A Deep Artificial Neural Network Model for Predicting the Mechanical Behavior of Triply Periodic Minimal Surfaces under Damage Loading

The triply periodic minimal surface (TPMS) is being potentially considered in innovative applications, including robotics, biomedical engineering, impact energy absorption, and so on, so that the information on mechanical property and energy absorption of TPMS components under the damage loading is significant to understand, with a considerably reduced cost before being put into use. For the first time, a deep artificial neural network (ANN)-powered prediction method for TPMS lattices, including sheet gyroid, sheet primitive, sheet I-graph-wrapped package curved surface (I-WP) and solid I-WP subjected to damage loading, with an extremely low cost is introduced in this work where a loop with multiple conditions (LMC) inserted to improve its accuracy. It is a low-cost model due to the fact that it only requires a training experimental data set from 9 TPMS samples with relative density ranging from 0.1 to 0.55, subjected to the damage test to train and then generates the mechanical information and energy absorption at almost any point of the relative density (Rd). Impressively, the ANN prediction method can well comprehend and learn from experimental samples, and then accurately provide the information of mechanical behavior of TPMS architectures, including the stress-strain response, Young's modulus, and yield strength at almost any relative density in the range, under the damage load. Specifically, Young's modulus and yield strength obtained from ANN model agree well with that from the experimental damage test data, which does not belong to the training samples, with maximum percent differences found approximately 1%, and 2%, respectively. Surprisingly, ANN approach demonstrates an ability to predict the mechanical response of TPMSs, with thousands of times faster and significantly lower financial cost than that of the experiment. Thus, we move forward, by using the approach, to map 2-dimensionally the energy absorption of lattices with respect to varying relative density and deformation, and plot the energy dissipation density versus the relative density under damage loadings.