Generalized self-consistent like method for mechanical degradation of fibrous composites

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2011-12, Vol.91 (12), p.967-978
• Main Authors: Boso, D.P., Lefik, M., Schrefler, B.A.
• Format: Article
• Language: English
• Subjects: brittle fibre breakage; Exact sciences and technology; Generalized self-consistent homogenisation; Mathematical analysis; Mathematics; multiscale modelling; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Sciences and techniques of general use; superconducting strands; thermo-mechanics
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201000209

This paper deals with homogenization of heterogeneous, fibre‐reinforced material. One of the main points of the work consists in taking into account the breakage of the fibres, to compute the effective behaviour of the damaged composite. Furthermore, the possible yielding of the matrix material is considered. The problem is solved for the coupled thermo‐mechanical field, that is all material characteristics can be temperature dependent and thermal loads can be simulated. The method is based on a self consistent type scheme, suitably extended for the case at hand. The effective behaviour is obtained by considering isotropic elastic‐brittle cylindrical inclusions surrounded by a shell of elasto‐plastic matrix material immersed in an infinite medium endowed with the effective properties. Usually in the framework of the self consistent scheme, the homogenised material behaviour is obtained with a symbolic approach. On the contrary, in this work the solution is found in a non‐classical way, as we use the finite element method to find the solution of the thermo‐mechanical problem as a function of the effective material characteristics. This paper deals with homogenization of heterogeneous, fibre‐reinforced material. One of the main points of the work consists in taking into account the breakage of the fibres, to compute the effective behaviour of the damaged composite. Furthermore, the possible yielding of the matrix material is considered. The problem is solved for the coupled thermomechanical field, that is all material characteristics can be temperature dependent and thermal loads can be simulated. The method is based on a self consistent type scheme, suitably extended for the case at hand. On the contrary, in this work the solution is found in a non‐classical way, as we use the finite element method to find the solution of the thermomechanical problem as a function of the effective material characteristics.