PSI - Issue 52

Roman Vodička et al. / Procedia Structural Integrity 52 (2024) 242 – 251 R. Vodicˇka / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 10. Distributions of the phase-field variable α (a), the stress trace [MPa] (b), and norm of deviatoric stress [MPa] (c) in the block at the instant t = 80 µ s for the inviscid case. Displacements are magnified 100 times in the case of α .

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Fig. 11. Distributions of the phase-field variable α (a), the stress trace [MPa] (b), and norm of deviatoric stress [MPa] (c) in the block at the instant t = 80 µ s for the case with τ r1 = 1 µ s. Displacements are magnified 100 times in the case of α .

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Fig. 12. Distributions of the phase-field variable α (a), the stress trace [MPa] (b), and norm of deviatoric stress [MPa] (c) in the block at the instant t = 80 µ s for the case with τ r1 = 1 µ s and τ r2 = 1 µ s. Displacements are magnified 100 times in the case of α .

is important to consider the fracture energy being dependent on the mixity of the crack mode, though detailed analysis is not provided here. Though, there appeared a di ff erence between the two options with various values of parameters τ r1 and τ r2 , it is not significant for the present values. Anyhow, adding these rheological properties may modify the crack formation processes in materials.

5. Conclusions

A computational model for fracture in quasi-brittle materials appearing generally in a mixed mode is presented for a time dependent loading which requires to take inertial forces into account. Simultaneously, material is considered visco-elastic which incorporates some damping in elastic wave propagation and modifies the process of crack prop agation. As long as the rheology is described by a rather general four parametric model, any of the simple solid-like models like Kelvin-Voigt or Poynting-Thomson can be considered by appropriate adjusting of the material parameters. It is clear that the model needs not only those rheological parameters to be set but also those pertinent to crack formation processes. Of course, the values of such parameters modify degradation processes in materials, setting of them have to be done in comparison with experimental measurements. The details of computational implementation were not provided. Anyhow, they included a staggered time stepping which gave possibility to obtain a variationally based solution process, in which methods of sequential quadratic programming were used, and the spatial discretisation by finite elements was implemented. All such computations were performed in an in-house MATLAB code. Following the presented results it is believed that the computational approach will be adequate also in other calcu lations for dynamic crack propagation.