSDDSDDE(K1,K1)=EG3END DODO K1=1,NTENSDO K2=1,NTENSSTRESS(K1)=STRESS(K1)+DDSDDE(K1,K2)*DSTRAN(K2)END DOEND DO注意：UMAT子程序中并不是一定要写成增量形式，建立Jacobian矩阵，只要能做到更新应力即可，写成全量形式也可以。
2010年4月 Rock and Soil Mechanics Apr. 2010收稿日期：2009-05-27第一作者简介：潘晓明，男，1979年生，博士研究生，主要从事隧道及地下结构方面。
E-mail: pxm155138@文章编号：1000－7598 (2010) 04－1092－07统一弹塑性本构模型在ABAQUS 中的开发与应用潘晓明1, 2 ，孔 娟1, 2， 杨 钊1, 2， 刘 成1, 2（1.同济大学 地下建筑与工程系，上海 200092；2.同济大学 岩土及地下工程教育部重点实验室，上海 200092）摘 要：基于统一弹塑性本构模型的有限元理论格式，根据ABAQUS 的UMAT 格式要求，编制相应的接口程序，将统一弹塑性本构模型引入ABAQUS 中。
采用退化的统一强度模型（0b =时，为Mohr-Coulomb 模型）与ABAQUS 自带的Mohr-Coulomb 模型，对单轴试验和圆形硐室进行弹塑性分析，验证所开发材料子程序的正确性及高效性。
考虑到统一强度模型的一般情况（0b ≠）和屈服面硬化条件，对圆形硐室进行弹塑性计算，得到应力场的变化规律。
所提出的研究思路具有普遍性，为采用ABAQUS 平台进行本构模型的二次开发提供了借鉴和参考。
关 键 词：统一强度理论；屈服面；流动矢量；奇异点；应力拉回算法；ABAQUS 中图分类号：TD 353.6 文献标识码：ASecondary development and application of unified elastoplasticconstitutive model to ABAQUSPAN Xiao-ming 1, 2, KONG Juan 1, 2, YANG Zhao 1, 2, LIU Cheng 1,2(1.Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;2.Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China)Abstract: Based on finite element theoretical scheme of unified elastoplastic constitutive model, and according to the UMAT interface requirement of ABAQUS, the corresponding UMAT codes are programmed, which will be called by the main analytical module of ABAQUS. Adopting degenerative model of the unified strength (0b =，Mohr-Coulomb model) and the built-in Mohr-Coulomb model of ABAQUS, the uniaxial tests and circular chamber are analyzed to verify the correctness and efficiency of the developed material subroutine. Finally, considering the general situation form of unified elastoplastic constitutive model (0b ≠) and hard condition of yield surface, which are not available in ABAQUS software, circular chamber is simulated and variational discipline of stress field is obtained. The provided basic procedures and programming essentials of the UMAT redefining in ABAQUS are universal and can offer a reference for other developers.Key words: unified strength theory; yield surface; flow vector; singular points; return stress algorithm; ABAQUS1 引 言我国力学专家俞茂宏教授从多滑移单元体力学模型出发，考虑了作用在双剪应力单元体上的所有应力分量对材料屈服或破坏的不同影响，提出了一个能够适用于各种岩土类材料的统一强度理论和统一形式的数学表达式。
目录摘要.................................................................... ABSTRACT.................................................................1.绪论..................................................................1.1.课题的研究背景 ..................................................1.2.本文的研究内容和方法 ............................................2.基于ABAQUS软件的二次开发.............................................2.1.ABAQUS介绍......................................................2.2.ABAQUS各模块简介................................................2.3.ABAQUS的二次开发平台............................................2.4.ABAQUS的二次开发语言............................................3.用户材料子程序UMAT...................................................3.1.UMAT开发环境设置................................................3.2.UMAT注意事项....................................................3.3.UMAT接口的原理..................................................3.4.UMAT的使用方法..................................................4.材料非线性问题........................................................4.1.材料的弹塑性本构关系 ............................................4.2.非线性有限元算法理论 ............................................4.3.增量理论常刚度法公式推导 ........................................4.4.增量理论切线刚度法公式推导 ......................................5.UMAT程序设计和编码...................................................5.1.