XVIII GIMC Conference Siracusa, 22--24 September 2010 A DOMAIN DECOMPOSITION APPROACH FOR ELASTIC SOLIDS WITH DAMAGEABLE INTERFACES Federica Confalonieri 1 , Giuseppe Cocchetti 2 and Alberto Corigliano 3 Dipartimento di Ingegneria Strutturale, Politecnico di Milano Piazza Leonardo da Vinci 32, Milano e-mail: 1 federica.confalonieri@mail.polimi.it 2 giuseppe.cocchetti@polimi.it 3 alberto.corigliano@polimi.it Keywords: Domain decomposition method, interface, localized non-linearities Abstract. This paper concerns a dual domain decomposition approach, able to handle the presence of localized nonlinearity in an elastic solid, due to damage and fracture phenomena. The proposal extends the multi-time-step coupling method for structural dynamics, proposed by Gravouil and Combescure. The main idea is to concentrate the non linearity due to dam- age at the interface level, there enforcing a non linear interface law. 1 INTRODUCTION This paper focuses on the formulation of a domain decomposition approach for the solu- tion of a dynamic problem, able to deal with localized non-linearity, which can be described as an interface between elastic subdomains. That applies, for example, to the cases of loca- lized damage, delamination or fracture problems. The proposed technique belongs to the framework of the FETI method’s family and its ex- tensions. The FETI method was developed for static problems by Farhat and Roux [2] to di- vide a structural mesh into subdomains and solve them separately. Starting from it, Gravouil and Combescure in [1] formulated a coupling multi-time-step for dynamics. Both methods are based on element partitioning of the domain and use Lagrange multipliers to impose continui- ty conditions at the interface. The main idea of the present work is to extend the domain decomposition approach, pre- sented in [1], to the more general case of a non linear law acting at the interface between the subdomains and within them. As a result, the non linear problem becomes condensated at the interface level. Similar approaches can be found in [4] for the static problem and in [5] for the analysis of debonding in composite materials. After a short presentation of the reference problem, the method is formulated in section 2; subsequently some bidimensional examples are presented in section 3; section 4 concludes the paper, giving some final remarks.