In polymer composites, inclusions (fillers) are introduced into the glassy polymeric matrixes in order to improve the toughness properties as the brittleness is one of the fatal drawbacks for glassy polymers. The first time in our current study, the stress analysis has been performed on the interaction between a circular inclusion and a craze with an internal small crack in polymeric composites. A craze can be treated as a crack with fibrils bridging the two crack surfaces. The forces applied by the fibrils to the crack surfaces (pulling the two surfaces closer) depend on the crack opening displacement. However, the crack opening displacement is directly related on the forces applied by the craze fibrils. To solve this dilemma, an iterative procedure is proposed for the first time to solve the formulated singular integral equations. The craze thickness profiles, the cohesive stress distribution and the fracture toughness of the polymeric composites are investigated thoroughly. Moreover, due to the influence of the inclusion, the uneven craze thickness profiles are observed from the left to the right part of the entire craze zone.
Flexoelectric material under inhomogeneous electric field can be used as control and actuation systems in engineering applications based on the converse flexoelectric effect. The electric field gradient can be generated by using the atomic force microscope probe placed on the top of flexoelectric layer and coupled with a bottom electrode surface. The induced membrane force and the corresponding control moment in turn influence the dynamic response of the beam. The response of a laminated cantilever beam with initial vibration caused by an external loading is studied. The beam was modelled as a laminated beam to explore the influence of flexoelectric layer stiffness on the dynamic response of the structure. When the flexoelectric layer has higher Young’s modulus and mass density than the elastic layer, with increasing the thickness of the flexoelectric layer, the tip displacement of the laminated beam decreased rapidly. Through case studies, the optimal control positions for each mode of vibration were found to be dependent on the flexoelectric layer properties as well. A displacement-based feedback control was introduced to avoid overactuation caused by open-loop control.
A flexoelectric cantilever beam actuated by the converse flexoelectric effect is evaluated and its analytical and experimental data are compared in this study. A line-electrode on the top beam surface and a bottom surface electrode are used to generate an electric field gradient in the beam, so that internal stresses can be induced and applied to distributed actuations. The dynamic control effectiveness of the beam is investigated with a mathematical model and is validated by laboratory experiments. Analyses show that the actuation stress induced by the converse flexoelectric effect is in the longitudinal direction and results in a bending control moment to the flexoelectric beam since the stress in the thickness is inhomogeneous. It is found that thinner line-electrode radius and thinner flexoelectric beam lead to larger control effects on the beam. The position of the line-electrode on the top surface of the beam also influences the control effect. When the line-electrode is close to the fixed end, it induces a larger tip displacement than that is close to the free end. Analytical results agree well with laboratory experimental data. This study of flexoelectric actuation and control provides a fundamental understanding of flexoelectric actuation mechanisms.
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