内容发布更新时间 : 2024/6/3 7:57:05星期一 下面是文章的全部内容请认真阅读。

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