abaqus中UMAT子程序编写方法

UMAT

User subroutine to define a material's mechanical behavior.

Product:

Abaqus/Standard

Warning:

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

Overview

User 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 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 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; and

?

is described further in

“

User-defined mechanical material

behavior,

”

Section 25.7.1 of the Abaqus Analysis User's Manual

.

Storage of stress and strain components

In 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 orientations

If 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.

Stability

You 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 rate

DDSDDE and

—

for coupled temperature- displacement and coupled

thermal- 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 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 types

There are several special considerations that need to be noted.

Availability of deformation gradient

The 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 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 gradient

is 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 energy

If

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 elements

When

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 as

where

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 modes

If 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 elements

The 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 nonlinearity

If 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 as

and

For rate-form constitutive laws, the exact consistent Jacobian is given

by

Use with incompressible elastic materials

For

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 from

If

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 defined

Abaqus/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 routines

Several 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 interface

SUBROUTINE UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,

1 RPL,DDSDDT,DRPLDE,DRPLDT,

2 STRA N,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME ,

3 NDI,NSHR,NTENS,NSTATV,PROPS,NP ROPS,COORDS,DROT,PNEWDT,

4 CELENT, DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,KSTEP,KINC)

C

INCLUDE 'ABA_'

C

CHARACTER*80 CMNAME

DIMENSION 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(NPR OPS),COORDS(3),DROT(3,3),DFGRD0(3,3),DFGRD1(3,3)

user coding to define

DDSDDE, STRESS, STATEV, SSE, SPD, SCD

and, if necessary,

RPL, DDSDDT, DRPLDE, DRPLDT, PNEWDT

RETURN

END

Variables to be defined

In all situations

DDSDDE(NTENS,NTENS)

Jacobian matrix of the constitutive model,

, where

are the

stress 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 the

increment

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, SCD

Specific 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 coupled

thermal- electrical-structural analysis

RPL

Volumetric

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.

DRPLDT

Variation of RPL with respect to the temperature.

Only in a geostatic stress procedure or a coupled pore fluid

diffusion/stress analysis for pore pressure cohesive elements

RPL

RPL 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 updated

PNEWDT

Ratio 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.