SPH Method part3

1. The Meshfree Simulation of Friction Stir
Welding/Processing
Part3

2. large plastic deformation and material mixing common to FSW are well captured by the mesh-
free method.
I. SPH Capabilities
This simulation approach allows the determination of temperature evolution, elastic and
plastic deformation, defect formation, residual stresses, and material flow all within the same
model.

3. SPH uses an evolving interpolation scheme to approximate a field variable at any
point in a domain. The value of a variable at a particle of interest n be approximated
by summing the contributions from a set of neighboring particles, denoted by
subscript j, for which the “kernel” function, W, is not zero
The smoothing length, h, determines how many
particles influence the interpolation for a particular
point
W- Kernel (Smoothing) function,
In SPH, the material is discretized with separate sets of points or particles and a
continuous field f(xi) is approximated at the discretization points

4. The implementation is based on the classical smoothed particle hydrodynamic
theory as outlined in the references
below. You also have the option of using a mean flow correction configuration
update, commonly referred to in
the literature as the XSPH method (see Monaghan, 1992), as well as the
corrected kernel of Randles and Libersky,
1997, also referred to as the normalized SPH (NSPH) method.
The characteristic length is half the length of the cube side.

5. For these methods you do not define nodes and elements as you would
normally define in a finite element analysis; instead, only a collection of
points are necessary to represent a given body. In smoothed particle
hydrodynamics these nodes are commonly referred to as particles or
pseudo-particles.
Smoothed particle hydrodynamics is a fully Lagrangian modeling scheme permitting the
discretization of a prescribed set of continuum equations by interpolating the properties
directly at a discrete set of points distributed over the solution domain without the need to
define a spatial mesh