This paper presents a locally resonant metamaterial periodically rearranged as a local resonator, that is hexagonal holes arranged in a thin plate replace the elastic local resonator to achieve the quantum valley Hall effect. Due to the $C_{3v}$ symmetry in the primitive hexagonal lattice, one Dirac point emerges at high symmetry points in the Brillouin zone in the sub-wavelength area. Rotating the beam element of the resonator can break the spatial inversion symmetry to lift the Dirac degeneracy and form a new bandgap. Thus, the band inversion is discovered by computing the relationship between the associated bandgap and the rotational parameter. We also confirmed this result by analyzing the vortex chirality and calculating the Chern number. We can discover two kinds of edge states in the projected band obtained by computing the supercell composed of different topological microstructures. Finally, the propagation behavior in various heterostructures at low frequencies was analyzed. It is shown that these valley Hall elastic insulators can guide elastic waves along sharp interfaces and are immune to backscattering from defects or disorder. By utilizing elastic resonators, a simple reconfigurable topological elastic metamaterial is realized in the sub-wavelength area.

We investigate the propagation behavior of the low-frequency topological interface state of the flexural wave in the locally resonant metastructure and analyze the tunability of the sub-wavelength interface states by the piezoelectric shunting circuit. One homogeneous thin beam is periodically attached with local resonant beams, which connect shunted piezoelectric actuators. The folding band obtained by merging two primitive unit cells into one new element can generate a Dirac point below the low-frequency locally resonant bandgap. This folding point is opened to develop one new bandgap originated from the Bragg scattering effect by breaking the mirror symmetry. Then, topological transitions are demonstrated during the distance variation between two adjacent resonances. The interface state’s existence is further confirmed by using steady and transient analysis of the heterostructure composed of two media with different topological properties. Finally, we show the relationship between the interface frequency and the capacitance ratio and research the influence of the distance parameter on the topological interface state. Because of the tunability of elastic waves by the piezoelectric shunting circuit, our design has potential for applications such as energy harvesters, filters, and physical switches.

Accurate evaluation of mechanical states in steel structures is vital to structural integrity and service safety. While micromagnetic techniques offer a non-destructive and physically grounded approach to stress and strain sensing, any single technique alone falls short of capturing the full complexity of ferromagnetic behavior. To address this limitation, we propose a novel framework that integrates an advanced multi-micromagnetic parameter technique with a tailored one-dimensional convolutional neural network (1DCNN) to predict stress and strain in steel specimens under uniaxial tensile load. To ensure robustness and mitigate the risk of high-dimensional data redundancy, coefficient of variation filtering and RReliefF feature selection algorithms are applied. The model achieves high predictive accuracy, as confirmed by K -fold cross-validation. Its generalization capability is further validated by predicting the mechanical states of additional unseen specimens, with error consistently within acceptable bounds. Finally, we introduce an explainable learning strategy by coupling 1DCNN with shapley additive explanations, enabling us to uncover the most influential magnetic features contributing to model predictions. This interpretable framework not only accelerates the evaluation process but also strengthens the physical interpretability of the correlation between micromagnetic signals and mechanical states. Overall, our work provides a scalable and physically interpretable solution for non-destructive mechanical characterization, with strong potential for deployment in field applications involving complex stress paths.

Finite Element Modeling For Simulation Quasi Static Compression