6. Generic subprogram specifications EQUTHM#

6.1. Routine arguments#

ARGUMENTS OF ENTREE: IN

COMPOR

Behaviour description

OPTION

Option to be calculated

NDIM

Space dimension

2 or 3

NDDL

Total number of degrees of freedom for the calling element

DIMDEF

Dimension of the table of generalized deformations at the Gauss point

DIMCON

Dimension of the table of generalized stresses at the Gauss point

NVIMEC

Number of « mechanical » internal variables

ADVIME

Address of mechanical internal variables in the table of internal variables at the Gauss point

NVIHY

Number of « hydraulic » internal variables

ADVIHY

Address of hydraulic internal variables in the table of internal variables at the Gauss point

NVITM

Number of « thermal » internal variables

ADVITM

Address of thermal internal variables in the table of internal variables at the Gauss point

B (1:dimdef,1:nddl)

Matrix \({\left[B\right]}_{g}^{\mathit{el}}\)

DEFGEP (1:dimdef)

Generalized deformation values at the Gauss point (time plus)

DEFGEM (1:dimdef)

Generalized deformation values at the Gauss point (time minus)

CONGEM (1:dimcon)

Generalized stress values at the Gauss point (time minus)

VINTM (1:nvimec+nvihy+nvitm)

Values of internal variables at the Gauss point (time minus)

MECA (1:5)

YAMEC = MECA (1)

Logical if 1 there is a mechanical equation

ADDEME = MECA (2)

Address in the tables of deformations at the Gauss point DEFGEPet DEFGEMdes deformations corresponding to mechanics

ADCOME = MECA (3)

Address in the tables of constraints at the Gauss point CONGEPet CONGEMdes constraints corresponding to the equation ieq

NDEFME = MECA (4)

Number of mechanical deformations

NCONME = MECA (5)

Number of mechanical stresses

PRESS1 (1:5)

YAP1 = PRESS1 (1)

Logical if 1 there is an equation constituting 1

NBPHA1 = PRESS1 (2)

number of phases for component 1

ADDEP1 = PRESS1 (3)

Address in the tables of deformations at the Gauss point DEFGEPet DEFGEMdes deformations corresponding to the first pressure

ADCP11 = PRESS1 (4)

Address in the tables of stresses at the Gauss point CONGEPet CONGEMdes: constraints corresponding to the first phase of the first constituent

ADCP12 = PRESS1 (5)

Address in the tables of stresses at the Gauss point CONGEPet CONGEMdes: constraints corresponding to the second phase of the first constituent

NDEFP1 = PRESS1 (6)

Number of pressure deformations 1

NCONP1 = PRESS1 (7)

Number of constraints for each phase of component 1

PRESS2 (1:5)

YAP2 = PRESS2 (1)

Logical if 1 there is an equation constituting 2

NBPHA2 = PRESS2 (2)

number of phases for component 2

ADDEP2 = PRESS2 (3)

Address in the tables of the deformations at the Gauss point DEFGEPet DEFGEMdes deformations corresponding to PRE2

ADCP21 = PRESS2 (4)

Address in the tables of stresses at the Gauss point CONGEPet CONGEMdes: constraints corresponding to the first phase of the second constituent

ADCP22 = PRESS2 (5)

Address in the tables of stresses at the Gauss point CONGEPet CONGEMdes: constraints corresponding to the second phase of the second constituent

NDEFP2 = PRESS2 (6)

Number of pressure deformations 2

NCONP2 = PRESS2 (7)

Number of constraints for each phase of component 2

TEMPE (1:5)

YATE = TEMPE (1)

Logical if 1 there is a thermal equation

ADDETE = TEMPE (2)

Address in the tables of the deformations at the Gauss point DEFGEPet DEFGEMdes deformations corresponding to the thermal

ADCOTE = TEMPE (3)

Address in the tables of the constraints at the Gauss point CONGEPet first CONGEMdes stresses corresponding to the thermal

NDEFT = TEMPE (4)

Number of thermal deformations

NCONT = TEMPE (5)

Number of thermal stresses

ARGUMENTS OF SORTIE: OUT

CONGEP (1:dimcon)

Generalized stress values at the Gauss point (time plus)

VINTP (1:nvimec+nvihy+nvitm)

Values of the internal variables at the Gauss point (time plus)

V (1:nddl)

\(\left\{{\text{V}}_{g}^{\mathit{el}}\right\}={\left[{\text{B}}_{g}^{\mathit{el}}\right]}^{T}\left\{R\right\}\)

MAT (1:nddl,1:nddl)

\(\left[{{\text{DF}}_{g}^{\mathit{el}}}_{i({u}_{n}^{\text{+}},{P}_{n}^{\text{+}},{T}_{n}^{\text{+}})}\right]={\left[{\text{B}}_{g}^{\mathit{el}}\right]}^{T}\cdot \left[\text{DRDE}\right]\cdot \left[{\text{B}}_{g}^{\mathit{el}}\right]\)

TABLEAUX OF TRAVAIL

R (1:dimdef)

DRDS (1:dimdef,1:dimcon)

DSDE (1:dimcon,1:dimdef)

6.2. Addressing in deformation and stress tables#

6.2.1. Addressing in deformations#

6.2.1.1. Deformations less time#

Party (local name in routine COMTHM )

Meaning

Address in DEFGEM

Address in ****

DEMECM

\(\text{u},\underline{\underline{\epsilon }}(\text{u})\)

ADDEME

DEP1M

\({p}_{\mathrm{1,}}\nabla {p}_{1}\)

ADDEP1

DEP2M

\({p}_{\mathrm{2,}}\nabla {p}_{2}\)

ADDEP2

DETM

\(T,\nabla T\)

ADDETE

6.2.1.2. Time plus deformations#

Party (local name in routine COMTHM )

Meaning

Address in DEFGEP

Address in ****

DEMECP

\(\text{u},\underline{\underline{\epsilon }}(\text{u})\)

ADDEME

DEP1P

\({p}_{\mathrm{1,}}\nabla {p}_{1}\)