本构关系描述 ....................................................5.2.常刚度法程序设计 ................................................5.3.常刚度法程序编码 ................................................5.4.切线刚度法程序设计 ..............................................5.5.切线刚度法程序编码 ..............................................5.6.程序的调试 ......................................................6.程序验证..............................................................6.1.问题描述 ........................................................6.2.本构关系 ........................................................6.3.ABAQUS自带材料模型计算..........................................6.4.常刚度法的UMAT验证 .............................................6.5.切线刚度法的UMAT验证 ...........................................6.6.两种算法的比较分析 ..............................................7.结论与展望............................................................7.1.结论 ............................................................7.2.展望 ............................................................ 致谢.................................................................... 参考文献................................................................. 附1：ABAQUS自带弹塑性材料验证的INP文件................................. 附2：用于算法验证的INP文件..............................................摘要ABAQUS软件功能强大，特别是能够模拟复杂的非线性问题，它包括了多种材料本构关系及失效准则模型，并具有良好的开放性，提供了若干个用户子程序接口，允许用户以代码的形式来扩展主程序的功能。
非线性本构关系在abaqus中的实现
ABAQUS中非线性本构关系的实现可以通过定义一个UMAT子程序，通过计算输入的应力和应变，来实现非线性本构关系。
具体步骤如下：
1. 在ABAQUS中定义一个UMAT子程序，用于计算应力和应变之间的非线性本构关系；
2. 在ABAQUS中定义材料模型，指定使用的UMAT子程序；
3. 在ABAQUS中定义材料参数，并将其传递给UMAT子程序
4. 在UMAT子程序中，根据输入的应力和材料参数，计算应变；
5. 将计算的应变传递给ABAQUS，ABAQUS根据计算的应变计算应力；
6. 将应力传递给UMAT子程序，重复步骤4和5，直到应力和应变收敛为止。
前言有限元法是工程中广泛使用的一种数值计算方法。
它是力学、计算方法和计算机技术相结合的产物。
在工程应用中，有限元法比其它数值分析方法更流行的一个重要原因在于：相对与其它数值分析方法，有限元法对边界的模拟更灵活，近似程度更高。
所以，伴随着有限元理论以及计算机技术的发展，大有限元软件的应用证变得越来越普及。
ABAQUS软件一直以非线性有限元分析软件而闻名，这也是它和ANSYS,Nastran等软件的区别所在。
非线性有限元分析的用处越来越大，因为在所用材料非常复杂很多情况下，用线性分析来近似已不再有效。
比方说，一个复合材料就不能用传统的线性分析软件包进行分析。
任何与时间有关联，有较大位移量的情况都不能用线性分析法来处理。
多年前，虽然非线性分析能更适合、更准确的处理问题，但是由于当时计算设备的能力不够强大、非线性分析软件包线性分析功能不够健全，所以通常采用线性处理的方法。
这种情况已经得到了极大的改善，计算设备的能力变得更加强大、类似ABAQUS这样的产品功能日臻完善，应用日益广泛。
非线性有限元分析在各个制造行业得到了广泛应用，有不少大型用户。
航空航天业一直是非线性有限元分析的大客户，一个重要原因是大量使用复合材料。
新一代波音 787客机将全部采用复合材料。
只有像 ABAQUS这样的软件，才能分析包括多个子系统的产品耐久性能。
在汽车业，用线性有限元分析来做四轮耐久性分析不可能得到足够准确的结果。
分析汽车的整体和各个子系统的性能要求（如悬挂系统等）需要进行非线性分析。
在土木工程业， ABAQUS能处理包括混凝土静动力开裂分析以及沥青混凝土方面的静动力分析，还能处理高度复杂非线性材料的损伤和断裂问题，这对于大型桥梁结构，高层建筑的结构分析非常有效。
瞬态、大变形、高级材料的碰撞问题必须用非线性有限元分析来计算。
线性分析在这种情况下是不适用的。
以往有一些专门的软件来分析碰撞问题，但现在ABAQUS在通用有限元软件包就能解决这些问题。
目录摘要 (I)ABSTRACT (II)1.绪论 (1)1.1.课题的研究背景 (1)1.2.本文的研究内容和方法 (2)2.基于ABAQUS软件的二次开发 (3)2.1.ABAQUS介绍 (3)2.2.ABAQUS各模块简介 (3)2.3.ABAQUS的二次开发平台 (5)2.4.ABAQUS的二次开发语言 (6)3.用户材料子程序UMAT (8)3.1.UMAT开发环境设置 (8)3.2.UMAT注意事项 (9)3.3.UMAT接口的原理 (10)3.4.UMAT的使用方法 (12)4.材料非线性问题 (14)4.1.材料的弹塑性本构关系 (14)4.2.非线性有限元算法理论 (17)4.3.增量理论常刚度法公式推导 (20)4.4.增量理论切线刚度法公式推导 (21)5.UMAT程序设计和编码 (25)5.1.本构关系描述 (25)5.2.常刚度法程序设计 (27)5.3.常刚度法程序编码 (29)5.4.切线刚度法程序设计 (32)5.5.切线刚度法程序编码 (36)5.6.程序的调试 (39)6.程序验证 (40)16.1.问题描述 (41)6.2.本构关系 (42)6.3.ABAQUS自带材料模型计算 (42)6.4.常刚度法的UMAT验证 (44)6.5.切线刚度法的UMAT验证 (46)6.6.两种算法的比较分析 (48)7.结论与展望 (52)7.1.结论 (52)7.2.展望 (52)致谢 (54)参考文献 (55)附1：ABAQUS自带弹塑性材料验证的INP文件 (56)附2：用于算法验证的INP文件 (62)摘要ABAQUS软件功能强大，特别是能够模拟复杂的非线性问题，它包括了多种材料本构关系及失效准则模型，并具有良好的开放性，提供了若干个用户子程序接口，允许用户以代码的形式来扩展主程序的功能。
本文主要研究了ABAQUS用户子程序UMAT的开发方法，采用FORTRAN语言编制了各向同性硬化材料模型的接口程序，研究该类材料的弹塑性本构关系极其实现方法。
（完整word版）Abaqus弹塑性分析简单实例
Abaqus弹塑性分析简单实例
ABAQUS默认的塑性材料特性应用金属材料的经典塑性理论，采用MISES屈服面来定义各向屈服。
