 CPFEM: Crystal Plasticity – Finite Element Method 
Definition:  Finite element
method restricting
the mechanical
degrees of freedom
to the
crystallographic
slip and twin
systems of the
crystal. 
Explanation:  The Finite Element
Method (FEM) can be
viewed as a
quasistandard for
simulating
micromechanical
deformation
processes. In the
standard form, the
materials are
modelled as
continuum that can
be elastically
and/or plastically
deformed. However,
it is known since
the 1930s that
crystals deform
plastically by the
motion of
dislocations along
specific shear
directions and
planes. This
dislocation motion
creates a shear of
the crystal lattice
on distinct planes
in distinct
directions. In terms
of a continuum
method as FEM,
this means that the
plastic part of the
deformation has to
be built from these
elementary shears.
The resulting method
has been called as
CPFEM. The first
simulation
using this approach
haa been performed
by Peirce et
al. in
1982. Since then,
the
CPFEM has developed
into a versatile
tool for
describing the
mechanical response
of crystalline
materials on all
length scales from
single crystals to
engineering parts
(Roters et
al. 2010
a/b). While it
originally accounted
for dislocation slip
as the only deformation
mechanism, there
now exist
extensions of
CPFEM,
that also account
for other
deformation
mechanisms such
as
the twinning induced
plasticity (→TWIP)
and the
transformation
induced plasticity
(→TRIP). 
Picture / Figure / Diagram: 

Two examples for the application of CPFEM. (a) Simulation of a mini tensile sample resolving the grain structure. (b) Simulation of a deep drawing experiment using macro texture data.


SFBLink:  The constitutive model developed for TWIP steels is also implemented in the framework of CPFEM. 
References:  Peirce D., Asaro R.J., Needleman A.; Acta Metall. 30, 1982, p 1087 Roters F., Eisenlohr P., Hantcherli L., Tjahjanto D.D., Bieler T.R., Raabe D.; Acta Mater. 58, 2010, p 1152 Roters F. Eisenlohr P., Bieler T.R., Raabe D.; Crystal Plasticity Finite Element Methods, 2010 WILEYVCH 

