VUMAT-中英文对照

对于如同应力及应变张量等的对称张量，含有

ndir+nshr

分量，分量的序号按张量索引号的自

然排序给出。首先是直接分量，然 后是从

12

分量开始的间接分量。例如，包含

< br>ndir

正应力分

量及

nshr

的剪应力张量的应力张量被按照下面的顺序传入

Component

2-D Case

3-D Case

1

2

3

4

5

6

The shear strain components in user subroutine VUMAT are stored as tensor components and not as

engineering components; this is different from user subroutine UMAT in ABAQUS/Standard,

which uses engineering components.

Nonsymmetric tensors

非对称张量

For nonsymmetric tensors there are ndir+2*nshr components, and the component order is given as a

natural permutation of the indices of the tensor. The direct components are first and then the

indirect components, beginning with the 12-component. For example, the deformation gradient is

passed as

对于非对称张量含有

ndir+2* nshr

分量，

分量的顺序按照张量索引号的自然排序给出。首 先是

直接分量，其次是从

12

分量开始 的间接分量。例如，位移梯度按照下面的顺序传递

Component

2-D Case

3-D Case

1

2

3

4

5

6

7

8

9

Initial calculations and checks

最初计算和检查

25.3.4-2

In the data check phase of the analysis ABAQUS/Explicit calls user subroutine VUMAT with a set

of fictitious strains and a totalTime and stepTime both equal to 0.0. This is done as a check on your

constitutive relation and to calculate the equivalent initial material properties, based upon which the

initial elastic wave speeds are computed.

在

ABAQUS /Explicit

调用用户子程序

VUMAT

分析的数据检查阶段

,

小应变、

总时间及时间步

都为

0

。这作为对用 户本构关系的一个检查，基于计算得到的初始材料波速来计算等效初始

材料属性。

Defining local orientations

定义局部方向

All stresses, strains, stretches, and state variables are in the orientation of the local material axes.

These local material axes form a basis system in which stress and strain components are stored.

This represents a corotational coordinate system in which the basis system rotates with the material.

If a user-specified coordinate system (

“Orientations,” Section 2.2.5

) is used, it defines the local

material axes in the undeformed configuration.

所有的应力、应变、延伸及状态变量均按局部材料轴的 方向。这些局部材料轴形成一个应力

与应变分量存储的基本系统。即这个基本系是随着材 料联合转动的坐标系。如果使用用户指

定坐标系，则它在无变形结构中定义局部材料轴。

Special considerations for various element types

不同单元类型的特殊考虑

The use of user subroutine VUMAT requires special consideration for various element types.

用户子程序

VUMAT

的使用需要对不同的单元类型进行特殊的考虑。

Shell and plane stress elements

壳及平面应力单元

You must define the stresses and internal state variables. In the case of shell or plane stress elements,

you must define strainInc(*,3), the thickness strain increment. The internal energies can be defined

if desired. If they are not defined, the energy balance provided by ABAQUS/Explicit will not be

meaningful.

用户必须定义应力和初始状态变量。在壳或平面应力单元的情况下，用户必须定义应变包 括

（

*,3

），厚度应变增量。如果需 要的话还需要定义初始能量。如果没有定义，那么

ABAQUS/Explicit

提供的能量平衡将没有意义。

Shell elements

壳单元

When VUMAT is used to define the material response of shell elements, ABAQUS/Explicit cannot

calculate a default value for the transverse shear stiffness of the element. Hence, you must define

the element's transverse shear stiffness. See

“Shell section behavior,” Section 15.6.4

, for guidelines

on choosing this stiffness.

当使用

VUMAT

定义壳单元的材料响 应时，

ABAQUS/Explicit

不能计算单元的缺省横 向剪切

刚度。因此，用户需要定义单元的横向剪切刚度。关于选择横行剪切刚度的详细资 料请参考

“Shell section behavior,” Section 15.6.4

Beam elements

梁单元

For beam elements the stretch tensor and the deformation gradient tensor are not available. For

beams in space you must define the thickness strains, strainInc(*,2) and strainInc(*,3). strainInc(*,4)

25.3.4-3

is the shear strain associated with twist. Thickness stresses, stressNew(*,2) and stressNew(*,3), are

assumed to be zero and any values you assign are ignored.

对于梁单元不能使用拉伸张量及位移梯度张量。对于空间梁，用户必须定义厚度应变、应变

增量（

*

，

2

）及应变增量（

*

，

3

）。应变增量（

*

，

4

）时与扭曲有关的剪应变。厚度应力，

（

*

，

2

）及（

*

，

3

）假定为

0

，并且用户分配的任何相关张量都被忽略。

Deformation gradient

位移梯度

The polar decomposition of the deformation gradient is written as

, where

and

are the right and left symmetric stretch tensors, respectively. The constitutive model is

defined in a corotational coordinate system in which the basis system rotates with the material. All

stress and strain tensor quantities are defined with respect to the corotational basis system. The right

stretch tensor,

, is used. The relative spin tensor

represents the spin (the antisymmetric

part of the velocity gradient) defined with respect to the corotational basis system.

