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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 14
INNOVATION IN COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero, R. Montenegro
Chapter 7
Spatial and Temporal Multiscale Simulations of Damage Processes for Concrete C. Könke, S. Eckardt and S. Häfner
Institute of Structural Mechanics, BauhausUniversity Weimar, Germany C. Könke, S. Eckardt, S. Häfner, "Spatial and Temporal Multiscale Simulations of Damage Processes for Concrete", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Innovation in Computational Structures Technology", SaxeCoburg Publications, Stirlingshire, UK, Chapter 7, pp 133157, 2006. doi:10.4203/csets.14.7
Keywords: spatial and temporal multiscale models, damage and fracture, multigrid solver, heterogeneous materials, concrete.
Summary
The damage behaviour of heterogeneous materials, such as concrete, is often
described by continuum damage theories on the macroscale, using homogenized
material parameters. These models have the advantage of being applied in
simulations of largescale structures, but the experimental determination of
necessary material parameters, especially for the description of material damage
effects, is demanding and often a direct identification of these parameters is not
possible. Furthermore these models are not capable of describing all the physical
effects applying to the continuum theories, for example, the decohesion effects
between grain and matrix material. At the mesoscale the heterogeneous material
structure is described explicitly, representing the aggregates and the matrix material,
and thereby allowing a detailed description of the separate constituents. This paper
describes various aspects of simulating the damage effects of concrete materials in
heterogeneous multiscale models, integrating aggregatematrix models on the
mesoscale into continuum damage models for the macroscale. Beginning with the
generation of grainmatrix models we will discuss numerical discretization
techniques. Different iterative schemes following the nonlinear response paths,
including softening branches and appropriate solver strategies such as multigrid
solvers will be presented. The material description on the mesoscale will be
discussed, indicating the advantages of applied simulation techniques. Coupling
between models on different spatial scales, for example meso and macroscales,
resulting into heterogeneous multiscale models is proposed via constraint
conditions. Thereby it becomes possible to simulate largescale constructional
components and to obtain detailed information on local microdamage effects at the
same time. An example of a multiscale simulation is shown in Figure 1. In this
example a priori information about the zone where the localised damage is expected
can be used. This information can, for example, be obtained by a linear analysis in
advance. The stress concentration in the corner region can be used as an indicator to
model the subregion in the vicinity of the reentering corner with a mesoscale
model, while the rest of the structure is kept as a macroscale model.
The load is applied as displacement u at the lower right hand edge and is increased incrementally. The constitutive law for the matrix material is coupling a microplane model with an isotropic damage model for the softening regime. Figure 2 shows the propagation of the damage zone, starting from the reentering corner, through the model for different load situations. The corresponding loaddisplacement curve is given in Figure 3.
Similar strategies as applied for spatial multiscale problems can be adopted for simulation of temporal multiscale problems, as found for example in concrete creeping problems. The paper will give an outlook into adequate methods. purchase the fulltext of this chapter (price £20)
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