Iform = 2

Block Format Keyword This boundary material enables to impose sub-material states (density, energy, and volumetric fraction) which are also used to compute global material state. Submaterial EOS parameters must be consistent with the ones in adjacent element (from the domain).


law51_iform2
Figure 1.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW51/mat_ID/unit_ID
mat_title
Blank Format
Iform                  
#Global Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Scaletime PEXT   VE L in   fct_I D VEL
#Material1 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 mat _ 1 ρ 0 mat _ 1 E 0 m a t _ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamyramaaDaaaleaacaaIWaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaWLa8UaaGzaVlaayIW7caaIYaaaaaaa@45FB@ fct_IDα1 fct_ID ρ 1 fct_I D E1  
C 1 m a t _ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIXaaaaaaa@4156@ C 2 m a t _ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIXaaaaaaa@4156@ C 3 m a t _ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIXaaaaaaa@4156@ C 4 m a t _ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIXaaaaaaa@4156@ C 5 m a t _ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIXaaaaaaa@4156@
Δ P min mat _ 1 C 0 m a t _ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIXaaaaaaa@4156@          
#Material2 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 mat _ 2 ρ 0 mat _ 2 E 0 m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamyramaaDaaaleaacaaIWaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaWLa8UaaGzaVlaayIW7caaIYaaaaaaa@45FB@ fct_IDα2 fct_ID ρ 2 fct_IDE2  
C 1 m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 2 m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 3 m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 4 m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 5 m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@
Δ P min mat _ 2 C 0 m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@          
#Material3 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 mat _ 3 ρ 0 mat _ 3 E 0 m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamyramaaDaaaleaacaaIWaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaWLa8UaaGzaVlaayIW7caaIYaaaaaaa@45FB@ fct_IDα3 fct_ID ρ 3 fct_IDE3  
C 1 m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 2 m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 3 m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 4 m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ C 5 m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@
Δ P min mat _ 3 C 0 m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@          

Definitions

Field Contents SI Unit Example
mat_ID Material identifier

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier.

(Interger, maximum 10 digits)

 
mat_title Material title

(Character, maximum 100 characters)

 
Iform Formulation flag

(Integer)

=2 : Imposed state

 
Scaletime Abscissa scale factor for input functions

Default = 1 (Real)

 
VE L in Scale factor for inlet velocity 5

(Real)

[ m s ]
fct_IDVEL Optional identifier for velocity function f V E L ( t ) 5

= 0 : f ρi (t)

> 0 : v ( t ) = V E L i n f V E L ( t )

(Integer)
 
α 0 mat _ i Initial imposed volumetric fraction 2

(Real)

 
ρ 0 mat _ i Initial imposed density

(Real)

[ kg m 3 ]
E 0 m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamyramaaDaaaleaacaaIWaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaWLa8UaaGzaVlaayIW7caaIYaaaaaaa@45FB@ Initial imposed energy per unit volume

(Real)

[ J m 3 ]
fct_IDαi Optional identifier for Volumetric fraction scaling function f α i ( t ) 3

= 0 : α m a t _ i ( t ) = α 0 m a t _ i

> 0 : α mat_i ( t )= α 0 mat_i f α i ( t )

(Integer)

 
fct_ID ρ i Optional identifier for Density fraction scaling function f ρ i ( t ) 3

= 0 : ρ m a t _ i ( t ) = ρ 0 m a t _ i

> 0 : ρ mat_i ( t )= ρ 0 mat_i f ρ i ( t )

(Integer)

 
fct_IDEi Optional identifier for density energy scaling function identifier f E i ( t ) 3

= 0: E mat i ( t ) = E 0 mat _ i

> 0 : E mat_i ( t )= E 0 mat_i f E i ( t )

(Integer)

 
C 1 m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ Coefficient for Polynomial EOS

(Real)

[ Pa ]
C 2 m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ Coefficient for Polynomial EOS

(Real)

[ Pa ]
C 3 m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ Coefficient for Polynomial EOS

(Real)

[ Pa ]
C 4 m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ Coefficient for Polynomial EOS

(Real)

 
C 5 m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ Coefficient for Polynomial EOS

