Abstract
SummaryAccurate numerical modeling of fracture in solids is a challenging undertaking that often involves the use of computationally demanding modeling frameworks. Model order reduction techniques can be used to alleviate the computational effort associated with these models. However, the traditional offline‐online reduction approach is unsuitable for complex fracture phenomena due to their excessively large parameter spaces. In this work, we present a reduction framework for fracture simulations that leaves out the offline training phase and instead adaptively constructs reduced solutions spaces online. We apply the framework to the thick level set (TLS) method, a novel approach for modeling fracture able to model crack initiation, propagation, branching, and merging. The analysis starts with a fully‐solved load step, after which two consecutive reduction operations—the proper orthogonal decomposition and the empirical cubature method—are performed. Numerical features specific to the TLS method are used to define an adaptive domain decomposition scheme that allows for three levels of model reduction coexisting on the same finite element mesh. Special solutions are proposed that allow the framework to deal with enriched nodes and a dynamic number of integration points. We demonstrate and assess the performance of the framework with a number of numerical examples.
Highlights
The search for numerical methods capable of accurately capturing the complex mechanisms involved in the fracture of solids is still one of the most active research fields in computational mechanics, despite its long history and vast body of literature
Two new approaches to couple damage and fracture mechanics in a single regularized framework based on superposed solution fields have been introduced, namely the phase field method[9] and the thick level set (TLS) method.[10]
In a recent work,[23] we propose an adaptive reduction framework that starts with a fully-solved load step and combines a number of state-of-the-art Model order reduction (MOR) techniques[17,19,22,24] in order to progressively build a hyper-reduced model that allows for different levels of reduction coexisting on different subdomains of a single finite element mesh
Summary
The search for numerical methods capable of accurately capturing the complex mechanisms involved in the fracture of solids is still one of the most active research fields in computational mechanics, despite its long history and vast body of literature. In Reference 18, the authors employ a mesh morphing technique that effectively reduces the size of the reduced space necessary to accurately approximate the solution, while authors in Reference 19 combine POD with domain decomposition in order to allow for locally-refined bases to be used in zones of strain localization Promising, these approaches still rely on the construction of a reduced basis offline. In a recent work,[23] we propose an adaptive reduction framework that starts with a fully-solved load step and combines a number of state-of-the-art MOR techniques[17,19,22,24] in order to progressively build a hyper-reduced model that allows for different levels of reduction coexisting on different subdomains of a single finite element mesh. The performance of the modified framework is assessed and additional numerical examples are shown
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
