PSI - Issue 32

R.I. Izyumov et al. / Procedia Structural Integrity 32 (2021) 87–92 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3. Results of modeling As a result of modeling, the values of the force required for indentation at a given depth u were obtained. By the values of such a force, we mean the concept of surface rigidity K . or the case of a model without inclusion, the parameter K 0 is introduced. The influence of the depth H of the particle with the same particle size R v is shown in Fig. 3 and Fig. 5 by lines of different colors.

Fig. 3. Dependence of the relative stiffness of the material K/K 0 on the probe displacement L . The color indicates the different depths H of the inclusion. Inclusion radii R V =5 R and R V =10 R. In the first graph of Fig. 3, we can note some oddity (this area is highlighted by a box). When the probe moves relative to the center of the inclusion by a distance greater than the radius of this inclusion (approximately L= 6-7 R at R v = 5 R ), we see that the dependence of the relative stiffness on the depth of the inclusion K/K 0 ( H ) becomes inverse. For example, for a shift L= 10 R with an increase in the depth of the inclusion H (from R to 10 R ) we will observe, contrary to expectations, an increase in the relative stiffness K/K 0 = [1.047 1.053 1.066 1.079]. This effect has a rather weak value, which means that it is not significant in practice. However, I would like to give an illustration explaining the physicality of this effect in order to get rid of suspicions of a large systematic calculation error.

Fig. 4. Illustration of the impact on the probe of an inclusion located at depths H=R and H= 10 R . The red arrow shows the direction of the force, which is the contribution from the presence of an inclusion in the material. Consider the following combination of parameters: R V =5 R, L= 10 R . For this case, we will give a schematic illustration, in which we will not take into account the complex displacements of the inclusion in the process of