ADDEP1

DEP2P

\({p}_{\mathrm{2,}}\nabla {p}_{2}\)

ADDEP2

DETP

\(T,\nabla T\)

ADDETE

6.2.2. Addressing under constraints#

6.2.2.1. Less time constraints#

Party (local name in routine COMTHM )

Meaning

Address in CONGEM

Address in ****

COMECM

\(\underline{\underline{\sigma \text{'}}},{\sigma }_{p}\)

ADCOME

CP11M

\({m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{1}\text{ou}{m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{\mathrm{1,}}{h}_{\mathrm{1m}}^{1}\)

ADCP11

CP12M

\({m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{2}\text{ou}{m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{\mathrm{2,}}{h}_{\mathrm{1m}}^{2}\)

ADCP12

CP21M

\({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{1}\text{ou}{m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{\mathrm{1,}}{h}_{\mathrm{2m}}^{1}\)

ADCP21

CP22M

\({m}_{2}^{\mathrm{2,}}{\text{M}}_{2}^{2}\text{ou}{m}_{2}^{\mathrm{2,}}{\text{M}}_{2}^{\mathrm{2,}}{h}_{\mathrm{2m}}^{2}\)

ADCP22

COTM

\(Q\text{'},\text{q}\)

ADCOTE

6.2.2.2. Time constraints plus#

Party (local name in routine COMTHM )

Meaning

Address in CONGEP

Address in ****

COMECP

\(\underline{\underline{\sigma \text{'}}},{\sigma }_{p}\)

ADCOME

CP11P

\({m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{1}\text{ou}{m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{\mathrm{1,}}{h}_{\mathrm{1m}}^{1}\)

ADCP11

CP12P

\({m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{2}\text{ou}{m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{\mathrm{2,}}{h}_{\mathrm{1m}}^{2}\)

ADCP12

CP21P

\({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{1}\text{ou}{m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{\mathrm{1,}}{h}_{\mathrm{2m}}^{1}\)

ADCP21

CP22P

\({m}_{2}^{\mathrm{2,}}{\text{M}}_{2}^{2}\text{ou}{m}_{2}^{\mathrm{2,}}{\text{M}}_{2}^{\mathrm{2,}}{h}_{\mathrm{2m}}^{2}\)

ADCP22

COTP

\(Q\text{'},\text{q}\)

ADCOTE

6.2.3. Addressing in internal variables (example)#

6.2.3.1. Internal variables at least#

Party (local name in routine COMTHM )

Meaning

Address in VINTM

Address in ****

VIMEM

\(\varphi\)

ADVIME

VIHYM

\({S}_{\mathit{lq}},{P}_{\mathit{vq}},{P}_{\mathit{lq}}\)

ADVIHY

6.2.3.2. Internal variables over time#

Party (local name in routine COMTHM )

Meaning

Address in VINTP

Address in ****

VIMEP

\(\varphi\)

ADVIME

VIHYP

\({S}_{\mathit{lq}},{P}_{\mathit{vq}},{P}_{\mathit{lq}}\)

ADVIHY

6.3. R, DRDS, DSDE addressing#

6.3.1. Addressing in R#

Subpart of R

Associated with

Address in R

R1

\(\text{v}\)

ADDEME

R2

\(\epsilon (\text{v})\)

ADDEME + NDIM

R3

\({\pi }_{1}\)

ADDEP1

R4

\(\nabla {\pi }_{1}\)

ADDEP1 +1

R5

\({\pi }_{2}\)

ADDEP2

R6

\(\nabla {\pi }_{2}\)

ADDEP2 +1

R7

\(\tau\)

ADDETE

R8

\(\nabla \tau\)

ADDETE +1

6.3.2. Addressing in DRDS#

Part of the table DRDS

Meaning

Address in DRDS

DR1DS

\(\left[\begin{array}{cc}\frac{\partial {R}_{1}}{\partial {\sigma }^{\text{'}\text{+}}}& \frac{\partial {R}_{1}}{\partial {\sigma }_{p}^{\text{+}}}\end{array}\right]\)

ADDEME, ADCOME

DR2DS

ADDEME + NDIM -1, ADCOME

DR1P11

\(\begin{array}{c}\left[\begin{array}{cc}\frac{\partial {R}_{1}}{\partial {m}_{1}^{1\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{1}^{1\text{+}}}\end{array}\right]\mathit{ou}\\ \left[\begin{array}{ccc}\frac{\partial {R}_{1}}{\partial {m}_{1}^{1\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{1}^{1\text{+}}}& \frac{\partial {R}_{1}}{\partial {h}_{\mathrm{1m}}^{1\text{+}}}\end{array}\right]\end{array}\)

ADDEME, ADCP11

DR2P11

ADDEME + NDIM -1, ADCP11

DR1P12

\(\begin{array}{c}\left[\begin{array}{cc}\frac{\partial {R}_{1}}{\partial {m}_{1}^{2\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{1}^{2\text{+}}}\end{array}\right]\mathit{ou}\\ \left[\begin{array}{ccc}\frac{\partial {R}_{1}}{\partial {m}_{1}^{2\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{1}^{2\text{+}}}& \frac{\partial {R}_{1}}{\partial {h}_{\mathrm{1m}}^{2\text{+}}}\end{array}\right]\end{array}\)

ADDEME, ADCP12

DR2P12

ADDEME + NDIM -1, ADCP12

DR1P21

\(\begin{array}{c}\left[\begin{array}{cc}\frac{\partial {R}_{1}}{\partial {m}_{2}^{1\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{2}^{1\text{+}}}\end{array}\right]\mathit{ou}\\ \left[\begin{array}{ccc}\frac{\partial {R}_{1}}{\partial {m}_{2}^{1\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{2}^{1\text{+}}}& \frac{\partial {R}_{1}}{\partial {h}_{\mathrm{2m}}^{1\text{+}}}\end{array}\right]\end{array}\)

