# Category 9: Stress Equations#

The following conditions provide a means to set boundary conditions for the hyperbolic viscoelastic stress equations

## STRESS_DEVELOPED#

BC = STRESS_DEVELOPED SS <bc_id>


### Description / Usage#

(SIC/POLYMER_STRESS)

This is a fully developed flow condition from Xie and Pasquali for viscoelastic flows

<bc_id>

The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (side set in EXODUS II) in the problem domain.

### Examples#

BC = STRESS_DEVELOPED SS 1

BC = S11_1 NS 7   4.0   1.0


### Technical Discussion#

Replaces boundary contributions of stress equations with stress equations where the advective term is removed ($$v\cdot\nabla S \rightarrow 0$$)

### References#

Xie, Xueying, and Matteo Pasquali. “A new, convenient way of imposing open-flow boundary conditions in two-and three-dimensional viscoelastic flows.” Journal of non-newtonian fluid mechanics 122, no. 1-3 (2004): 159-176.

## S11#

BC = {bc_name} NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/STRESS11)

This Dirichlet boundary condition specification is used to set a constant xx-stress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:

 {S11 | S11_1 | S11_2 | S11_3 | S11_4 | S11_5 | S11_6 | S11_7} Boundary condition name () that defines the xx-stress for a given mode, where: S11 xx-component of stress tensor for mode 1 S11_1 xx-component of stress tensor for mode 2 S11_2 xx-component of stress tensor for mode 3 S11_3 xx-component of stress tensor for mode 4 S11_4 xx-component of stress tensor for mode 5 S11_5 xx-component of stress tensor for mode 6 S11_6 xx-component of stress tensor for mode 7 S11_7 xx-component of stress tensor for mode 8 NS Type of boundary condition (), where NS denotes node set in the EXODUS II database. The boundary flag identifier, an integer associated with that identifies the boundary location (node set in EXODUS II) in the problem domain. Value of xx-stress. [float2] An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

Following are sample cards for applying a Dirichlet condition on the xx-stress component for mode 2 on node set 7:

BC = S11_1 NS 7   4.0

BC = S11_1 NS 7   4.0   1.0


where the second example uses the “residual” method for applying the same Dirichlet condition.

### Technical Discussion#

See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.

For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).

### References#

GT-014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao

## S12#

BC = {bc_name} NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/STRESS12)

This Dirichlet boundary condition specification is used to set a constant xy-stress (also known as the shear stress) for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:

 {S12 | S12_1 | S12_2 | S12_3 | S12_4 | S12_5 | S12_6 | S12_7} Boundary condition name () that defines the xy-stress for a given mode, where: S12 xy-component of stress tensor for mode 1 S12_1 xy-component of stress tensor for mode 2 S12_2 xy-component of stress tensor for mode 3 S12_3 xy-component of stress tensor for mode 4 S12_4 xy-component of stress tensor for mode 5 S12_5 xy-component of stress tensor for mode 6 S12_6 xy-component of stress tensor for mode 7 S12_7 xy-component of stress tensor for mode 8 NS Type of boundary condition (), where NS denotes node set in the EXODUS II database. The boundary flag identifier, an integer associated with that identifies the boundary location (node set in EXODUS II) in the problem domain. Value of xy-stress. [float2] An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

Following are sample cards for applying a Dirichlet condition on the xy-stress component for mode 5 on node set 10:

BC = S12_4 NS 10   1.25

BC = S12_4 NS 10  1.25   1.0


where the second example uses the “residual” method for applying the same Dirichlet condition.

### Technical Discussion#

See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.

For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).

### References#

GT-014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao

## S13#

BC = {bc_name} NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/STRESS13)

This Dirichlet boundary condition specification is used to set a constant xz-stress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:

 {S13 | S13_1 | S13_2 | S13_3 | S13_4 | S13_5 | S13_6 | S13_7} Boundary condition name () that defines the xz-stress for a given mode, where: S13 xz-component of stress tensor for mode 1 S13_1 xz-component of stress tensor for mode 2 S13_2 xz-component of stress tensor for mode 3 S13_3 xz-component of stress tensor for mode 4 S13_4 xz-component of stress tensor for mode 5 S13_5 xz-component of stress tensor for mode 6 S13_6 xz-component of stress tensor for mode 7 S13_7 xz-component of stress tensor for mode 8 NS Type of boundary condition (), where NS denotes node set in the EXODUS II database. The boundary flag identifier, an integer associated with that identifies the boundary location (node set in EXODUS II) in the problem domain. Value of xz-stress. [float2] An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

Following is a sample card for applying a Dirichlet condition for the xz-stress component for mode 5 on node set 10:

BC = S13_4 NS 10   1.3

BC = S13_4 NS 10   1.3   1.0


where the second example uses the “residual” method for applying the same Dirichlet condition.

