Indentation size effects in poly(methyl methacrylate) (PMMA) were studied through nanoindentation. Two factors of indentation size effects in PMMA, namely yield criterion and shear transformation-mediated plasticity, were analysed in detail. The yield criterion that considers strength differential (SD) effects and pressure sensitivity was constructed by performing the combined shear-compression experiments. The relationship between hardness and normal stress can then be obtained based on Tabot’s relation. Shear transformation-mediated plasticity was also applied to model the measured hardness as a function of the indentation depth at different strain rates. Results show that the yield criterion contains the terms of SD effects and pressure sensitivity gives the best description of the yielding of PMMA. Additionally, the volume of single shear transformation zone calculated through the presented criterion agrees well with simulation and exhibits increases with increasing strain rate. Indentation size effects in PMMA under different strain rates were discussed and an appropriate indentation depth range was suggested for calculating the hardness and modulus.

This study systematically investigates the tensile anisotropic mechanical behavior of ferritic steel under different orientations through an integrated experimental, theoretical modeling, and simulation approach employing advanced characterization techniques including electron backscatter diffraction (EBSD), digital image correlation (DIC), scanning electron microscopy (SEM), and finite element analysis. The results demonstrate pronounced orientation dependence in mechanical response, with initial yield strengths of 391, 391, and 405 MPa and fracture strains of 0.237, 0.220, and 0.212 observed for 0°, 45°, and 90° orientations, respectively, corresponding to orientation-induced variations of 3.6% in yield strength and 11.8% in fracture strain. These anisotropic characteristics are primarily attributed to the predominant α-fiber texture ||RD, which accounts for 59.8% of the texture components. Furthermore, crystallographic texture significantly influences fracture behavior, as evidenced by the distinct orientation-dependent macroscopic contraction characteristics and morphological features of fracture surfaces.

In this study, a machine learning model for the anisotropic mechanical behavior of AA7075-T6 was successfully developed by combining classical plasticity theory with neural network algorithms. First, a yield criterion incorporating strength asymmetry and orientation dependence was constructed based on a fourth-order linear transformation of invariants, and a stress update algorithm was implemented using the return mapping and implicit integration schemes. Subsequently, a dataset comprising experimental results from tension, compression, and shear tests at multiple orientations, as well as theoretically generated data from additional strain paths, was established to train a genetic algorithm-optimized two-hidden-layer neural network. Plastic-stage assessments indicated that, for the equal-biaxial path, the RMSE values of the stress–strain curves predicted by the machine learning model relative to the constitutive implementation were 31.87 and 39.24 MPa. It should be noted that the stress–strain response under equal-biaxial loading represents an additional prediction case. The trained model exhibited satisfactory predictive performance when compared against experimental data for tension, compression, and shear and was capable of reproducing the theoretical stress paths derived from the classical constitutive model. This approach leverages the physical interpretability of conventional constitutive modeling and the high efficiency of data-driven methods, providing a viable solution for efficiently predicting the anisotropic mechanical response of metallic materials under complex stress states.