ADDEME, ADCP21

DR2P21

ADDEME + NDIM -1, ADCP21

DR1P22

\(\begin{array}{c}\left[\begin{array}{cc}\frac{\partial {R}_{1}}{\partial {m}_{2}^{2\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{2}^{2\text{+}}}\end{array}\right]\mathit{ou}\\ \left[\begin{array}{ccc}\frac{\partial {R}_{1}}{\partial {m}_{2}^{2\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{M}}_{2}^{2\text{+}}}& \frac{\partial {R}_{1}}{\partial {h}_{\mathrm{2m}}^{2\text{+}}}\end{array}\right]\end{array}\)

ADDEME, ADCP22

DR2P22

ADDEME + NDIM -1, ADCP22

DR1DT

\(\left[\begin{array}{cc}\frac{\partial {R}_{1}}{\partial {Q}^{\text{'}\text{+}}}& \frac{\partial {R}_{1}}{\partial {\text{q}}^{\text{+}}}\end{array}\right]\)

ADDEME, ADCOTE

DR2DT

ADDEME + NDIM -1, ADCOTE

DR3DS

ADDEP1, ADCOME

DR4DS

ADDEP1 +1, ADCOME

DR3P11

ADDEP1, ADCP11

DR4P11

ADDEP1 +1, ADCP11

DR3P21

ADDEP1, ADCP21

DR4P21

ADDEP1 + 1, ADCP21

DR3DT

ADDEP1, ADCOTE

DR4DT

ADDEP1 + 1, ADCOTE

DR5DS

ADDEP2, ADCOME

DR6DS

ADDEP2 + 1, ADCOME

DR5P11

ADDEP2, ADCP11

DR6P11

ADDEP2 + 1, ADCP11

DR5P21

ADDEP2, ADCP21

DR6P21

ADDEP2 +1, ADCP21

DR5DT

ADDEP2, ADCOTE

DR6DT

ADDEP2 + 1, ADCOTE

DR7DS

ADDETE, ADCOME

DR8DS

ADDETE + 1, ADCOME

DR7P11

ADDETE, ADCP11

DR8P11

ADDETE + 1, ADCP11

DR7P21

ADDETE, ADCP21

DR8P21

ADDETE + 1, ADCP21

DR7DT

ADDETE, ADCOTE

DR8DT

ADDETE +1, ADCOTE

6.3.3. Addressing in DSDE#

Party (local name to COMTHM )) **

Significance

Address in** DSDE **

DMECDE

\(\left[\begin{array}{c}\frac{\partial \sigma \text{'}}{\partial \epsilon }\\ \frac{\partial {\sigma }_{p}}{\partial \epsilon }\end{array}\right]\)

ADCOME, ADDEME

DMECP1

\(\left[\begin{array}{cc}\frac{\partial \sigma \text{'}}{\partial {p}_{1}}& \frac{\partial \sigma \text{'}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\sigma }_{p}}{\partial {p}_{1}}& \frac{\partial {\sigma }_{p}}{\partial \nabla {p}_{1}}\end{array}\right]\)

ADCOME, ADDEP1

DMECP2

\(\left[\begin{array}{cc}\frac{\partial \sigma \text{'}}{\partial {p}_{2}}& \frac{\partial \sigma \text{'}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\sigma }_{p}}{\partial {p}_{2}}& \frac{\partial {\sigma }_{p}}{\partial \nabla {p}_{2}}\end{array}\right]\)

ADCOME, ADDEP2

DMECDT

\(\left[\begin{array}{cc}\frac{\partial \sigma \text{'}}{\partial T}& \frac{\partial \sigma \text{'}}{\partial \nabla T}\\ \frac{\partial {\sigma }_{p}}{\partial T}& \frac{\partial {\sigma }_{p}}{\partial \nabla T}\end{array}\right]\)

ADCOME, ADDETE

DP11DE

\(\left[\begin{array}{c}\frac{\partial {m}_{1}^{1}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \epsilon }\end{array}\right]\)

ADCP11, ADDEME

DP11P1

\(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{1}}{\partial {p}_{1}}& \frac{\partial {m}_{1}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{1}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \nabla {p}_{1}}\end{array}\right]\)

ADCP11, ADDEP1

DP11P2

\(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{1}}{\partial {p}_{2}}& \frac{\partial {m}_{1}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{1}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \nabla {p}_{2}}\end{array}\right]\)

ADCP11, ADDEP2

DP11DT

\(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{1}}{\partial T}& \frac{\partial {m}_{1}^{1}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial T}& \frac{\partial {\text{M}}_{1}^{1}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial T}& \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \nabla T}\end{array}\right]\)

ADCP11, ADDETE

DP12DE

\(\left[\begin{array}{c}\frac{\partial {m}_{1}^{2}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \epsilon }\end{array}\right]\)

ADCP12, ADDEME

DP12P1

\(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{2}}{\partial {p}_{1}}& \frac{\partial {m}_{1}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{1}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \nabla {p}_{1}}\end{array}\right]\)

ADCP12, ADDEP1

DP12P2

\(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{2}}{\partial {p}_{2}}& \frac{\partial {m}_{1}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{1}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \nabla {p}_{2}}\end{array}\right]\)

ADCP12, ADDEP2

DP12DT

\(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{2}}{\partial T}& \frac{\partial {m}_{1}^{2}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial T}& \frac{\partial {\text{M}}_{1}^{2}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial T}& \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \nabla T}\end{array}\right]\)

ADCP12, ADDETE

DP21DE

\(\left[\begin{array}{c}\frac{\partial {m}_{2}^{1}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \epsilon }\end{array}\right]\)

ADCP21, ADDEME

DP21P1

\(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{1}}{\partial {p}_{1}}& \frac{\partial {m}_{2}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{2}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \nabla {p}_{1}}\end{array}\right]\)

ADCP21, ADDEP1

DP21P2

\(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{1}}{\partial {p}_{2}}& \frac{\partial {m}_{2}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{2}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \nabla {p}_{2}}\end{array}\right]\)

ADCP21, ADDEP2

DP21DT

\(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{1}}{\partial T}& \frac{\partial {m}_{2}^{1}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial T}& \frac{\partial {\text{M}}_{2}^{1}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial T}& \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \nabla T}\end{array}\right]\)

