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

Elastoplasticity
The strain and stress increments are given by:
dɛ rs = dɛ E rs + dɛ P rs
dσ ij = C E ijrs (dɛ rs − dɛ P rs)
where C E ijrs are the components of the elastic constitutive tensor and dɛ rs, dɛ E rs,
dɛ P rs are the components of the total strain increment.
To calculate the plastic strains we use the following three properties:
Yield Function f y(σ, ɛ P )
f y < 0 ⇒ Elastic behavior
f y = 0 ⇒ Plastic behavior
f y > 0 ⇒ Inadmissible
Flow rule
The yield function is used in the flow rule in order to obtain the plastic
strain increments
λ is a scalar to be determined
dɛ P ij = λ ∂fy
∂σ ij
Hardening rule
This specifies how the yield function is modified during plastic flow
Institute of Structural Engineering Method of Finite Elements II 23