Predicting the complex stress-strain curves of polymeric solids by classification-embedded dual neural network

Predicting stress–strain curves is key to facilitate the design of polymer materials and their products with tailored mechanical response. However, due to their structural complexity, polymeric solids generally feature complex stress–strain curves, which renders it challenging to model their stress–strain behaviors. Here, using the categorized knowledge of stress–strain curves, a “Classification-Embedded Dual Neural Network (CDNN)” framework is introduced to accurately predict the mechanical evolution of polymeric solids, by taking the example of injection-molded isotactic polypropylene. Upon built, the dual model is a parallel coupling of a “curve type classifier” and a “curve feature predictor” that predict, respectively, the stress–strain curve categories and their feature points that dictate the extent of similarity between two arbitrary curves in the same category, regardless of the curve complexity. Importantly, with the aid of curve-categorized knowledge, the CDNN strategy offers an update-to-date best balance in model accuracy (20% curve error in maximum) and simplicity (300 neurons in total), which greatly enhances the model’s extrapolability and interpretability and, in turn, mitigates the demanding data requirement (27 samplings from a 4D space, that is, a material design space consisting of 4 design dimensions to tune the structure). Overall, this work establishes a simple, robust methodology in predicting polymeric solids’ stress–strain curves and is potentially generic to a variety of materials.