ADCP21, ADDETE

DP22DE

\(\left[\begin{array}{c}\frac{\partial {m}_{2}^{2}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \epsilon }\end{array}\right]\)

ADCP22, ADDEME

DP22P1

\(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{2}}{\partial {p}_{1}}& \frac{\partial {m}_{2}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{2}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \nabla {p}_{1}}\end{array}\right]\)

ADCP22, ADDEP1

DP22P2

\(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{2}}{\partial {p}_{2}}& \frac{\partial {m}_{2}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{2}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \nabla {p}_{2}}\end{array}\right]\)

ADCP22, ADDEP2

DP22DT

\(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{2}}{\partial T}& \frac{\partial {m}_{2}^{2}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial T}& \frac{\partial {\text{M}}_{2}^{2}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial T}& \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \nabla T}\end{array}\right]\)

ADCP22, ADDETE

DTDE

\(\left[\begin{array}{c}\frac{\partial Q\text{'}}{\partial \epsilon }\\ \frac{\partial \text{q}}{\partial \epsilon }\end{array}\right]\)

ADCOTE, ADDEME

DTDP1

\(\left[\begin{array}{cc}\frac{\partial Q\text{'}}{\partial {p}_{1}}& \frac{\partial Q\text{'}}{\partial \nabla {p}_{1}}\\ \frac{\partial \text{q}}{\partial {p}_{1}}& \frac{\partial \text{q}}{\partial \nabla {p}_{1}}\end{array}\right]\)

ADCOTE, ADDEP1

DTDP2

\(\left[\begin{array}{cc}\frac{\partial Q\text{'}}{\partial {p}_{2}}& \frac{\partial Q\text{'}}{\partial \nabla {p}_{2}}\\ \frac{\partial \text{q}}{\partial {p}_{2}}& \frac{\partial \text{q}}{\partial \nabla {p}_{2}}\end{array}\right]\)

ADCOTE, ADDEP2

DTDT

\(\left[\begin{array}{cc}\frac{\partial \sigma \text{'}}{\partial T}& \frac{\partial \sigma \text{'}}{\partial \nabla T}\\ \frac{\partial \text{q}}{\partial T}& \frac{\partial \text{q}}{\partial \nabla T}\end{array}\right]\)

ADCOTE, ADDETE

6.4. Routine algorithm EQUTHM#

YAMEC = MECA (1)

ADDEME = MECA (2)

ADCOME = MECA (3)

NDEFME = MECA (4)

NCONME = MECA (5)

YAP1 = PRESS1 (1)

NBPHA1 = PRESS1 (2)

ADDEP1 = PRESS1 (3)

ADCP11 = PRESS1 (4)

ADCP12 = PRESS1 (5)

NDEFP1 = PRESS1 (6)

NCONP1 = PRESS1 (7)

YAP2 = PRESS2 (1)

NBPHA2 = PRESS2 (2)

ADDEP2 = PRESS2 (3)

ADCP21 = PRESS2 (4)

ADCP22 = PRESS2 (5)

NDEFP2 = PRESS2 (6)

NCONP2 = PRESS2 (7)

YATE = TEMPE (1)

ADDETE = TEMPE (2)

ADCOTE = TEMPE (3)

NDEFT = TEMPE (4)

NCONT = TEMPE (5)

CALL COMTHM (

COMPOR

OPTION

NDIM

NDDL

DIMDEF

DIMCON

NVIMEC

NVIHY, NVITM

NDEFME

NDEFP1

NDEFP2

NDEFT

NCONME

NCONP1

NCONP2

NCONT

YAP1

NBPHA1

YAP2

NBPHA2

DEFGEM (ADDEME)

DEFGEM (ADDEP1)

DEFGEM (ADDEP2)

DEFGEM (ADDETE)

DEFGEP (ADDEME)

DEFGEP (ADDEP1)

DEFGEP (ADDEP2)

DEFGEP (ADDETE)

CONGEM (ADCOME)

CONGEM (ADCOTE)

CONGEM (ADCP11)

CONGEM (ADCP12)

CONGEM (ADCP21)

CONGEM (ADCP21)

VINTM (ADVIME)

VINTM (ADVIHY)

VINTM (ADVITM)

CONGEP (ADCOME)

CONGEP (ADCP11)

CONGEP (ADCP21)

CONGEP (ADCOTE)

VINTP (ADVIME)

VINTP (ADVIHY)

VINTP (ADVITM)

DSDE (ADCOME, ADDEME)

DSDE (ADCOME, ADDEP1)

DSDE (ADCOME, ADDEP2)

DSDE (ADCOME, ADDETE)

DSDE (ADCP11, ADDEP1)

DSDE (ADCP11, ADDEME)

DSDE (ADCP11, ADDEP2)

DSDE (ADCP11, ADDETE)

DSDE (ADCP12, ADDEP1)

DSDE (ADCP12, ADDEME)

DSDE (ADCP12, ADDEP2)

DSDE (ADCP12, ADDETE)

DSDE (ADCP21, ADDEP2)

DSDE (ADCP21, ADDEME)

DSDE (ADCP21, ADDEP1)

DSDE (ADCP21, ADDETE)

DSDE (ADCP22, ADDEP2)

DSDE (ADCP22, ADDEME)

DSDE (ADCP22, ADDEP1)

DSDE (ADCP22, ADDETE)

DSDE (ADCOTE, ADDETE)

DSDE (ADCOTE, ADDEME)

DSDE (ADCOTE, ADDEP1)

DSDE (ADCOTE, ADDEP2)

)

If FULL_MECA or RAPH_MECA

If YAMEC

Injecting \(\sigma {\text{'}}^{\text{+}}+{\sigma }_{p}^{\text{+}}I\) terms into R (ADDEME + NDIM -1)

Injecting terms: \(-{r}_{0}{\text{F}}^{{m}^{\text{+}}}\) into R (ADDEME)

If YAP1

Injecting \(-{m}_{1}^{1\text{+}}+{m}_{1}^{1\text{-}}\text{ou}-{m}_{1}^{1\text{+}}-{m}_{1}^{2\text{+}}+{m}_{1}^{1\text{-}}+{m}_{1}^{2\text{-}}\) terms into R (ADDEP1)

