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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