Technological progress and discovery and mastery of increasingly sophisticated
structural materials have been inexorably tied together since the dawn
of history. In the present era — the so-called Space Age —-, the prevailing
trend is to design and create new materials, or improved existing ones, by
meticulously altering and controlling structural features that span across all
types of length scales: the ultimate aim is to achieve macroscopic proper-
ties (yield strength, ductility, toughness, fatigue limit . . . ) tailored to given
practical applications. Research efforts in this aspect range in complexity
from the creation of structures at the scale of single atoms and molecules —
the realm of nanotechnology —, to the more mundane, to the average civil
and mechanical engineers, development of structural materials by changing
the composition, distribution, size and topology of their constituents at the
microscopic/mesoscopic level (composite materials and porous metals, for
instance).
Abstract
Technological progress and discovery and mastery of increasingly sophisticated
structural materials have been inexorably tied together since the dawn
of history. In the present era — the so-called Space Age —-, the prevailing
trend is to design and create [...]
We examine a residual and matrix-free Jacobian formulation of compressible and nearly incompressible (v → 0.5) displacement-only linear isotropic elasticity with high-order hexahedral finite elements. A matrix-free p-multigrid method is combined with algebraic multigrid on the assembled sparse coarse grid matrix to provide an effective preconditioner. The software is verified with the method of manufactured solutions. We explore convergence to a predetermined L2 error of 10-4, 10-5 and 10-6 for the compressible case and 10-4, 10-5 for the nearly-incompressible cases, as the Poisson's ratio approaches 0.5, based upon grid resolution and polynomial order. We compare our results against results obtained from C3D20H mixed/hybrid element available in the commercial finite element software ABAQUS that is quadratic in displacement and linear in pressure. We determine, for the same problem size, that our matrix-free approach for displacement-only implementation is faster and more efficient for quadratic elements compared to the C3D20H element from ABAQUS that is specially designed to handle nearly-incompressible and incompressible elasticity problems. However, as we approach the near incompressibility limit, the number of Conjugate Gradient iterations required to achieve the desired solution increases significantly.
Abstract
We examine a residual and matrix-free Jacobian formulation of compressible and nearly incompressible (v → 0.5) displacement-only linear isotropic elasticity with high-order hexahedral finite elements. A matrix-free p-multigrid method is combined with algebraic [...]
High-performance model reduction procedures in multiscale simulations 