Obtaining stress invariants, principal stress/strain values and directions, and rotating tensors in an Abaqus/Standard analysis

Utility routines are available for calculating stress invariants, principal stress/strain values, and principal stress/strain directions from the relevant tensors, as well as for transforming tensors to a new basis.

These utility routines are available for Abaqus/Standard user subroutines that store stress and strain components according to the convention presented in Conventions. They are most commonly called from user subroutine UMAT.

An identifier. LSTR=1 indicates that S contains stresses; LSTR=2 indicates that S contains strains.

NDI

Number of direct components.

NSHR

Number of shear components.

Variables returned from the utility routine

PS(I), I=1,2,3

The three principal values.

SPRIND (calculate principal values and directions)

Utility routine interface

CALL SPRIND(S,PS,AN,LSTR,NDI,NSHR)

Variables to be provided to the utility routine

S

A stress or a strain tensor.

LSTR

An identifier. LSTR=1 indicates that S contains stresses; LSTR=2 indicates that S contains strains.

NDI

Number of direct components.

NSHR

Number of shear components.

Variables returned from the utility routine

PS(I), I=1,2,3

The three principal values.

AN(K1,I), I=1,2,3

The direction cosines of the principal directions corresponding to PS(K1).

ROTSIG (rotate a tensor)

Utility routine interface

CALL ROTSIG(S,R,SPRIME,LSTR,NDI,NSHR)

Variables to be provided to the utility routine

S

A stress or strain tensor.

NDI

Number of direct components.

NSHR

Number of shear components.

R

Rotation matrix.

LSTR

An identifier. LSTR$=1$ indicates S contains stresses; LSTR$=2$ indicates S contains strains.

Variables returned from the utility routine

SPRIME

The rotated stress or strain tensor.

Typical usage

In user subroutine UMAT it is often necessary to rotate tensors during a finite-strain analysis. The matrix DROT that is passed into UMAT represents the incremental rotation of the material basis system in which the stress and strain are stored. For an elastic-plastic material that hardens isotropically, the elastic and plastic strain tensors must be rotated to account for the evolution of the material directions. In this case S is the elastic or plastic strain tensor and R is the incremental rotation DROT.