Injection of terms

\(\begin{array}{c}\Delta t\theta {\text{M}}_{1}^{1\text{+}}+(1-\theta )\Delta t{\text{M}}_{1}^{1\text{-}}\text{ou}\\ \theta \Delta t\left({\text{M}}_{1}^{1\text{+}}+{\text{M}}_{1}^{2\text{+}}\right)+(1-\theta )\Delta t\left({\text{M}}_{1}^{1\text{-}}+{\text{M}}_{1}^{2\text{-}}\right)\end{array}\)

in R (ADDEP1 +1)

IF YAMEC

Injection of terms:

\(-{m}_{1}^{1\text{+}}{\text{F}}^{{m}^{\text{+}}}\text{ou}-\left({m}_{1}^{1\text{+}}+{m}_{1}^{2\text{+}}\right){\text{F}}^{{m}^{\text{+}}}\) in R (ADDEME)

If YATE

Injection of terms:

\(\begin{array}{c}\Delta t\left(\theta {h}_{\mathrm{1m}}^{1\text{+}}+(1-\theta ){h}_{\mathrm{1m}}^{1\text{-}}\right)\left({m}_{1}^{1\text{+}}-{m}_{1}^{1\text{-}}\right)-\theta \Delta t{\text{M}}_{1}^{1\text{+}}{F}^{m}-(1-\theta )\Delta t{\text{M}}_{1}^{1\text{-}}{F}^{m}\\ \text{ou}\\ \Delta t\left(\theta {h}_{\mathrm{1m}}^{1\text{+}}+(1-\theta ){h}_{\mathrm{1m}}^{1\text{-}}\right)\left({m}_{1}^{1\text{+}}-{m}_{1}^{1\text{-}}\right)+\Delta t\left(\theta {h}_{\mathrm{1m}}^{2\text{+}}+(1-\theta ){h}_{\mathrm{1m}}^{2\text{-}}\right)\left({m}_{1}^{2\text{+}}-{m}_{1}^{2\text{-}}\right)\\ -\theta \Delta t{\text{M}}_{1}^{1\text{+}}{F}^{m}-(1-\theta )\Delta t{\text{M}}_{1}^{1\text{-}}{F}^{m}-\theta \Delta t{\text{M}}_{1}^{2\text{+}}{F}^{m}-(1-\theta )\Delta t{\text{M}}_{1}^{2\text{-}}{F}^{m}\end{array}\)

in R (ADDETE)

Injection of terms

\(\begin{array}{c}-\theta \Delta t{h}_{\mathrm{1m}}^{1\text{+}}{\text{M}}_{1}^{1\text{+}}-(1-\theta )-\theta \Delta t{h}_{\mathrm{1m}}^{1\text{-}}{\text{M}}_{1}^{1\text{-}}\text{ou}\\ -\theta \Delta t\left({h}_{\mathrm{1m}}^{1\text{+}}{\text{M}}_{1}^{1\text{+}}+{h}_{\mathrm{1m}}^{2\text{+}}{\text{M}}_{1}^{2\text{+}}\right)-(1-\theta )\Delta t\left({h}_{\mathrm{1m}}^{1\text{-}}{\text{M}}_{1}^{1\text{-}}+{h}_{\mathrm{1m}}^{2\text{-}}{\text{M}}_{1}^{2\text{-}}\right)\end{array}\)

in R (ADDETE +1)

If YAP2

Injecting \(+{m}_{2}^{1\text{+}}-{m}_{2}^{1\text{-}}\text{ou}+{m}_{2}^{1\text{+}}+{m}_{2}^{2\text{+}}-{m}_{2}^{1\text{-}}-{m}_{2}^{2\text{-}}\) terms into R (ADDEP2)

Injection of terms

\(\begin{array}{c}\Delta t\theta {\text{M}}_{2}^{1\text{+}}+(1-\theta )\Delta t{\text{M}}_{2}^{1\text{-}}\text{ou}\\ \theta \Delta t\left({\text{M}}_{2}^{1\text{+}}+{\text{M}}_{2}^{2\text{+}}\right)+(1-\theta )\Delta t\left({\text{M}}_{2}^{1\text{-}}+{\text{M}}_{2}^{2\text{-}}\right)\end{array}\)

in R (ADDEP2 +1)

IF YAMEC

Injection of terms:

\(-{m}_{2}^{1\text{+}}{\text{F}}^{{m}^{\text{+}}}\text{ou}-\left({m}_{2}^{1\text{+}}+{m}_{2}^{2\text{+}}\right){\text{F}}^{{m}^{\text{+}}}\) in R (ADDEME)

If YATE

Injection of terms:

\(\begin{array}{c}\Delta t\left(\theta {h}_{\mathrm{2m}}^{1\text{+}}+(1-\theta ){h}_{\mathrm{2m}}^{1\text{-}}\right)\left({m}_{2}^{1\text{+}}-{m}_{2}^{1\text{-}}\right)-\theta \Delta t{\text{M}}_{2}^{1\text{+}}{F}^{m}-(1-\theta )\Delta t{\text{M}}_{2}^{1\text{-}}{F}^{m}\\ \text{ou}\\ \Delta t\left(\theta {h}_{\mathrm{2m}}^{1\text{+}}+(1-\theta ){h}_{\mathrm{2m}}^{1\text{-}}\right)\left({m}_{2}^{1\text{+}}-{m}_{2}^{1\text{-}}\right)+\Delta t\left(\theta {h}_{\mathrm{2m}}^{2\text{+}}+(1-\theta ){h}_{\mathrm{2m}}^{2\text{-}}\right)\left({m}_{2}^{2\text{+}}-{m}_{2}^{2\text{-}}\right)\\ -\theta \Delta t{\text{M}}_{2}^{1\text{+}}{F}^{m}-(1-\theta )\Delta t{\text{M}}_{2}^{1\text{-}}{F}^{m}-\theta \Delta t{\text{M}}_{2}^{2\text{+}}{F}^{m}-(1-\theta )\Delta t{\text{M}}_{2}^{2\text{-}}{F}^{m}\end{array}\)

in R (ADDETE)

