A continuum mechanics model for mechanical fatigue analysis Sergio Oller * , Omar Salomo ´n, Eugenio On ˜ate Departamento de Resistencia de Materiales y Estructuras en la Ingenierı ´a, Universidad Polite ´cnica de Catalun ˜a, International Center for Numerical Methods in Engineering (CIMNE), Jordi Girona 1-3, Mo ´ dulo C1 Campus Norte UPC, 08034 Barcelona, Spain Received 13 January 2004; received in revised form 22 July 2004; accepted 3 August 2004 Abstract In this paper, a thermo-mechanical constitutive model for the predictions of fatigue in structures using the finite ele- ment method is formulated. The model is based on the damage mechanics of the continuous medium and allows the treatment in a unified way of coupled phenomena such as fatigue with damage, plasticity, viscosity and temperature effects. Basically it is gotten sensitive models to cyclic loads starting from classical non-linear constitutive formulations incorporating the special variable influenced by the characteristics of the cyclic load. A formulation based on the theories of damage and plasticity is developed. The necessary modifications of these theories are outlined in order to include the fatigue phenomena. A brief description of the finite element implementation is given. Finally, results of the performance of the proposed model are shown through the simple fatigue test and the fatigue analysis of an aluminium engine alternator support. Ó 2004 Elsevier B.V. All rights reserved. PACS: 81.40.N; 83.20; 81.40.L; 83.50; 02.70.D; 02.60 Keywords: Fatigue numerical analysis; Plasticity-damage constitutive model; Finite element method 1. Introduction Time varying cyclic loads produce failure of structural parts for values of stress lower than those obtained in static tests. This phenomenon is called fatigue and it is defined more generally in the ASTM [1] code as: ‘‘the process of perma- nent, progressive and localized structural change which occurs to a material point subjected to strains and stresses of variable amplitudes which produces cracks which lead to total failure after a certain number of cycles’’. Fatigue is the main cause of failure of machine parts in service, in mechanisms and structural 0927-0256/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2004.08.001 * Corresponding author. Fax: +34 93 401 10 48. E-mail addresses: oller@cimne.upc.es (S. Oller), salomon@ cimne.upc.es (O. Salomo ´ n), onate@cimne.upc.es (E. On ˜ ate). Computational Materials Science 32 (2005) 175–195 www.elsevier.com/locate/commatsci