Plastic model with non-local damage applied to concrete

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86P. GRASSL AND M. JIRÁSEKFigure 16. (a) Geometry and loading set-up of the eccentric compression test;and (b) the coarse finite element mesh.full three-dimensional analysis. Again, three different meshes with element sizes of 7.5, 5 and2:5 mm were used (see Figure 16(b) for the coarse mesh).The model parameters were set to E ¼ 30 GPa; n ¼ 0:2; f t ¼ 4 MPa; f c ¼ 46 MPa; e f ¼0:001042; A s ¼ 2; R ¼ 15 mm and m ¼ 1: The other parameters of the local model were takenby their default values [24].The model response in terms of the overall load versus the mean compressive strain on thecompressed side (Figure 16(a)) obtained on the fine mesh is compared to the experimental resultin Figure 17. The load capacity and the strain at peak are underestimated by the model. Theoverall behaviour, however, is captured well.The comparison of the relations between the load and the average compressive strain foranalyses run on meshes of different sizes (Figure 18(a)) indicates that the description of this typeof compressive failure is nearly mesh independent. The evolution of the damage zone for theanalysis on the coarse mesh is depicted in Figure 19 for three stages of analyses (marked byhollow circles in Figure 18(a)). On the tensile side, several zones of localized damage form,whereas the failure pattern on the compressive side is characterized by a diffuse damage zone.Despite the complicated failure mode, the load–displacement curves are mesh independent,which confirms that the non-local model can describe both types of failure in an objective way.It is important to realize that, for such combined failure modes, the local model exhibits strongmesh sensitivity even if the softening law is adjusted depending on the element size. This isclearly documented by the load–average-strain diagrams in Figure 18(b). As the mesh is refined,Copyright # 2005 John Wiley & Sons, Ltd. Int. J. Numer. Anal. Meth. Geomech. 2006; 30:71–90
PLASTIC MODEL WITH NON-LOCAL DAMAGE 87400350fine meshexperiment300load [kN]250200150100500-8 -7 -6 -5 -4 -3 -2 -1 0average strain [mm/m]Figure 17. Comparison of the analysis of the eccentric compression test with the experiment.350300coarse meshmedium meshfine mesh350300coarse meshmedium meshfine mesh250250load [kN]200150load [kN]2001501001005050(a)0-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0average strain [mm/m](b)0-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0average strain [mm/m]Figure 18.Load–average-strain curves for the eccentric compression test simulated on three differentmeshes with: (a) non-local model; and (b) local model.the global response of the local model with adjustment of the softening modulus is getting moreductile. The reason is that the adjustment is based on the assumption that the failure pattern islocalized into one layer of elements, but this is the case only in the region of tensile cracking butnot in the region of compressive crushing.7. CONCLUSIONSIn the present study we have proposed a framework for non-local damage-plastic models,combining local plasticity with integral-type non-local damage. The damage evolution is drivenby the plastic strain.Copyright # 2005 John Wiley & Sons, Ltd. Int. J. Numer. Anal. Meth. Geomech. 2006; 30:71–90
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