Category 9: Stress Equations#

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

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 (<bc_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 (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

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

<float1>

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 (<bc_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 (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

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

<float1>

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 (<bc_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 (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

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

<float1>

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 (<bc_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 (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

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

<float1>

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 (<bc_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 (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

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

<float1>

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 (<bc_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 (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

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

<float1>

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