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

Alberto Corigliano,Federica Confalonieri,Stefano Mariani,Martino Dossi

doi:10.1186/s40323-016-0081-9

Alberto Corigliano, Federica Confalonieri + Show 2 more

Open Access

https://doi.org/10.1186/s40323-016-0081-9

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Abstract

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.

Highlights

One of the most active sectors in computational mechanics looks for more and more efficient strategies for the highly realistic simulation of complex phenomena
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
The computational gain attained through the coupled use of DD and proper orthogonal decomposition (POD) 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

Summary

Background

One of the most active sectors in computational mechanics looks for more and more efficient strategies for the highly realistic simulation of complex phenomena. As far as the continuity along the inter-domain boundaries is concerned, the hypothesis of velocity continuity proposed in [11,40] is here substituted by a local enforcement of a stiff, linear relationship between tractions and displacement jumps [15,41,42] This is required by the coupling of the DD approach with POD, which is adopted next to reduce the order of the problem; to better understand the rationale of the adopted approach, details are provided in what follows once the Singular Value Decomposition (SVD) procedure has been described.

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Conclusion