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Gradient structured (GS) metals processed by severe plastic deformation techniques can be designed to achieve simultaneously high strength and high ductility. Significant kinematic hardening is key to their excellent strain hardening capacity which results in a favorable strength-ductility combination. Unfortunately, no constitutive model has been established to simulate and analyze the characteristic kinematic hardening behavior of GS metal to understand the relationship between their microstructure and macroscopic response. In this work, we developed a deformation-mechanismbased strain gradient plasticity model considering the plasticity heterogeneities from the grain to the sample scale. A back stress model, which accounts for the dependency of dislocation pile-ups on grain size, is established to describe the cyclic deformation properties of GS materials. The established model unified the geometrically necessary dislocations accommodating internal plasticity heterogeneities, the resulting back stress and reversible dislocations during reverse loading into a strain gradient plasticity framework, without introducing excessive numbers of independent material parameters. A finite element implementation of the model quantitatively predicts the uniaxial tensile and tensile-compressive responses of a GS copper bar as well as of a reference sample with homogeneous grain size. It is found that GS copper exhibits enhanced kinematic hardening which results mainly from fine grains in the GS layer and contributes to the considerable ductility of the GS material. The model allows to investigate the mechanical response and optimize the properties of materials with various types of spatially heterogeneous grain microstructures.

The fundamental shear horizontal (SH0) wave in plate-like structures is of practical importance in structural health monitoring due to its non-dispersive characteristics. However, compared with Lamb wave, SH0 wave is less used in practice since it is difficult to be excited by using conventional piezoelectric transducers. Recently, face-shear piezoelectric mode has been realized in PZT ceramics and several face-shear piezoelectric transducers have been developed to excite pure SH0 wave in plates. However, when controllable radiation pattern of SH0 wave is required, it is found that no mathematical basis is available for designers to optimize the transducer's parameters. In this work, based on the reciprocal theorem of elastodynamics and Huygens' principle, a theoretical model is proposed to describe the SH0 wave field generated by arbitrary-shaped face-shear transducers bonded on an infinite isotropic plate. It is proved that the wave field generated by a face-shear transducer is equivalent to that generated by uniform in-plane tractions along its perimeter. Then the proposed model is applied to two specific cases of a single square face-shear (d24) PZT wafer and a bidirectional SH0 wave piezoelectric transducer(BSH-PT).Explicit analytical expressions for both cases are successfully obtained. The accuracy of the obtained analytical model is verified by both experiments and FEM simulations. Furthermore, some general guidelines based on the analytical model are presented for optimization of the transducer's dimensions. Finally, based on the guidelines, a new bidirectional SH0 wave piezoelectric transducer is proposed with very small beam divergence., Comment: Some statements mentioned in Section 2 are not strict enough. We need to do further work, thus we decided to withdraw this manuscript with great pity