Simulation of non-local damage and size effects in composite materials by means of FFT-based homogenization

Marco Magri
MOX, Dipartimento di Matematica, Politecnico di Milano
Wednesday 16th February 2022
Online seminar:
In composite materials the mechanisms controlling the overall strength and ductility typically operate at different length scales since heterogeneities of different size characterize their material microstructure. As a result of that, a prominent size effect - connected to the size of the reinforcements - is often observed. For instance, in particle reinforced metal matrix composites, it has been observed an increase in strength with decreasing particle size at a constant volume fraction of the reinforcement. In addition to that, the size of the particles influences the ductility of the composite material, although in this case bigger particles can increase or decrease the ductility depending on the dominant damage mechanism. The numerical simulation of such size effects require the implementation of non-local mechanical models incorporating combined inelastic and damage theories. It this contribution, we present a non-local micro mechanical model based on (i) the incorporation of a lower-order strain gradient plasticity model and (ii) the application of an implicit gradient regularization technique to the Gurson-Tvergaard-Needleman ductile damage model for metals. In this way, the extended model is equipped with two length-scale parameters, one for each non-local extension, which modulate the size dependent character of the formulation. The resulting formulation is a non-conventional mechanical problem consisting of three coupled partial differential equations. This problem is numerically solved via a purposely developed staggered algorithm that exploits the sequential usage of FFT-Galerkin and conjugate gradient based solvers. The resulting approach is robust and efficient allowing for the simulation of complex three dimensional micromechanical problems with millions of voxels and different phases. The numerical results show that the employed non-local extension of damage successfully suppresses the spurious grid dependence typical of (local) damage models. Moreover, the combined effect of damage and strain gradient plasticity is analyzed in the simulated size dependent homogenized response of such composites. References: M. Magri, L. Adam, J. Segurado. Particle size effects in ductile composites: An FFT homogenization study. Journal of the Mechanics and Physics of Solids 160, 104759 (2022). M. Magri, S. Lucarini, G. Lemoine, L. Adam, J. Segurado. An FFT framework for simulating non- local ductile failure in heterogeneous materials. Computer Methods in Applied Mechanics and Engineering 380, 113759 (2021). Contatto: