A computational multi-scale framework for fracture mechanics
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In this contribution, we present a multi-scale fracture framework, allowing us to con- sider individual fracture behaviour on a macro and a micro scale. We follow the style of FEM2 /IGA2 -concept for macroscopically modeling complex materials with heterogeneities on the micro-scale, see Schmidt et al. [1]. In this talk we address additionally the established phase-field method for fracture mechanics, see Hesch et al. [2]. To be specific, we apply the macroscopic deformation at a given point to a epresentative volume element via suitable boundary conditions and super-impose the macro-phasefield in this point onto the micro-phasefield of the RVE. Introdcing a suitable homogenization technique including different fracture dissipations on the micro- and macro-scale, we obtain an energy preserving formulation. Moreover, we are able to derive consistent linearization of macroscopic stresses, the phase-field driving force and multi-field contributions for the Newton-Raphson iteration. The dual phase-field allows by choosing sufficient transition criteria to model a variety of effects within the fracture and damaging field, which are exemplary demonstrated in a variety of simulations, e.g. two-dimensional fracture mode tests for the macro-scale and classical deformation benchmarks. We investigate different crack growth behaviours, from pure micro- or macro-fracture to combined or accumulated fracture and draw comparisons to other damaging models. REFERENCES [1] F. Schmidt, M. Krüger, M.-A. Keip and C. Hesch, Computational homogenization of higher-order continua. International Journal for Numerical Methods in Engineering, https://doi.org/10.1002/nme.6948, 123:2499–2529, 2022. [2] M. Dittmann, J. Schulte, F. Schmidt, and C. Hesch, A strain-gradient formulation for fiber reinforced polymers: Hybrid phase-field model for porous-ductile fracture. Com- putational Mechanics, https://doi.org/10.1007/s00466-021-02018-0, 67:1747– 1768, 2021.