PSI - Issue 43

Vladislav Kozák et al. / Procedia Structural Integrity 43 (2023) 47–52

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V. Koza´k & J. Vala / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 4. Smeared damage model, after initial state of loading (left part) and crack growth (right part).

algorithms; for more details (Giry et al., 2011) and (Grassl et al., 2014). Smeared model is actually a slightly di ff erent method of non-local approach, based on damage mechanics. Again, problem is concerned on some averaging of the stresses in front of the crack tip. Thus, the proposed procedure combines the possibilities of several approaches for modelling crack propagation in fibre composites. The primary method is XFEM, the stress in front of the crack crack recalculates according to the nonlocal approach, in the whole body according to the exponential law of violation. The influence of microstructure is applied via the Mazars’s model (see (Giry et al., 2011) and (Jira´sek, 2011)), the evaluation of damage factor is given by the exponential law, detailed information can be found in (Vala, 2021). Crack propagation is changed very distinctly. Fig. 4 presents some results of smeared damage modelling. The boundary conditions are as follows: a body with a prior circular crack, the stress is concentrated on the surface of the hole. Cement paste has Young’s modulus E = 3.1 GPa, Poisson’s constant is equal to 0.3, tensile strength is 10 MPa. The fibres are 3 mm long and have a Young’s modulus E equal to 190 GPa. This conference paper is concentrated to numerical testing of a proper physical, mathematical and computational deterministic model suitable for modelling building materials with fibre micro structure, namely cement-based com posites. Credibility of computational modelling of engineering structures and their elements caused by mechanical, thermal, etc. loads, is conditioned by the precise formulation and implementations of an appropriate material model, involving elastic, viscous and plastic deformation of material together with the type and measure of its damage. Special attention is concentrated to materials models covering class so called non-local approaches, revising the classical Mazars’ (Pijaudier-Cabot and J. Mazars, 2001) model end the needed damage factor is introduced utilizing the Eringen’s non-local strain stress relation closely connected to the software development. Mathematical approach can be found in paper (Vala and Koza´k, to be published), basic information as to numerical approaches, mainly for quasi-static loading, in papers (Vala and Koza´k, 2020) and (Vala and Koza´k, 2021). 6. Conclusions and applications