位移梯度写成

，其中

及

分别为右边及左边的对称拉伸张量。本

构模型定义为联合旋转坐标系，在该坐标系中基 系随着材料转动。所有的应力和应变张量值

按照联合旋转坐标系定义。使用右边的拉伸位 移

。相应的旋转张量

代表与联合旋转

基 系相应的转动。

Special considerations for hyperelasticity

超弹性的特殊考虑

Hyperelastic constitutive models in VUMAT should be defined in a corotational coordinate system

in which the basis system rotates with the material. This is most effectively accomplished by

formulating the hyperelastic constitutive model in terms of the stretch tensor,

, instead of in terms

of the deformation gradient,

. Using the deformation gradient can present some

difficulties because the deformation gradient includes the rotation tensor and the resulting stresses

would need to be rotated back to the corotational basis.

在

VUMAT

中的超弹性本构模型可以被定义在联合选择坐标系中。这可以通过用拉伸张量

表示的超 弹性本构模型很好的实现，而不是使用位移梯度

来表示。使用位移梯度

< br>可能会带来一些困难，因为位移梯度包括旋转张量并且导致应力需要选择返回到联合旋转基

系。

Objective stress rates

目标应力率

The Green-Naghdi stress rate is used when the mechanical behavior of the material is defined using

user subroutine VUMAT. The stress rate obtained with user subroutine VUMAT may differ from

that obtained with a built-in ABAQUS material model. For example, most material models used

with solid (continuum) elements in ABAQUS/Explicit employ the Jaumann stress rate. This

difference in the formulation will cause significant differences in the results only if finite rotation of

a material point is accompanied by finite shear. For a discussion of the objective stress rates used in

ABAQUS, see

“Stress rates,” Section 1.5.3

of the ABAQUS Theory Manual

.

在用户子程序

VUM AT

中使用

Green-Naghdi

应力率来定义材料的力学本构关系。

通过用户子

程序

获得的应力率可能会与在

ABAQUS

建立的材料模型获得的应力率有所不同。

例如，在

ABAQUS/Explicit

中大多数实体（连续）单元材料模型使用< /p>

Jaumann

应力率。只要

材料点的有 限旋转伴随有限剪切，这种表达方式的不同将导致计算结果的明显差异。关于

ABAQU S

中使用的目标应力率的详细讨论参考

“Stress rates,” Section 1.5.3 of the ABAQUS

Theory Manual

.

25.3.4-4

Material point deletion

材料点删除

Material points that satisfy a user- defined failure criterion can be deleted from the model (see

“User

-

defined mechanical material behavior,” Section 12.8.1

). You must specify the state variable

number controlling the element deletion flag when you allocate space for the solution-dependent

state variables, as explained in

“User

-

defined mechanical material behavior,” Section 12.

8.1

. The

deletion state variable should be set to a value of one or zero in VUMAT. A value of one indicates

that the material point is active, while a value of zero indicates that ABAQUS/Explicit should delete

the material point from the model by setting the stresses to zero. The structure of the block of

material points passed to user subroutine VUMAT remains unchanged during the analysis; deleted

material points are not removed from the block. ABAQUS/Explicit will pass zero stresses and strain

increments for all deleted material points. Once a material point has been flagged as deleted, it

cannot be reactivated.

满足用户定义的破坏准则的材料点可以被从模型中删除（参考

“User

-defined mechanical

material behavior,” Secti

on 12.8.1

)

。当用户给结果依赖状态变量分配空间时，用户需要指定控

制单元删 除标示的状态变量号，在

“User

-

defined mechanical material behavior,” Section 12. 8.1

中进行详细说明。在

VUMAT

中删除状态变量可以被赋予

1

或者

0< /p>

。

1

表示材料点时激活的，

0

表示

ABAQUS/Explicit

0

删除材料点。在分析过程中传 递给用户子程序

VUMAT

的材料点结构保持不变；

ABAQUS/Explicit

将传递

0

应力及应变给所有删除的材料点。一旦 一个材料点被标示为删除，该材料点将不能够被再次

激活。

User subroutine interface

用户子程序

subroutine vumat(

C Read only (unmodifiable)variables -

1

nblock, ndir, nshr, nstatev, nfieldv, nprops, lanneal,

2

stepTime, totalTime, dt, cmname, coordMp, charLength,

3

props, density, strainInc, relSpinInc,

4

tempOld, stretchOld, defgradOld, fieldOld,

5

stressOld, stateOld, enerInternOld, enerInelasOld,

6

tempNew, stretchNew, defgradNew, fieldNew,

C Write only (modifiable) variables -

7

stressNew, stateNew, enerInternNew, enerInelasNew )

