multiPlas - Dynardo GmbH

3 THEORY OF THE MULTIPLAS MATERIAL MODELS IN ANSYS
3.1 Basics of elasto-plasticity in multiPlas
The material models in multiPlas uses a rate-independent plasticity. The material models are characterized
by the irreversible strain that occurs once yield criteria are violated. It is assumed that the total strain
vector can be divided into a elastic and a plastic component.
where:
{ } { } { } pl
el
tot
ε ε + ε
= (3-1)
{ε} el – elastic strain vector (EPEL)
{ε} pl – plastic strain vector (EPPL)
The plastic strains are assumed to develop instantaneously, that is, independent of time.
The yield criterion
where:
{ σ}
, κ)
0
F ( ≤
(3-2)
{σ} - stress vector
κ - hardening parameter
limit the stress domain. If the computed stress, using the elastic deformation matrix, exceeds the yield
criteria (F>0), then plastic strain occurs. Plastic strains will computed by flow rule
where:
d pl
ε
∂Q
= λ
∂σ
λ - plastic multiplier (which determines the amount of plastic straining)
Q - plastic potential (which determines the direction of plastic straining)
The plastic strains reduce the stress state so that it satisfies the yield criterion (F=0). By using associated
flow rules, the plastic potential is equal the yield criterion and the vector of plastic strains is arranged perpendicularly
to the yield surface.
Q = F
(3-4)
By using non-associated flow rules
Q ≠ F
(3-5)
effects that are known from experiments like dilatancy can be controlled more realistically.
The hardening / softening function Ω(κ) describes the expansion and the reduction of the initial yield surface
dependant on the load path, as well as the translation of the yield criterion in the stress domain. For
the strain driven hardening/softening equations in multiPlas the scalar value κ serves as a weighting factor
for plastic strain.
pl pl
dκ = dκ
ε ) = dε
eq
7
(3-3)
( (3-6)
The introduction of a separate softening function for each strength parameter made it possible to formulate
an orthotropic softening model that is dependent from the failure mode. Existing relations, for example
shear-tension interaction (mixed mode), were recognised.
USER’S MANUAL, January, 2013