Journal of Engineering Mechanics ASCE, 130 (2004), 720-732.
ADAPTIVE RESOLUTION OF LOCALIZED DAMAGE IN QUASIBRITTLE MATERIALS
Czech Technical University in Prague
Swiss Federal Institute of Technology
LSC - ENAC, EPFL,
1015 Lausanne, Switzerland
This paper presents an adaptive mesh refinement technique suitable for the
resolution of highly localized damage in concrete and other quasibrittle materials.
Objectivity of the description of softening is ensured by using regularized
material models based on the concept of nonlocal averaging, which is applied
to isotropic and anisotropic damage formulations. The distributions of strain
and internal variables produced by such regularized models are continuous,
which facilitates the projection of information from one finite element mesh
onto another. However, not all mapping algorithms for the transfer of internal
variables preserve the basic characteristics of the localized process zone.
The paper evaluates and compares three mapping algorithms, which are based
on the closest-point transfer, least-square projection, and shape-function
projection. It also briefly comments on other important components of a complete
adaptive strategy, i.e., on the error indicator, refinement rules and mesh
generator. The efficiency of the proposed strategy is illustrated by examples
that treat straight as well as curved crack trajectories. The underlying
material model is a nonlocal integral formulation of anisotropic damage based
on the microplane concept.
In this paper we have presented and discussed various aspects of mesh-adaptive
techniques applied to nonlocal continuum models with softening. Intuitively
it is clear that adaptive mesh refinement can provide a good balance between
accuracy and speed of the simulation, but the components of an adaptive strategy
must be selected with care. For instance, we have shown that certain transfer
operators for the mapping of internal variables can lead to an artificial
diffusion of the process zone. Another important factor is the element size
in the damage process zone, which must be small enough to permit nonlocal
interaction of each Gauss point with a sufficient number of its neighbors.
But even on a fine mesh, the actual curved crack trajectory is not reproduced
correctly if the material model does not properly take into account the anisotropic
character of damage.
The complete paper can be downloaded in an electronic form: gzipped PostScript, gzipped PDF
EPFL / 22 January 2003 / firstname.lastname@example.org