(Real)

 
Δ P min mat _ i Cut off pressure 4

Default = -10-30 (Real)

[ Pa ]
C 0 m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaaGjc Vlaac+facaaIYaaaaaaa@4157@ Coefficient for Polynomial EOS

(Real)

[ Pa ]

Comments

  1. This formulation imposes sub-material states from user data.
    Volumetric fraction: (1)
    α m a t _ i ( t )
    Density: (2)
    ρ m a t _ i ( t )
    Density Energy: (3)
    E m a t _ i ( t )
    This enables to compute pressure from given polynomial EOS:(4)
    Δ P ( t ) = min { Δ P min , C 0 + C 1 μ + C 2 ' μ 2 + C 3 ' μ 3 + ( C 4 + C 5 μ ) E ( t ) }

    Where, P = Δ P + P E X T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbGaey ypa0JaaeiLdiaadcfacqGHRaWkcaWGqbWaaSbaaSqaaiaadweacaWG ybGaamivaaqabaaaaa@3E8B@ and μ ( t ) = ρ ( t ) ρ 0 = 1 , E ( t ) = E int ( t ) / V 0 , C 2 ' = C 2 δ μ 0 , and C 3 ' = C 3 δ μ 0 , which means that EOS is linear in expansion and cubic for in compression.

    Then global material state is determined by:
    Pressure
    Δ P = i α m a t _ i ( t ) Δ P m a t _ i
    Density
    ρ = i α m a t _ i ( t ) ρ m a t _ i
    Energy
    E i n t V = i α m a t _ i ( t ) E m a t _ i
  2. Volumetric fractions enable the sharing of elementary volume within the three different materials.

    For each material α 0 mat _ i must be defined between 0 and 1.

    Sum of initial volumetric fractions i = 1 3 α 0 mat _ i must be equal to 1.

    For automatic initial fraction of the volume, refer to /INIVOL.

  3. If a function is not defined, then related quantity remains constant and set to its initial value. However, input quantity can be defined as time dependent function using provided function identifiers. Abscissa functions can also be scaled using Fscalet parameter which leads to use f ( S c a l e t i m e , t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaabm aabaGaam4uaiaadogacaWGHbGaamiBaiaadwgadaWgaaWcbaGaamiD aiaadMgacaWGTbGaamyzaaqabaGccaGGSaGaamiDaaGaayjkaiaawM caaaaa@428F@ , instead of f ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaabm aabaGaamiDaaGaayjkaiaawMcaaaaa@3965@ .
  4. Δ P min mat _ i flag is the minimum value for the computed pressure.

    Since P = Δ P + P E X T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbGaey ypa0JaaeiLdiaadcfacqGHRaWkcaWGqbWaaSbaaSqaaiaadweacaWG ybGaamivaaqabaaaaa@3E8B@ , defining P E X T = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacaWGfbGaamiwaiaadsfaaeqaaOGaeyypa0JaaGimaaaa@3B42@ implies Δ P = P MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaadc facqGH9aqpcaWGqbaaaa@39C1@ and Δ P min = P min MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaadc fadaWgaaWcbaGaciyBaiaacMgacaGGUbaabeaakiabg2da9iaadcfa daWgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa@3FC7@ .

    Fluid materials pressure must remain positive to avoid any tensile strength, then,

    P min = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaaciGGTbGaaiyAaiaac6gaaeqaaOGaeyypa0JaaGimaaaa@3B94@ or Δ P min = P E X T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaqGuoGaam iuamaaBaaaleaaciGGTbGaaiyAaiaac6gaaeqaaOGaeyypa0JaeyOe I0IaamiuamaaBaaaleaacaWGfbGaamiwaiaadsfaaeqaaaaa@40C9@ .

    For solid materials, default value for Δ P min mat _ i = 1030 is suitable.

  5. If the velocity is not defined, the user must define it using /IMPVEL with nodes. Otherwise normal velocity can be entered. The normal velocity is applied to the global material with the same velocity used for each submaterial. If only the state at the stagnation point is known, use /MAT/LAW51 with Iform=4,5 instead.