Injection of terms

\(\begin{array}{c}-\theta \Delta t{h}_{\mathrm{2m}}^{1\text{+}}{\text{M}}_{2}^{1\text{+}}-(1-\theta )-\theta \Delta t{h}_{\mathrm{2m}}^{1\text{-}}{\text{M}}_{2}^{1\text{-}}\text{ou}\\ -\theta \Delta t\left({h}_{\mathrm{2m}}^{1\text{+}}{\text{M}}_{2}^{1\text{+}}+{h}_{\mathrm{2m}}^{2\text{+}}{\text{M}}_{2}^{2\text{+}}\right)-(1-\theta )\Delta t\left({h}_{\mathrm{2m}}^{1\text{-}}{\text{M}}_{2}^{1\text{-}}+{h}_{\mathrm{2m}}^{2\text{-}}{\text{M}}_{2}^{2\text{-}}\right)\end{array}\)

in R (ADDETE +1)

If YATE

Injecting terms: \(Q{\text{'}}^{\text{+}}-Q{\text{'}}^{\text{-}}\) into R (ADDETE)

Injecting \(-\theta \Delta t{\text{q}}^{\text{+}}-(1-\theta )\Delta t{\text{q}}^{\text{-}}\) terms into R (ADDETE +1)

Accumulation in vector V:

\(\left\{\text{V}\right\}=\left\{\text{V}\right\}+{\left[{\text{B}}_{g}^{\mathit{el}}\right]}^{T}\left\{R\right\}\)

IF RAPH_MECA or RIGI_MECA_TANG

IF YAMEC

Calculation of DR1DS and injection in DRDS (ADDEME, ADCOME)

calculation of DR2DS and injection in DRDS (ADDEME + NDIM -1, ADCOME)

IF YAP1

Calculation of DR1P11 and injection in DRDS (ADDEME, ADCP11)

calculation of DR2P11 and injection in DRDS (ADDEME + NDIM -1, ADCP11)

SI NBPHA1 > 1

Calculation of DR1P12 and injection in DRDS (ADDEME, ADCP12)

calculation of DR2P12 and injection in DRDS (ADDEME + NDIM -1, ADCP12)

IF YAP2

Calculation of DR1P21 and injection in DRDS (ADDEME, ADCP21)

calculation of DR2P21 and injection in DRDS (ADDEME + NDIM -1, ADCP21)

SI NBPHA2 > 1

Calculation of DR1P22 and injection in DRDS (ADDEME, ADCP22)

calculation of DR2P22 and injection in DRDS (ADDEME + NDIM -1, ADCP22)

IF YATE

Calculation of DR1DT and injection in DRDS (ADDEME, ADCOTE)

calculation of DR2DT and injection in DRDS (ADDEME + NDIM -1, ADCOTE)

IF YAP1

Calculation of DR3P11 and injection in DRDS (ADDEP1, ADCP11)

calculation of DR4P11 and injection in DRDS (ADDEP1 +1, ADCP11)

SI NBPHA1 > 1

Calculation of DR3P12 and injection in DRDS (ADDEP1, ADCP12)

calculation of DR4P12 and injection in DRDS (ADDEP1 +1, ADCP12)

IF YAMEC

Calculation of DR3DS and injection in DRDS (ADDEP1, ADCOME)

calculation of DR4DS and injection in DRDS (ADDEP1 +1, ADCOME)

IF YAP2

Calculation of DR3P21 and injection in DRDS (ADDEP1, ADCP21)

calculation of DR4P21 and injection in DRDS (ADDEP1 + 1, ADCP21)

SI NBPHA2 > 1

Calculation of DR3P22 and injection in DRDS (ADDEP1, ADCP22)

calculation of DR4P21 and injection in DRDS (ADDEP1 + 1, ADCP22)

IF YATE

Calculation of DR3DT and injection in DRDS (ADDEP1, ADCOTE)

calculation of DR4DT and injection in DRDS (ADDEP1 + 1, ADCOTE)

IF YAP2

Calculation of DR5P21 and injection in DRDS (ADDEP2, ADCP21)

calculation of DR6P21 and injection in DRDS (ADDEP2 +1, ADCP21)

SI NBPHA2 > 1

Calculation of DR5P22 and injection in DRDS (ADDEP2, ADCP22)

calculation of DR6P22 and injection in DRDS (ADDEP2 +1, ADCP22)

IF YAMEC

Calculation of DR5DS and injection in DRDS (ADDEP2, ADCOME)

calculation of DR6DS and injection in DRDS (ADDEP2 + 1, ADCOME)

YAP1 so:

Calculation of DR5P11 and injection in DRDS (ADDEP2, ADCP11)

calculation of DR6P11 and injection in DRDS (ADDEP2 + 1, ADCP11)

SI NBPHA1 > 1

Calculation of DR5P12 and injection in DRDS (ADDEP2, ADCP12)

calculation of DR6P12 and injection in DRDS (ADDEP2 + 1, ADCP12)

IF YATE

Calculation of DR5DT and injection in DRDS (ADDEP2, ADCOTE)

calculation of DR6DT and injection in DRDS (ADDEP2 + 1, ADCOTE)

IF YATE

Calculation of DR7DT and injection in DRDS (ADDETE, ADCOTE)

calculation of DR8DT and injection in DRDS (ADDETE +1, ADCOTE)

IF YAMEC

Calculation of DR7DS and injection in DRDS (ADDETE, ADCOME)

calculation of DR8DS and injection in DRDS (ADDETE + 1, ADCOME)

IF YAP1

Calculation of DR7P11 and injection in DRDS (ADDETE, ADCP11)

calculation of DR8P11 and injection in DRDS (ADDETE + 1, ADCP11)

SI NBPHA1 > 1

Calculation of DR7P12 and injection in DRDS (ADDETE, ADCP12)

calculation of DR8P12 and injection in DRDS (ADDETE + 1, ADCP12)

