 FEM: Finite Element Method 
Definition:  Finite Element
Method 
Explanation:  FEM is a
computer based
numerical method for
solving engineering
problems in bodies
of user defined
geometry. It reduces
a problem in a
continuous field
variable to a finite
number of points
(nodes) which are
interconnected via
interpolation
functions defined on
finite volumes
(elements). Flexible
choice of the
interconnectivity
(i.e. elements)
allows user to
optimize the problem
complexity as
required [1].
The finite element
method consists of
the following steps:
(i) Preprocessing,
(ii) developing
elemental equations,
(iii) assembling
equations, (iv)
applying boundary
conditions, (v)
solving the system
of equations, and
(v) postprocessing
[2]. 
Picture / Figure / Diagram: 

Simulation of high temperature compression test using FEM. Depending on the constitutive law, it is possible to obtain spatially resolved dynamic recrystallization (DRX) fraction and grain size information along with stresses and strains.


SFBLink:  Twinning induced plasticity (→TWIP) steels owe their extraordinary mechanical properties to their strain hardening behavior, and these properties become more and more evident at large strains. For large strain applications, such as metal forming processes or crash, FEM is required to determine the complex constitutive response of the material 
References:  [1] D.L. Dewhirst, “Finite Element Analysis”, ASM Metals Handbook V20, pp.409423, 1997. [2] P.M. Dixit, “Modeling of Metal Forming and Machining Processes”, p.274, 2008. 

