Issue 39

J. Eliáš, Frattura ed Integrità Strutturale, 39 (2017) 1-6; DOI: 10.3221/IGF-ESIS.39.01 4 N UMERICAL EXAMPLE erformance of the proposed adaptive algorithm is demonstrated on simulation of four-point bending test with incorporated material randomness. The computer code used for calculation is an in-house software. The beam geometry is shown in Fig 2. The deterministic model parameters were taken from simulation of experimental series in three-point bending [22]. The average tensile strength is f t =2.2 MPa, fracture energy in tension is G F =35 J/m 2 and elastic modulus is 60 GPa. All these parameters are applied on the meso-level, they are not equal to the corresponding macroscopic properties of the model. The adaptive algorithm uses the following parameters: r f =60 mm, r c =120 mm, l f =10 mm and l c =30 mm. The parameters of the probabilistic extension are arbitrarily chosen according to [19]. The correlation length and the coefficient of variation of the random field is 80 mm and 0.25, respectively. Three model types are used: (i) the fine model, that uses fine discretization everywhere from the beginning; (ii) the coarse model, that uses coarse discretization all the time; and (iii) the adaptive model, that starts with coarse discretization and refines it adaptively. Fig. 3 shows on the left-hand side identical responses of one simulation using the fine model and one simulation using the adaptive model with the same refined meso-structure and also the same random field realization. The resulting crack patterns as well as the random field applied are shown in Fig. 4. Figure 2 : Dimensions of the simulated beam loaded in four-point bending. Figure 3 : Left: Load-displacement response of one four-point-bending test simulation using the fine model and the adaptive model with the same refined meso-structure. Right: Average response of 30 simulation of four-point-bending test. All three model types were then compared statistically. The same 30 realizations of the random field were used for every model type. The average responses together with standard deviations are shown in Fig. 3 on the right hand side. The fine and the adaptive model exhibit the same behavior while the coarse model deviates from them. In average, the computational time consumed by the adaptive model was only 47% of the time consumed by the fine model. P