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Material Models LS-DYNA Theory Manual
19.14
Material Model 1: ElasticIn this elastic material we compute the co-rotational rate of the deviatoric Cauchy stress
tensor as
112
22n
n
ij ijs Gε
++∇
′= (19.1.1)
and pressure
1 1lnn n p K V + += − (19.1.2)
where G and K are the elastic shear and bulk moduli, respectively, and V is the relative
volume, i.e., the ratio of the current volume to the initial volume.
Material Model 2: Orthotropic Elastic
The material law that relates second Piola-Kirchhoff stress S to the Green-St. Venant
strain E is
t
lS C E T C T E = ⋅ = ⋅ (19.2.1)
where T is the transformation matrix [Cook 1974].
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
2 2 2
1 1 1 1 1 1 1 1 1
2 2 2
2 2 2 2 2 2 2 2 2
2 2 2
3 3 3 3 3 3 3 3 3
1 2 1 2 1 2 1 2 1 1 1 2 2 1 1 2 2 1
2 3 2 3 2 3 2 3 3 2 2 3 3 2 2 3 3 2
3 1 3 1 3 1 3 1 1 3 3 1 1 3 3 1 1 3
2 2 2
2 2 2
2 2 2
l m n l m m n n l
l m n l m m n n l
l m n l m m n n lT
l l m m n n l m l m m n m n n l n l
l l m m n n l m l m m n m n n l n l
l l m m n n l m l m m n m n n l n l
= + + +
+ + +
+ + +
(19.2.2)
il , im , in are the direction cosines
'
1 2 3 1,2,3i i i i x l x m x n x for i= + + = (19.2.3)
and'
i x denotes the material axes. The constitutive matrix lC is defined in terms of the material
axes as
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