Adaptive and variable model order reduction method for fracture modelling using explicit time integration

Damage modelling in modern material architectures using explicit time integration is a computationally expensive task. To reduce such expenses, model training methods based on simulation data is a suitable approach, for instance, model order reduction using proper orthogonal decomposition. However, such approaches require extensive offline training and a complete replacement of full-order modelling will hinder damage evolution that requires accurate modelling of local stress states. To overcome these problems, this works presents an adaptive reduced-order modelling framework without the need for offline training whilst having the ability to vary the level of approximations within a solution. This is achieved by adaptively calculating the reduced-bases and the hyper-reduction parameters after solving the full-order model for a few increments. Domain decomposition is enabled to separate damage modelling from reduced-order modelling and a computationally efficient method for history recovery is presented. To model the non-linearities, the reduced-order modelling parameters are updated as the solution progresses. The reduced-order modelling approximation switches to full-order modelling at regular intervals to achieve the linear momentum balance between the spatially same but dimensionally different domains. The performance of the developed method is demonstrated using benchmark composites damage modelling examples. In these examples, strong discontinuities are modelled using adaptively initiated cohesive segments and the overall framework requires minimal user intervention.