金属材料的弹塑性行为可以简述如下：在小应变时，材料性质基本为线弹性，弹性模量E为常数；应力超过屈服应力后，刚度会显著下降，此时材料的应变包括塑性应变和弹性应变两部分；在卸载后，弹性应变消失，而塑性应变是不可恢复的；如果再次加载，材料的屈服应力会提高，即所谓的加工硬化。
在abaqus中，等效塑性应变PEEQ大于0表明材料发生了屈服。
在工程结构中，等效塑性应变一般不应超过材料的破坏应变。
对于金属成形等大变形问题，应根据生产工艺要求来确定许可的等效塑性应变量。
需要注意的是在比例加载时，大多数材料的PEMAG和PEEQ相等。
这两个量的区别在于，PEMAG描述的是变形过程中某一时刻的塑性应变，与加载历史无关，而PEEQ是整个变形过程中塑性应变的累积结果。
下面我们以单向压缩过程的模拟来演示ABAQUS弹塑性仿真设置。
模型如图所示，压头用解析刚体来模拟，试样用SHELL来模拟。
采用轴对称模型。
试样的截面属性设置如下图所示，注意塑性应变必须从0开始。
在压头与试样之间定义无摩擦的接触。
固定对称轴
上的径向位移U1和底边的轴向位移U2。
压头是轴对称刚体，U2边界条件需要施加在压头的参考点上。
设定两个分析步，第一个分析步让压头与试样建立平稳的接触，设置压头下移-5.001mm。
第二个分析步，设定压头下移20mm。
具体如下图所示：
提交分析，结果如下图所示：有限元在线因为专注所以卓越。
UMATUser subroutine to define a material's mechanical behavior.Product: Abaqus/StandardWarning: The use of this subroutine generally requires considerable expertise. You are cautioned that the implementation of any realistic constitutive model requires extensive development and testing. Initial testing on a single-element model with prescribed traction loading is strongly recommended.References∙“User-defined mechanical material behavior,” Section 25.7.1 of the Abaqus Analysis User's Manual∙“User-defined thermal material behavior,” Section 25.7.2 of the Abaqus Analysis User's Manual∙*USER MATERIAL∙“SDVINI,” Section 4.1.11 of the Abaqus Verification Manual∙“UMAT and UHYPER,” Section 4.1.21 of the Abaqus Verification Manual OverviewUser subroutine UMAT:∙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 a user-defined materialbehavior;∙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 the increment for which it is called;∙must provide the material Jacobian matrix, , for the mechanical constitutive model;∙can be used in conjunction with user subroutine USDFLD to redefine any field variables before they are passed in; andis described further in “User-defined mechanical material behavior,” Section 25.7.1 of the Abaqus Analysis User's Manual. Storage of stress and strain componentsIn the stress and strain arrays and in the matrices DDSDDE, DDSDDT, and DRPLDE, direct components are stored first, followed by shear components. There are NDI direct and NSHR engineering shear components. The order of the components is defined in “Conventions,” Section 1.2.2 of the Abaqus Analysis User's Manual. Since the number of active stress and strain components varies between element types, the routine must be coded to provide 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 Manual) is used at the same point as user subroutine UMAT, 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.StabilityYou 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 UMAT.Convergence rateDDSDDE and—for coupled temperature-displacement and coupledthermal-electrical-structural analyses—DDSDDT, DRPLDE, and DRPLDT 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 (DDSDDE) is only slightly nonsymmetric (for example, a frictional material with a small frictionangle), 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. Availability 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 a3 × 3 matrix with component equivalence DFGRD0(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 UMAT. For more details, see “Solid isoparametric quadrilaterals and hexahedra,” Section 3.2.4 of the Abaqus Theory Manual.Beams and shells that calculate transverse shear energyIf user subroutine UMAT 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 28.6.4 of the Abaqus Analysis User's Manual, and “Choosing a beam element,” Section 28.3.3 