### Technical Discussion#

See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.

For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).

### References#

GT-014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao

## S22#

BC = {bc_name} NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/STRESS22)

This Dirichlet boundary condition specification is used to set a constant yy-stress (also known as the shear stress) for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:

 {S22 | S22_1 | S22_2 | S22_3 | S22_4 | S22_5 | S22_6 | S22_7} Boundary condition name () that defines the yy-stress for a given mode, where: S22 yy-component of stress tensor for mode 1 S22_1 yy-component of stress tensor for mode 2 S22_2 yy-component of stress tensor for mode 3 S22_3 yy-component of stress tensor for mode 4 S22_4 yy-component of stress tensor for mode 5 S22_5 yy-component of stress tensor for mode 6 S22_6 yy-component of stress tensor for mode 7 S22_7 yy-component of stress tensor for mode 8 NS Type of boundary condition (), where NS denotes node set in the EXODUS II database. The boundary flag identifier, an integer associated with that identifies the boundary location (node set in EXODUS II) in the problem domain. Value of yy-stress. [float2] An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

Following are sample cards for applying a Dirichlet condition on the yy-stress component for mode 8 on node set 20:

BC = S22_7 NS 20   5.0

BC = S22_7 NS 20   5.0   1.0


where the second example uses the “residual” method for applying the same Dirichlet condition.

### Technical Discussion#

See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.

For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).

### References#

GT-014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao

## S23#

BC = {bc_name} NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/STRESS23)

This Dirichlet boundary condition specification is used to set a constant yz-stress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:

 {S23 | S23_1 | S23_2 | S23_3 | S23_4 | S23_5 | S23_6 | S23_7} Boundary condition name () that defines the yz-stress for a given mode, where: S23 yz-component of stress tensor for mode 1 S23_1 yz-component of stress tensor for mode 2 S23_2 yz-component of stress tensor for mode 3 S23_3 yz-component of stress tensor for mode 4 S23_4 yz-component of stress tensor for mode 5 S23_5 yz-component of stress tensor for mode 6 S23_6 yz-component of stress tensor for mode 7 S23_7 yz-component of stress tensor for mode 8 NS Type of boundary condition (), where NS denotes node set in the EXODUS II database. The boundary flag identifier, an integer associated with that identifies the boundary location (node set in EXODUS II) in the problem domain. Value of yz-stress. [float2] An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

Following are sample cards for applying a Dirichlet condition on the yz-stress component for mode 8 on node set 20:

BC = S23_7 NS 20   5.0

BC = S23_7 NS 20   5.0   1.0


where the second example uses the “residual” method for applying the same Dirichlet condition.

### Technical Discussion#

See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.

For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).

### References#

GT-014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao

## S33#

BC = {bc_name} NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/STRESS33)

This Dirichlet boundary condition specification is used to set a constant zz-stress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:

 {S33 | S33_1 | S33_2 | S33_3 | S33_4 | S33_5 | S33_6 | S33_7} Boundary condition name () that defines the zz-stress for a given mode, where: S33 zz-component of stress tensor for mode 1 S33_1 zz-component of stress tensor for mode 2 S33_2 zz-component of stress tensor for mode 3 S33_3 zz-component of stress tensor for mode 4 S33_4 zz-component of stress tensor for mode 5 S33_5 zz-component of stress tensor for mode 6 S33_6 zz-component of stress tensor for mode 7 S33_7 zz-component of stress tensor for mode 8 NS Type of boundary condition (), where NS denotes node set in the EXODUS II database. The boundary flag identifier, an integer associated with that identifies the boundary location (node set in EXODUS II) in the problem domain. Value of zz-stress. [float2] An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

Following are sample cards for applying a Dirichlet condition on the zz-stress component for mode 1 on node set 100:

BC = S33 NS 100   5.0

BC = S33 NS 100   5.0   1.0


where the second example uses the “residual” method for applying the same Dirichlet condition.

### Technical Discussion#

See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.

For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).

### References#

GT-014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao