Examples

The application of the described parallel h-adaptive methodology is presented on a 2D simulation of the brazilian splitting test, which is a standard technique for determination of the tensile strength of concrete. In this test, a cylindrical specimen is loaded along its vertical diametral plane. The compressive load, transfered to the specimen via steel bearing plates at the top and bottom sides, induces tension stress in the horizontal direction leading finally to the rupture of the specimen along the loading plane. Due to the double symmetry, the analysis itself is performed only on the quarter of the specimen under plain strain conditions. The concrete behaviour is described by the nonlocal scalar damage model, while the steel bearing plates are assumed to be linearly elastic. The considered dimensions of the specimen and the relevant material parameters are shown in Figure 5 on the left.

The adaptive simulations was performed on 3 processors with a static partitioning displayed in Figure 5 on the right. The target relative error 10 % (taken as a common engineering tolerance) was prescribed. The sequence of meshes used in the simulation is displayed in Figure 6. The nonlinear problem was solved incrementally applying the cylindrical arc length method taking the horizontal displacement of point B (see Figure 5) as the arc length control parameter. The highly nonlinear response of the specimen is displayed in terms of the load-displacement diagrams of points A and B in Figure 7. The severe snap-back and the slight reloading on the loading path of point A is in qualitative agreement with the experimental observations reported in [31]. The obtained response is also in perfect agreement with the sequential analysis. The evolution of the relative error sketched in Figure 8 (on the left) reveals that the global relative error defined by Eq. (16) was not used to trigger the rediscretization of the domain. Instead, the weighted global relative error that attempts to account for the nonuniform error distribution was employed. It is considered as

where

(21) |

The evolution of the weighted error is depicted in Figure 8 (on the right) which clarifies that the decrease of the weighted global relative error bellow 2.5 % was used to initiate the derefinement. The overlap of subsequent pairs of curves in Figures 7 and 8 is related to the restart of the analysis from the previous step.

*Daniel Rypl
2005-12-03*