of the Abaqus Analysis User's Manual, for information on specifying this stiffness.Open-section beam elementsWhen user subroutine UMAT 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,” Section 28.3.3 of the Abaqus Analysis User's Manual).Elements with 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 26.1.4 of the Abaqus Analysis User's Manual, 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 31.12.1 of the Abaqus Analysis User's Manual) 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” (STRAN and DSTRAN). The corresponding forces per unit length must be defined in the STRESS 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 (NTENS=NDI=2, and NSHR=0). For three-dimensional elements three components of “stress” and “strain” exist (NTENS=NDI=3, and NSHR=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 asandFor rate-form constitutive laws, the exact consistent Jacobian is given byUse with incompressible elastic materialsFor user-defined incompressible elastic materials, user subroutine UHYPER should be used rather than user subroutine UMAT. In UMAT 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 UMAT, Abaqus/Standard will replace the pressure stress calculated from your definition of STRESS 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 UMAT. 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 UMAT, which increases the risk of volumetric locking.Increments for which only the Jacobian can be definedAbaqus/Standard passes zero strain increments into user subroutine UMAT to start the first increment of all the steps and all increments of steps for which you have suppressed extrapolation (see “Procedures: overview,” Section 6.1.1 of the Abaqus Analysis User's Manual). In this case you can define only the Jacobian (DDSDDE).Utility routinesSeveral utility routines may help in coding user subroutine UMAT. 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.User subroutine interfaceSUBROUTINE UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,1 RPL,DDSDDT,DRPLDE,DRPLDT,2 STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME,3 NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,4 CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,KSTEP,KINC)CINCLUDE 'ABA_PARAM.INC'CCHARACTER*80 CMNAMEDIMENSION STRESS(NTENS),STATEV(NSTATV),1 DDSDDE(NTENS,NTENS),DDSDDT(NTENS),DRPLDE(NTENS),2 STRAN(NTENS),DSTRAN(NTENS),TIME(2),PREDEF(1),DPRED(1),3 PROPS(NPROPS),COORDS(3),DROT(3,3),DFGRD0(3,3),DFGRD1(3,3)user coding to define DDSDDE, STRESS, STATEV, SSE, SPD, SCDand, if necessary, RPL, DDSDDT, DRPLDE, DRPLDT, PNEWDTRETURNENDVariables to be definedIn all situationsDDSDDE(NTENS,NTENS)Jacobian matrix of the constitutive model, , where are thestress increments and are the strain increments. DDSDDE(I,J) defines the change in the Ith stress component at the end of the time increment caused by an infinitesimal perturbation of the Jth 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 DDSDDE. The symmetric part of the matrix is calculated by taking one half the sum of the matrix and its transpose.STRESS(NTENS)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 32.2.1 of the Abaqus Analysis User's Manual), this array will contain the initial stresses at the start of the analysis. The size of this array depends on the value of NTENS as defined below. In finite-strain problems the stress tensor has already been rotated to account for rigid body motion in theincrement before UMAT is called, so that only the corotational part of the stress integration should be done in UMAT. The measure of stress used is “true” (Cauchy) stress.STATEV(NSTATV)An array containing the solution-dependent state variables. These are passed in as the values at the beginning of the increment unless they are updated in user subroutines USDFLD or UEXPAN, in which case the updated values are passed in. In all cases STATEV 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 17.1.1 of the Abaqus Analysis User's Manual.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 constitutive behavior. The rotation increment matrix, DROT, is provided for this purpose.SSE, SPD, SCDSpecific 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 for energy output.Only in a fully coupled thermal-stress or a coupledthermal-electrical-structural analysisRPLVolumetric heat generation per unit time at the end of the increment caused by mechanical working of the material.DDSDDT(NTENS)Variation of the stress increments with respect to the temperature.DRPLDE(NTENS)Variation of RPL with respect to the strain increments.DRPLDTVariation of RPL with respect to the temperature.Only in a geostatic stress procedure or a coupled pore fluiddiffusion/stress analysis for pore pressure cohesive elementsRPLRPL is used to indicate whether or not a cohesive element is open to the tangential flow of pore fluid. Set RPL equal to 0 if there is no tangential flow; otherwise, assign a nonzero value to RPL if an element is open. Once opened, a cohesive element will remain open to the fluid flow.Variable that can be updatedPNEWDTRatio of suggested new time increment to the time increment being used (DTIME, 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 Manual), cannot be controlled from within the UMAT subroutine.PNEWDT is set to a large value before each call to UMAT.If PNEWDT is redefined to be less than 1.0, Abaqus/Standard must abandon the time increment and attempt it again with a smaller time increment. The suggested new time increment provided to the automatic time integration algorithms is PNEWDT × DTIME, where t he PNEWDT used is the minimum value for all calls to user subroutines that allow redefinition of PNEWDT for this iteration.If PNEWDT 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 suggested new time increment provided to the automatic time integration algorithms is PNEWDT × DTIME, where the PNEWDT 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 PNEWDT that are greater than 1.0 will be ignored and values of PNEWDT that are less than 1.0 will cause the job to terminate.Variables passed in for informationSTRAN(NTENS)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 UMAT are the mechanical strains only (that is, the thermal 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 UMAT is called and are approximations to logarithmic strain.DSTRAN(NTENS)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).TIME(1)Value of step time at the beginning of the current increment.TIME(2)Value of total time at the beginning of the current increment.DTIMETime increment.TEMPTemperature at the start of the increment.DTEMPIncrement of temperature.PREDEFArray 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.DPREDArray of increments of predefined field variables.CMNAMEUser-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 CMNAME.NDINumber of direct stress components at this point.NSHRNumber of engineering shear stress components at this