Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

In this paper, we discuss a strategy to reduce the computational costs of the simulation of dynamic fracture processes in quasi-brittle materials, based on a combination of domain decomposition (DD) and model order reduction (MOR) techniques. Fracture processes are simulated by means of three-dimensional finite element models in which use is made of cohesive elements, introduced on-the-fly wherever a cracking criterion is attained. The body is initially subdivided into sub-domains; for each sub-domain MOR is obtained through a proper orthogonal decomposition (POD) of the equations governing its evolution, until when it starts getting cracked. After crack inception within a sub-domain, the solution is switched back to the original full-order model for that sub-domain only. The computational gain attained through the coupled use of DD and POD thus depends on the geometry of the body, on the topology of sub-domains and, on top of all, on the spreading of cracking induced by load conditions. Numerical examples concerning well-established fracture tests are used for validation, and the attainable reduction of the computing time is discussed at varying decomposition into sub-domains, even in the absence of a full exploitation of parallel computing potentialities.