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**A multi-level computational model for multi-scale damage analysis in composite and porous materials.**
*(English)*
Zbl 1015.74058

Summary: We develop an adaptive multi-level methodology to create a hierarchy of computational sub-domains with varying resolution for multiple scale problems. It is intended to concurrently predict evolution of variables at structural and microstructural scales, as well as to track the incidence and propagation of microstructural damage in composite and porous materials. The microstructural analysis is conducted with Voronoi cell finite element model (VCFEM), while a conventional displacement-based FEM code executes the macroscopic analysis. The model introduces three levels in the computational domain which include macro, macro-micro and microscopic analysis. The model also differentiates between non-critical and critical regions, and ranges from macroscopic computations using continuum constitutive relations to zooming in at ‘hotspots’ for pure microscopic simulations. Coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization. An adaptive process significantly increases the efficiency while retaining an appropriate level of accuracy for each region. To demonstrate the potential of the model, numerical examples are conducted for composite and porous materials with a variety of microscopic architectures.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74R99 | Fracture and damage |

74Q05 | Homogenization in equilibrium problems of solid mechanics |

74E30 | Composite and mixture properties |