point.NTENSSize of the stress or strain component array (NDI + NSHR).NSTATVNumber of solution-dependent state variables that are associated with this material type (defined as described in “Allocating space” in “User subroutines: overview,” Section 17.1.1 of the Abaqus Analysis User's Manual).PROPS(NPROPS)User-specified array of material constants associated with this user material.NPROPSUser-defined number of material constants associated with this user material.COORDSAn array containing the coordinates of this point. These are the current coordinates if geometric nonlinearity is accounted for during the step (see “Procedures: overview,” Section 6.1.1 of the Abaqus Analysis User's Manual); otherwise, the array contains the original coordinates of the point.DROT(3,3)Rotation increment matrix. This matrix represents the increment of rigid body rotation of the basis system in which the components of stress (STRESS) and strain (STRAN) are stored. It is provided so that vector- ortensor-valued state variables can be rotated appropriately in this subroutine: stress and strain components are already rotated by this amount before UMAT 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 the material point rotates with the material (as in a shell element or when a local orientation is used).CELENTCharacteristic 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 reference surface. For axisymmetric elementsit is a characteristic length in the plane only. For cohesive elementsit is equal to the constitutive thickness.DFGRD0(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.”DFGRD1(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 withthis increment. For a discussion regarding the availability of the deformation gradient for various element types, see “Availability of deformation gradient.”NOELElement number.NPTIntegration point number.LAYERLayer number (for composite shells and layered solids).KSPTSection point number within the current layer.KSTEPStep number.KINCIncrement number.Example: Using more than one user-defined mechanical material modelTo use more than one user-defined mechanical material model, the variable CMNAME can be tested for different material names inside user subroutine UMAT as illustrated below:IF (CMNAME(1:4) .EQ. 'MAT1') THENCALL UMAT_MAT1(argument_list)ELSE IF(CMNAME(1:4) .EQ. 'MAT2') THENCALL UMAT_MAT2(argument_list)END IFUMAT_MAT1 and UMAT_MAT2 are the actual user material subroutines containing the constitutive material models for each material MAT1 and MAT2, respectively. Subroutine UMAT merely acts as a directory here. The argument list may be the same as that used in subroutine UMAT.Example: Simple linear viscoelastic materialAs a simple example of the coding of user subroutine UMAT, consider the linear, viscoelastic model shown in Figure 1.1.40–1. Although this is not a very useful model for real materials, it serves to illustrate how to code the routine.Figure 1.1.40–1 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 timeincrement.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 more realistic 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:SUBROUTINE UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,1 RPL,DDSDDT,DRPLDE,DRPLDT,2 STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME,3 NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,4 CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,KSTEP,KINC)CINCLUDE 'ABA_PARAM.INC'CCHARACTER*80 CMNAMEDIMENSION STRESS(NTENS),STATEV(NSTATV),1 DDSDDE(NTENS,NTENS),2 DDSDDT(NTENS),DRPLDE(NTENS),3 STRAN(NTENS),DSTRAN(NTENS),TIME(2),PREDEF(1),DPRED(1),4 PROPS(NPROPS),COORDS(3),DROT(3,3),DFGRD0(3,3),DFGRD1(3,3) DIMENSION DSTRES(6),D(3,3)CC EVALUATE NEW STRESS TENSORCEV = 0.DEV = 0.DO K1=1,NDIEV = EV + STRAN(K1)DEV = DEV + DSTRAN(K1)END DOCTERM1 = .5*DTIME + PROPS(5)TERM1I = 1./TERM1TERM2 = (.5*DTIME*PROPS(1)+PROPS(3))*TERM1I*DEVTERM3 = (DTIME*PROPS(2)+2.