Biaxial Network Constitutive Model

A plate element in plane stress state is simulated by a network obtained from a regular octagon in which all the diagonals are bars. Simple formulas govern the general nonlinear anisotropic behavior of the model. In order to calibrate the model on an initially isotropic material, all the bars are provided with uniaxial stress‐strain laws analogous to experimental ones. The proposed network model is compared with experimental data and rules of plasticity with respect to the following five items: (1) Poisson ratio for nonlinear elastic behavior and for uniaxial loading in plastic state; (2) proportional monotonic loadings with various ratios ${\sigma }_y/{\sigma }_x$ and $\tau =0$ in the cases of an aluminum alloy and a type of concrete; (3) initial yield curve and ultimate strength envelope on the plane ${\sigma }_x-{\sigma }_y;$ (4) study of the hardening rule of the model on the ${\sigma }_x-{\sigma }_y$ plane, distortion of the yield curve and formation of a corner on it; and (5) exact validity of the normality rule for the network model.