IF YAP2

Calculation of DR7P21 and injection in DRDS (ADDETE, ADCP21)

calculation of DR8P21 and injection in DRDS (ADDETE + 1, ADCP21)

SI NBPHA1 > 1

Calculation of DR7P22 and injection in DRDS (ADDETE, ADCP22)

calculation of DR8P22 and injection in DRDS (ADDETE + 1, ADCP22)

\(\left[\text{DRDE}\right]=\left[\text{DRDS}\right]\cdot \left[\text{DSDE}\right]\)

\(\left[{{\text{DF}}_{g}^{\mathit{el}}}_{i({u}_{n}^{\text{+}},{P}_{n}^{\text{+}},{T}_{n}^{\text{+}})}\right]={\left[{\text{B}}_{g}^{\mathit{el}}\right]}^{T}\cdot \left[\text{DRDE}\right]\cdot \left[{\text{B}}_{g}^{\mathit{el}}\right]\) accumulated in MAT

6.5. Arguments of the behavior laws calling routine#

SUBROUTINE COMTHM (

ARGUMENTS OF ENTREE: IN

COMPOR

OPTION

NDIM

NDDL

DIMDEF

DIMCON

NVIMEC

NVIHY, NVITM

NDEFME

NDEFP1

NDEFP2

NDEFT

NCONME

NCONP1

NCONP2

NCONT

YAP1

NBPHA1

YAP2

NBPHA2

DEMECM \(\text{u},\underline{\underline{\epsilon }}(\text{u})\) minus time

DEP1M \({p}_{\mathrm{1,}}\nabla {p}_{1}\) minus time

DEP2M \({p}_{\mathrm{2,}}\nabla {p}_{2}\) minus time

DETM \(T,\nabla T\) minus time

DEMECP \(\text{u},\underline{\underline{\epsilon }}(\text{u})\) plus time

DEP1P \({p}_{\mathrm{1,}}\nabla {p}_{1}\) plus time

DEP2P \({p}_{\mathrm{2,}}\nabla {p}_{2}\) plus time

DETP \(T,\nabla T\) plus time

COMECM \(\underline{\underline{\sigma \text{'}}},{\sigma }_{p}\) minus time

COTM \(Q\text{'},\text{q}\) minus time

CP11M \({m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{1}\) or \({m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{\mathrm{1,}}{h}_{\mathrm{1m}}^{1}\) time minus

CP12M \({m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{2}\) or \({m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{\mathrm{2,}}{h}_{\mathrm{1m}}^{2}\) time minus

CP21M \({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{1}\) or \({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{\mathrm{1,}}{h}_{\mathrm{2m}}^{1}\) time minus

CP21M \({m}_{2}^{\mathrm{2,}}{\text{M}}_{2}^{2}\) or \({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{\mathrm{1,}}{h}_{\mathrm{2m}}^{1}\) time minus

VIMEM internal variables mecha time minus

VIHYM internal variables hydro time minus

VITMM internal variables therm time minus

ARGUMENTS OF SORTIE: OUT

COMECP \(\underline{\underline{\sigma \text{'}}},{\sigma }_{p}\) plus time

COTP \(Q\text{'},\text{q}\) plus time

CP11P \({m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{1}\) or \({m}_{1}^{\mathrm{1,}}{\text{M}}_{1}^{\mathrm{1,}}{h}_{\mathrm{1m}}^{1}\) plus time

CP12P \({m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{2}\) or \({m}_{1}^{\mathrm{2,}}{\text{M}}_{1}^{\mathrm{2,}}{h}_{\mathrm{1m}}^{2}\) plus time

CP21P \({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{1}\) or \({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{\mathrm{1,}}{h}_{\mathrm{2m}}^{1}\) plus time

CP21P \({m}_{2}^{\mathrm{2,}}{\text{M}}_{2}^{2}\) or \({m}_{2}^{\mathrm{1,}}{\text{M}}_{2}^{\mathrm{1,}}{h}_{\mathrm{2m}}^{1}\) plus time

VIMEP internal variables mecha time plus

VIHYP internal variables hydro time plus

VITMP therm time plus internal variables

DMECDE \(\left[\begin{array}{c}\frac{\partial \sigma \text{'}}{\partial \epsilon }\\ \frac{\partial {\sigma }_{p}}{\partial \epsilon }\end{array}\right]\)

DMECP1 \(\left[\begin{array}{cc}\frac{\partial \sigma \text{'}}{\partial {p}_{1}}& \frac{\partial \sigma \text{'}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\sigma }_{p}}{\partial {p}_{1}}& \frac{\partial {\sigma }_{p}}{\partial \nabla {p}_{1}}\end{array}\right]\)

DMECP2 \(\left[\begin{array}{cc}\frac{\partial \sigma \text{'}}{\partial {p}_{2}}& \frac{\partial \sigma \text{'}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\sigma }_{p}}{\partial {p}_{2}}& \frac{\partial {\sigma }_{p}}{\partial \nabla {p}_{2}}\end{array}\right]\)

DMECDT \(\left[\begin{array}{cc}\frac{\partial \sigma \text{'}}{\partial T}& \frac{\partial \sigma \text{'}}{\partial \nabla T}\\ \frac{\partial {\sigma }_{p}}{\partial T}& \frac{\partial {\sigma }_{p}}{\partial \nabla T}\end{array}\right]\)

DP11DE \(\left[\begin{array}{c}\frac{\partial {m}_{1}^{1}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \epsilon }\end{array}\right]\)

DP11P1 \(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{1}}{\partial {p}_{1}}& \frac{\partial {m}_{1}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{1}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \nabla {p}_{1}}\end{array}\right]\)

DP11P2 \(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{1}}{\partial {p}_{2}}& \frac{\partial {m}_{1}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{1}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \nabla {p}_{2}}\end{array}\right]\)

DP11DT \(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{1}}{\partial T}& \frac{\partial {m}_{1}^{1}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{1}^{1}}{\partial T}& \frac{\partial {\text{M}}_{1}^{1}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial T}& \frac{\partial {h}_{\mathrm{1m}}^{1}}{\partial \nabla T}\end{array}\right]\)

