Download full text - ELSA - Europa

ALE description of structures (2)
• Major extra difficulty w/r to Newtonian fluids: necessity to transport
stresses and stress-related quantities across inter-element boundaries.
Fields are usually discontinuous and evaluated only at Gauss Points
• Previous attempts had used implicit interpolation techniques: too
expensive in the present explicit fast transient context
• Two distinct strategies, borrowed from the fluid dynamic experience:
a) a Lax-Wendroff scheme based on nodal averaging and smoothing
of the stress gradients, and b) a Godunov scheme inspired by
methods often used for conservation laws in finite volumes
• Both techniques implemented in 2D quadrilateral finite elements using
single-point as well as multiple-point spatial numerical integration
5
ALE description of structures (3)
• When ALE is applied to nonlinear path-dependent materials, three
conservation equations basically similar to Euler equations are
obtained and therefore the same techniques (time integration
strategy, rezoning algorithms, treatment of boundary conditions, etc.)
developed for the fluids can be directly applied, with the important
exception, however, of the stress transport algorithm
• Time integration is achieved by same fractional step strategy seen
above for fluids: 1) Lagrangian phase, in which it is assumed that
the mesh follows the material particles and transport terms vanish;
2) Convective flux calculation (transport terms only)
• The time integration procedure still remains completely explicit and
only an extra loop over the elements to deal with transport is required
at each time step, compared with the Lagrangian case
6
3