The Finite Element Method for the Analysis of Non-Linear and ...

Elastic Material
For the case of an elastic material we already saw that the TL
Formulation (used for large deformation analysis) yields:
t
0S ij = t t
0C ijrs 0ɛ rs
The elasticity tensor for 3D stress conditions is defined as:
t
C ijrs = λδ ij δrs + µ(δ ir δjs + δ is δjr)
where λ and µ are the Lamé constants and δ ij is the Kronecker delta,
Eν
λ =
(ν)(1 − 2ν) , µ = E
2(1 + ν)
{ 0 i ≠ j
δ ij =
1 i = j
Institute of Structural Engineering Method of Finite Elements II 8