Fig. 11.

Setup of the hyperelasticity problem. (a) A unit square is decomposed into ${\Omega }_{NN}$ and ${\Omega }_{FEM}$. We impose a non-uniform traction boundary condition on the top edge and fix the displacement at the bottom and train multiple DeepONets to represent the mechanics of an SPH model. The material is reinforced by fibers in the vertical direction. Information at the interface (displacement $u$ and first Piola–Kirchhoff stress $P$) is transmitted between DeepONet and FEM. (b) Traction and displacement in different directions are exchanged at the interface $\Gamma$. FEM predicts the external domain while the DeepONet is trained based on SPH data. (c) Two types of DeepONet are proposed to predict the mechanics of the system: predicting stresses based on displacement information (green boxes) and vice versa (yellow boxes).