*PROPS(4))*TERM1ICDO K1=1,NDIDSTRES(K1) = TERM2+TERM3*DSTRAN(K1)1 +DTIME*TERM1I*(PROPS(1)*EV2 +2.*PROPS(2)*STRAN(K1)-STRESS(K1))STRESS(K1) = STRESS(K1) + DSTRES(K1)END DOCTERM2 = (.5*DTIME*PROPS(2) + PROPS(4))*TERM1II1 = NDIDO K1=1,NSHRI1 = I1+1DSTRES(I1) = TERM2*DSTRAN(I1)+1 DTIME*TERM1I*(PROPS(2)*STRAN(I1)-STRESS(I1))STRESS(I1) = STRESS(I1)+DSTRES(I1)END DOCC CREATE NEW JACOBIANCTERM2 = (DTIME*(.5*PROPS(1)+PROPS(2))+PROPS(3)+1 2.*PROPS(4))*TERM1ITERM3 = (.5*DTIME*PROPS(1)+PROPS(3))*TERM1IDO K1=1,NTENSDO K2=1,NTENSDDSDDE(K2,K1) = 0.END DOEND DOCDO K1=1,NDIDDSDDE(K1,K1) = TERM2END DOCDO K1=2,NDIN2 = K1–1DO K2=1,N2DDSDDE(K2,K1) = TERM3DDSDDE(K1,K2) = TERM3END DOEND DOTERM2 = (.5*DTIME*PROPS(2)+PROPS(4))*TERM1II1 = NDIDO K1=1,NSHRI1 = I1+1DDSDDE(I1,I1) = TERM2END DOCC TOTAL CHANGE IN SPECIFIC ENERGYCTDE = 0.DO K1=1,NTENSTDE = TDE + (STRESS(K1)-.5*DSTRES(K1))*DSTRAN(K1) END DOCC CHANGE IN SPECIFIC ELASTIC STRAIN ENERGYCTERM1 = PROPS(1) + 2.*PROPS(2)DO K1=1,NDID(K1,K1) = TERM1END DODO K1=2,NDIN2 = K1-1DO K2=1,N2D(K1,K2) = PROPS(1)D(K2,K1) = PROPS(1)END DOEND DODEE = 0.DO K1=1,NDITERM1 = 0.TERM2 = 0.DO K2=1,NDITERM1 = TERM1 + D(K1,K2)*STRAN(K2)TERM2 = TERM2 + D(K1,K2)*DSTRAN(K2)END DODEE = DEE + (TERM1+.5*TERM2)*DSTRAN(K1)END DOI1 = NDIDO K1=1,NSHRI1 = I1+1DEE = DEE + PROPS(2)*(STRAN(I1)+.5*DSTRAN(I1))*DSTRAN(I1) END DOSSE = SSE + DEESCD = SCD + TDE – DEERETURNEND。
abaqus umat是一种在计算力学中广泛应用的有限元分析软件。
它可以通过用户自定义的子程序（也称为umat）进行材料本构关系的定义，使得在模拟复杂材料行为时能够更加精确地描述材料的非线性和非均匀性等特性。
abaqus umat能够有效地模拟材料的机械性能，并在工程领域具有广泛的应用。
1. 什么是abaqus umat？abaqus umat是abaqus软件中用于用户自定义材料本构关系的子程序。
它可以实现对材料行为的精确描述，包括材料的非线性、非均匀性等特性。
通过abaqus umat，用户可以自定义材料的本构关系和材料参数，以满足对于各种材料行为的精确模拟需求。
2. abaqus umat的实现原理abaqus umat的实现依赖于有限元分析方法。
用户可以通过编写程序，在abaqus中调用该程序来定义材料的本构关系。
在有限元分析中，材料的本构关系是描述材料应力和应变之间关系的重要参数，通过用户自定义的umat程序，可以实现对材料行为的更为精确的描述。
3. abaqus umat的应用领域abaqus umat在工程领域有着广泛的应用。
例如在航空航天领域，abaqus umat可以用于模拟飞机结构的材料行为，预测飞机在不同载荷下的应力应变分布，进行疲劳分析等。
在汽车工业中，abaqus umat可以用于模拟汽车结构在碰撞时的材料行为，以及进行车身强度分析等。
abaqus umat还被广泛应用于建筑、船舶、能源等领域，在模拟复杂材料行为时发挥着重要作用。
4. abaqus umat的优势相较于其他有限元分析软件，abaqus umat的优势在于其灵活性和精确性。
用户可以通过编写自定义的umat程序，实现对材料行为的精确描述，满足各种复杂条件下的模拟需求。
abaqus umat还具有较强的兼容性和扩展性，可以与abaqus的其他模块结合使用，实现更为全面的分析和模拟。
5. 用户如何编写abaqus umat程序编写abaqus umat程序需要一定的编程和材料力学知识。
各个楼层及内容索引2-------------------------------------什么是UMAT3-------------------------------------UMAT功能简介4-------------------------------------UMAT开始的变量声明5-------------------------------------UMAT中各个变量的详细解释6-------------------------------------关于沙漏和横向剪切刚度7-------------------------------------UMAT流程和参数表格实例展示8-------------------------------------FORTRAN语言中的接口程序Interface9-------------------------------------关于UMAT是否可以用Fortran90编写的问题10-17--------------------------------Fortran77的一些有用的知识简介20-25\30-32-----------------------弹塑性力学相关知识简介34-37--------------------------------用户材料子程序实例JOhn-cook模型压缩包下载38-------------------------------------JOhn-cook模型本构简介图40-------------------------------------用户材料子程序实例JOhn-cook模型完整程序+david详细注解[欢迎大家来看看,并提供意见,完全是自己的diy的,不保证完全正确,希望共同探讨,以便更正,带"?"部分,还望各位大师\同仁指教]1 什么是UMAT???1.1 UMAT功能简介!!