DP12DE \(\left[\begin{array}{c}\frac{\partial {m}_{1}^{2}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \epsilon }\end{array}\right]\)

DP12P1 \(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{2}}{\partial {p}_{1}}& \frac{\partial {m}_{1}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{1}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \nabla {p}_{1}}\end{array}\right]\)

DP12P2 \(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{2}}{\partial {p}_{2}}& \frac{\partial {m}_{1}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{1}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \nabla {p}_{2}}\end{array}\right]\)

DP12DT \(\left[\begin{array}{cc}\frac{\partial {m}_{1}^{2}}{\partial T}& \frac{\partial {m}_{1}^{2}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{1}^{2}}{\partial T}& \frac{\partial {\text{M}}_{1}^{2}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial T}& \frac{\partial {h}_{\mathrm{1m}}^{2}}{\partial \nabla T}\end{array}\right]\)

DP21DE \(\left[\begin{array}{c}\frac{\partial {m}_{2}^{1}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \epsilon }\end{array}\right]\)

DP21P1 \(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{1}}{\partial {p}_{1}}& \frac{\partial {m}_{2}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{2}^{1}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \nabla {p}_{1}}\end{array}\right]\)

DP21P2 \(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{1}}{\partial {p}_{2}}& \frac{\partial {m}_{2}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{2}^{1}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \nabla {p}_{2}}\end{array}\right]\)

DP21DT \(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{1}}{\partial T}& \frac{\partial {m}_{2}^{1}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{2}^{1}}{\partial T}& \frac{\partial {\text{M}}_{2}^{1}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial T}& \frac{\partial {h}_{\mathrm{2m}}^{1}}{\partial \nabla T}\end{array}\right]\)

DP22DE \(\left[\begin{array}{c}\frac{\partial {m}_{2}^{2}}{\partial \epsilon }\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial \epsilon }\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \epsilon }\end{array}\right]\)

DP22P1 \(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{2}}{\partial {p}_{1}}& \frac{\partial {m}_{2}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial {p}_{1}}& \frac{\partial {\text{M}}_{2}^{2}}{\partial \nabla {p}_{1}}\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial {p}_{1}}& \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \nabla {p}_{1}}\end{array}\right]\)

DP22P2 \(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{2}}{\partial {p}_{2}}& \frac{\partial {m}_{2}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial {p}_{2}}& \frac{\partial {\text{M}}_{2}^{2}}{\partial \nabla {p}_{2}}\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial {p}_{2}}& \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \nabla {p}_{2}}\end{array}\right]\)

DP22DT \(\left[\begin{array}{cc}\frac{\partial {m}_{2}^{2}}{\partial T}& \frac{\partial {m}_{2}^{2}}{\partial \nabla T}\\ \frac{\partial {\text{M}}_{2}^{2}}{\partial T}& \frac{\partial {\text{M}}_{2}^{2}}{\partial \nabla T}\\ \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial T}& \frac{\partial {h}_{\mathrm{2m}}^{2}}{\partial \nabla T}\end{array}\right]\)

DTDE \(\left[\begin{array}{c}\frac{\partial Q\text{'}}{\partial \epsilon }\\ \frac{\partial \text{q}}{\partial \epsilon }\end{array}\right]\)

DTDP1

\(\left[\begin{array}{cc}\frac{\partial Q\text{'}}{\partial {p}_{1}}& \frac{\partial Q\text{'}}{\partial \nabla {p}_{1}}\\ \frac{\partial \text{q}}{\partial {p}_{1}}& \frac{\partial \text{q}}{\partial \nabla {p}_{1}}\end{array}\right]\)

DTDP2

\(\left[\begin{array}{cc}\frac{\partial Q\text{'}}{\partial {p}_{2}}& \frac{\partial Q\text{'}}{\partial \nabla {p}_{2}}\\ \frac{\partial \text{q}}{\partial {p}_{2}}& \frac{\partial \text{q}}{\partial \nabla {p}_{2}}\end{array}\right]\)

DTDT \(\left[\begin{array}{cc}\frac{\partial Q\text{'}}{\partial T}& \frac{\partial Q\text{'}}{\partial \nabla T}\\ \frac{\partial \text{q}}{\partial T}& \frac{\partial \text{q}}{\partial \nabla T}\end{array}\right]\)

)

REAL *8

DEMECM (NDEFME), DEP1M (NDEFP1), DEP2M (NDEFP2), DETM (NDEFT)

DEMECP (NDEFME), DEP1P (NDEFP1), DEP2P (NDEFP2), DETP (NDEFT)

COMECM (NCONME), CP11M (NCONP1), CP21M (NCONP2), COTM (NCONT)

VIMEM (NVIMEC), VIHYM (NVIHY), VITMM (NVITM)

COMECP (NCONME), CP11P (NCONP1), CP21P (NCONP2), COTP (NCONT)

VIMEP (NVIMEC), VIHYP (NVIHY), VITMP (NVITM)

DMECDE (NCONME, NDEFME), DMECP1 (NCONME, NDEFP1),

DMECP2 (NCONME, NDEFP2), DMECDT (NCONME, NDEFT)

DP11DE (NCONP1, NDEFME), DP11P1 (NCONP1, NDEFP1),

DP11P2 (NCONP1, NDEFP2), DP11DT (NCONP1, NDEFT)

DP21DE (NCONP2, NDEFME), DP21P1 (NCONP2, NDEFP1,

DP21P2 (NCONP2, NDEFP2, DP21DT (NCONP2, NDEFT)

DP12DE (NCONP1, NDEFME), DP12P1 (NCONP1, NDEFP1),

DP12P2 (NCONP1, NDEFP2), DP12DT (NCONP1, NDEFT)

DP22DE (NCONP2, NDEFME), DP22P1 (NCONP2, NDEFP1,

DP22P2 (NCONP2, NDEFP2, DP22DT (NCONP2, NDEFT)

DTDE (NCONT2, NDEFME), DTDP1 (NCONT2, NDEFP1),

DTDP2 (NCONT2, NDEFP2), DTDT (NCONT2, NDEFT)