C

include 'vaba_'

C

dimension props(nprops), density(nblock), coordMp(nblock,*),

1

charLength(nblock), strainInc(nblock,ndir+nshr),

2

relSpinInc(nblock,nshr), tempOld(nblock),

3

stretchOld(nblock,ndir+nshr),

4

defgradOld(nblock,ndir+nshr+nshr),

5

fieldOld(nblock,nfieldv), stressOld(nblock,ndir+nshr),

6

stateOld(nblock,nstatev), enerInternOld(nblock),

7

enerInelasOld(nblock), tempNew(nblock),

25.3.4-5

8

stretchNew(nblock,ndir+nshr),

8

defgradNew(nblock,ndir+nshr+nshr),

9

fieldNew(nblock,nfieldv),

1

stressNew(nblock,ndir+nshr), stateNew(nblock,nstatev),

2

enerInternNew(nblock), enerInelasNew(nblock),

C

character*80 cmname

C

do 100 km = 1,nblock

user coding

100 continue

return

end

Variables to be defined

被定义的变量

stressNew (nblock, ndir+nshr)

Stress tensor at each material point at the end of the increment.

在增量结束时每个材料点的应力张量。

stateNew (nblock, nstatev)

State variables at each material point at the end of the increment. You define the size of this

array by allocating space for it (see

“User subroutines: overview,” Section 25.1.1

, for more

information).

增量结束时每个材料点的状态变 量。

用户通过分配空间来定义该矩阵的大小

（更多的资料

参考

“User subroutines: overview,” Section 25.1.1

）。

Variables that can be updated

可以更新的变量

enerInternNew (nblock)

Internal energy per unit mass at each material point at the end of the increment.

增量结束时每个材料点单位质量的内能。

enerInelasNew (nblock)

Dissipated inelastic energy per unit mass at each material point at the end of the increment.

增量结束时每个材料点单位质量的消散的无弹性能。

Variables passed in for information

nblock

Number of material points to be processed in this call to VUMAT.

调用

VUMAT

的材料 点号。

ndir

Number of direct components in a symmetric tensor.

对成张量的直接分量号。

nshr

Number of indirect components in a symmetric tensor.

25.3.4-6

对称张量的间接分量号。

nstatev

Number of user-defined state variables that are associated with this material type (you define

this as described in

“Allocating space” in “User subroutines: overview,” Section 25.1.1

).

与材料类型相关的用户定义状态变量号。

nfieldv

Number of user-defined external field variables.

用户定义外部场变量号。

nprops

User- specified number of user-defined material properties.

用户定义材料属性的用户指定号。

lanneal

Flag indicating whether the routine is being called during an annealing process. lanneal=0

indicates that the routine is being called during a normal mechanics increment. lanneal=1

indicates that this is an annealing process and you should re-initialize the internal state variables,

stateNew, if necessary. ABAQUS/Explicit will automatically set the stresses, stretches, and

state to a value of zero during the annealing process.

在退火处理过程中标示程序是否被调用。

Laneal=0

< br>表明程序在正常力学增量过程中被调

用。

Laneal< /p>

＝

1

表明这是一个退火过程，并且如果需 要的话用户需要重新初始化内部状态

变量

stateNew

。

ABAQUS/Explicit

将自动 设置应力，延展性及在退火过程中

0

值状态。

< br>

stepTime

Value of time since the step began.

从时间步开始时的的时间

totalTime

Value of total time. The time at the beginning of the step is given by totalTime - stepTime.

总时间值。时间步开始时的时间定义为

totalTime - stepTime

dt

Time increment size.

时间增量大小。

cmname

User- specified material name, left justified. It is passed in as an upper-case character string.

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.

用户指定材料名。按照大写字母传入。有些内 部材料本构以

ABQ_

字母开头赋名。为了避

< br>免冲突，用户不能使用

ABQ_

作为

cmname

的开头字母。

coordMp(nblock,*)

Material point coordinates. It is the midplane material point for shell elements and the centroid

for beam elements.

材料点坐标。对于壳单元为中平面材料点，对于梁单元为质心。

charLength(nblock)

Characteristic element length. This is a typical length of a line across an 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 elements, it is a characteristic

length in the

–

plane only. For cohesive elements it is equal to the constitutive thickness.

25.3.4-7