ABAQUS-⼆次开发资料-UMAT各个楼层及内容索引2-------------------------------------什么是UMAT3-------------------------------------UMAT功能简介4-------------------------------------UMAT开始的变量声明5-------------------------------------UMAT中各个变量的详细解释6-------------------------------------关于沙漏和横向剪切刚度7-------------------------------------UMAT流程和参数表格实例展⽰8-------------------------------------FORTRAN语⾔中的接⼝程序Interface9-------------------------------------关于UMAT是否可以⽤Fortran90编写的问题10-17--------------------------------Fortran77的⼀些有⽤的知识简介20-25\30-32-----------------------弹塑性⼒学相关知识简介34-37--------------------------------⽤户材料⼦程序实例JOhn-cook模型压缩包下载38-------------------------------------JOhn-cook模型本构简介图40-------------------------------------⽤户材料⼦程序实例JOhn-cook模型完整程序+david详细注解[欢迎⼤家来看看,并提供意见,完全是⾃⼰的diy的,不保证完全正确,希望共同探讨,以便更正,带"?"部分,还望各位⼤师\同仁指教]1什么是UMAT1.1 UMAT功能简介[-摘⾃庄茁⽼师的书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。
ABAQUS弹塑性分析简介ABAQUS是一种常用的有限元分析软件，广泛应用于工程领域。
它可以进行多种类型的分析，包括线性弹性分析、非线性分析以及弹塑性分析等。
本文将重点介绍ABAQUS中的弹塑性分析。
弹塑性分析概述弹塑性分析是指在加载过程中，材料同时存在弹性和塑性变形的情况下进行的分析。
相对于只考虑弹性变形的分析方法，弹塑性分析可以更加准确地描述材料的行为。
ABAQUS是一款强大的工具，提供了多种弹塑性材料模型以及相应的分析设置。
弹塑性材料模型ABAQUS中常用的弹塑性材料模型包括：1.von Mises模型 von Mises模型是最常用的塑性材料模型之一，它基于等效应力假设，适用于各向同性的材料。
在ABAQUS中，可以通过指定材料的屈服应力和硬化规律来定义von Mises模型。
2.Drucker-Prager模型Drucker-Prager模型适用于非各向同性的材料，特别是岩土材料。
它考虑了材料的摩擦和内聚力特性，可以模拟材料的塑性和蠕变行为。
3.Mohr-Coulomb模型 Mohr-Coulomb模型也是一种常用的非各向同性材料模型，适用于岩石等材料。
它考虑了材料的内聚力和摩擦特性。
以上只是ABAQUS中的部分弹塑性材料模型，用户可以根据具体材料的性质选择合适的模型。
弹塑性分析设置进行弹塑性分析时，需要在ABAQUS中进行相应的分析设置。
以下是一些常见的设置：1.材料属性定义在ABAQUS中，需要指定材料的弹性模量、泊松比以及塑性相关参数等。
根据选择的弹塑性材料模型，还需要指定其特定的参数。
2.加载条件弹塑性分析通常需要施加外部载荷或变形条件。
可以通过定义荷载和边界条件来实现。
ABAQUS提供了多种类型的荷载和边界条件，用户可以根据实际情况进行选择。
3.收敛准则弹塑性分析是一个迭代过程，在每次迭代中需要检查计算的收敛性。
ABAQUS提供了多种收敛准则，用户可以根据需要选择适合的准则。
弹塑性分析案例为了更好地理解ABAQUS中的弹塑性分析，以下将给出一个简单的案例。
ABAQUS中HOEK-BROWN弹塑性模型的二次开发及应用作为国际上最先进的大型通用有限元软件之一,ABAQUS已广泛应用于各个行业领域,但其现有功能并不能完全满足各行业高级用户的某些要求,如该程序现有岩土材料模型很有限或存在某些缺陷,特别对于岩体材料并没有合适的本构模型,以反映其非线性破坏规律。
为此,本文依托其二次开发平台,采用Fortran语言和向后欧拉隐式积分算法开发了若干用户材料子程序(UMAT),并应用于实际工程数值模拟和分析,本文主要研究内容如下:(1)介绍并梳理Hoek-Brown强度准则在各时期的不同形式。
当将其应用于有限元数值分析时,Hoek-Brown屈服准则在一般应力空间表现为弯曲六棱锥形状,存在尖角,会导致数值奇异。
本文提出在屈服面夹角处采用圆弧代替原屈服面,即“圆化”,推导了该圆弧屈服函数表达式。
同时,为了反映岩体抗拉强度较低的特征,引入拉伸截断面,与圆化后Hoek-Brown屈服面一同作为修正后的Hoek-Brown准则屈服面。
(2)本文应力更新算法采用完全隐式向后欧拉积分,考虑相关联流动法则,对屈服函数和塑形势函数求一阶和二阶导数,得到一致性刚度矩阵,确保结果更精确,程序收敛性更好。
为了实现修正Hoek-Brown准则的应用,借助ABAQUS平台编写了相应的UMAT。
用室内常规三轴压缩试验、单轴拉伸试验、圆形隧道力学响应、群桩-岩体相互作用模型和隧道开挖模型验证程序的正确性,说明其对真三维问题的适用性。
探讨了用线性等效Mohr-Coulomb准则近似非线性Hoek-Brown准则的原理及应用方法,对比不同准则下研究对象的力学行为,并简要阐述剪胀角的影响。
探讨隧道开挖空间效应,研究了不同开挖进尺、不同初始应力条件下的隧洞纵向变形规律曲线(LDP曲线)及围岩力学行为,介绍了收敛-约束法的基本原理和应用条件。
(3)介绍Hoek-Brown材料参数值获取的定性和定量方法,提出用非参数统计方法研究Hoek-Brown参数敏感度。
前言有限元法是工程中广泛使用的一种数值计算方法。
它是力学、计算方法和计算机技术相结合的产物。
在工程应用中，有限元法比其它数值分析方法更流行的一个重要原因在于：相对与其它数值分析方法，有限元法对边界的模拟更灵活，近似程度更高。
所以，伴随着有限元理论以及计算机技术的发展，大有限元软件的应用证变得越来越普及。
ABAQUS软件一直以非线性有限元分析软件而闻名，这也是它和ANSYS,Nastran等软件的区别所在。
非线性有限元分析的用处越来越大，因为在所用材料非常复杂很多情况下，用线性分析来近似已不再有效。
比方说，一个复合材料就不能用传统的线性分析软件包进行分析。
任何与时间有关联，有较大位移量的情况都不能用线性分析法来处理。
多年前，虽然非线性分析能更适合、更准确的处理问题，但是由于当时计算设备的能力不够强大、非线性分析软件包线性分析功能不够健全，所以通常采用线性处理的方法。
这种情况已经得到了极大的改善，计算设备的能力变得更加强大、类似ABAQUS这样的产品功能日臻完善，应用日益广泛。
非线性有限元分析在各个制造行业得到了广泛应用，有不少大型用户。
航空航天业一直是非线性有限元分析的大客户，一个重要原因是大量使用复合材料。
新一代波音 787客机将全部采用复合材料。
只有像 ABAQUS这样的软件，才能分析包括多个子系统的产品耐久性能。
在汽车业，用线性有限元分析来做四轮耐久性分析不可能得到足够准确的结果。
分析汽车的整体和各个子系统的性能要求（如悬挂系统等）需要进行非线性分析。
在土木工程业， ABAQUS能处理包括混凝土静动力开裂分析以及沥青混凝土方面的静动力分析，还能处理高度复杂非线性材料的损伤和断裂问题，这对于大型桥梁结构，高层建筑的结构分析非常有效。
瞬态、大变形、高级材料的碰撞问题必须用非线性有限元分析来计算。
线性分析在这种情况下是不适用的。
以往有一些专门的软件来分析碰撞问题，但现在ABAQUS在通用有限元软件包就能解决这些问题。
