Summary Accurate 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.

The Thick Level Set (TLS) method has been proposed as a new approach to the modeling of damage growth in solids. The fronts of damaged zones are implicitly represented as a level set of an auxiliary field whose evolution is accomplished by the level set method. The TLS model contains a characteristic length to obtain a non-local description that prevents spurious localization in the strain field. The update of the damage is indirectly performed by integrating local values of energy release rate over this characteristic length. This model offers an automatic transition from damage to fracture, and deals with merging and branching cracks as well as crack initiation in an easy and robust manner. In this paper, the TLS is applied to simulate the formation of cusps in a polymer matrix loaded in shear. Realistic simulation of this process requires the damage model to be combined with plasticity in order to capture the behavior of the material prior to failure. To accommodate for plasticity, several changes to the TLS framework are introduced. A strength-based criterion for initiation of damage based on the ultimate yield surface of such plasticity model is proposed. A mapping operator for transferring history is included if the integration scheme in element changes. Furthermore, a new loading scheme is devised that does not rely on secant unloading. Numerical experiments demonstrate the accuracy and effectiveness of the proposed model to handle simulation of crack growth in a medium with hardening plasticity.

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