摘  要

近年出现了大量的柔性压电器件，用于各种形式的人体能量收集，为可穿戴或可植入电子器件提供电源。对于这些压电器件的电学表征和力学行为研究具有十分重要的理论意义和应用价值。本论文对压电器件的电压测量问题及其软硬叠层结构受弯的力学行为进行了系统深入的研究，主要内容和创新点如下：

开路电压是衡量压电器件电学性能的重要参数，然而在最近发表的一些文献中，即使压电材料中的应变或应力在循环载荷期间保持正值，测量电压的符号也会出现交替的正负变化，这与开路压电理论不符。有研究者指出，压电器件的测量电压依赖于所使用电压表的内阻，这导致一个重要问题：即使对于同一压电器件，由于使用不同的测量仪器，很可能会产生不同的性能评估。为解决上述问题，本文在前人工作的基础上开展了深入研究：利用两个内阻相差3个量级（10 MΩ和55 GΩ）的电压表对同一柔性压电器件进行测量，发现其测量电压峰值相差一个量级（0.2 V和2 V），且其正负号截然不同，10 MΩ电压表所测的电压为正负交替曲线，而55 GΩ电压表所测的电压基本为非负曲线（开路电压），这进一步验证了压电器件的测量电压依赖于电压表的内阻；在已有研究的通用解析模型基础上，提出了易于使用的压电器件电压测量一般标准，使得压电器件的性能可以通过特定的测量电压值进行量化；利用场效应晶体管开发了一套满足所提标准要求的电压测量系统，实现了真正的开路电压测量；对商用压电器件进行了与柔性压电器件相同流程的实验测试和理论分析，验证了研究结果的普适性。

为了提高单位面积的输出功率，柔性压电器件可以采用叠层结构设计。本文通过能量法研究了柔性压电器件软硬叠层结构的几种典型的受弯力学行为。针对器件外层过早破坏的问题，研究了其屈曲力学行为，给出了位移和应变的解析表达式，并且提出了能够使中性轴分离的优化方案，从而避免外层的过早破坏。在圆柱上弯曲的工况常用于衡量柔性电子器件的弯曲能力，为此，本文研究了软硬叠层结构在圆柱上弯曲的解析模型，给出了其应变和中性轴位置的解析表达式，并发现结构长度对于中性轴分离具有重要影响。针对软硬叠层结构中软层的变形究竟是由剪应变主导还是正应变主导的争议，本文研究了受纯弯的三种小变形解析模型，即软层只考虑剪应变、只考虑正应变和同时考虑剪应变与正应变的情况；研究结果表明：在受弯问题中，软层以剪切变形为主导，从而定量地澄清了上述争议。

本文综合运用理论分析、有限元数值模拟和实验验证等方法开展研究，获得的成果实现了压电器件电学性能的准确表征，并可为基于软硬叠层结构的柔性压电器件设计提供重要指导。

Abstract

In recent years, a large number of flexible piezoelectric devices have been used as various forms of human body energy harvesters for power supply of wearable or implantable electronic devices. It is of great theoretical significance and practical value to study the electrical characterizations and mechanical behaviors of these piezoelectric devices. In this thesis, a systematic in-depth study of the voltage measurement problem of piezoelectric devices and the mechanical behaviors for bending of the laminated structures consisting of both hard and soft layers is carried out. The main contents and innovations are as follows.

Open-circuit voltage is an important parameter for measuring the electrical performances of piezoelectric devices. However, in some recently published literature, even if the strain or stress in the piezoelectric material maintains a positive value during the cyclic load, the sign of the measured voltage alternately changes positively and negatively, which is inconsistent with the open-circuit piezoelectric theory. Some researchers pointed out that the measured voltage of a piezoelectric device depends on the internal resistance of the voltmeter used, which leads to an important problem: even for the same piezoelectric device, it is likely that different performance evaluations are produced due to the use of different measuring instruments. In order to solve the above problem, an in-depth study has been conducted in this thesis on the basis of the previous studies. The same flexible piezoelectric device was measured using two voltmeters with an internal resistance difference of three orders of magnitude (10 MΩ and 55 GΩ). It was found that the measured voltage peaks differed by one order of magnitude (0.2 V and 2 V). The voltage measured by the 10 MΩ voltmeter showed a positive and negative alternation, while that by the 55 GΩ voltmeter kept non-negative (open-circuit voltage). This further validates that the measured voltage of a piezoelectric device depends on the internal resistance of the voltmeter. Based on the general analytical model that was previously established, a universal and easy-to-use standard for voltage measurement of piezoelectric devices is given, making it possible to quantify the performance of a piezoelectric device by a specific measured value of voltage. A voltage measuring system that satisfies the requirements of the proposed standard is developed using a field effect transistor, realizing the open-circuit voltage measurement. The experimental tests and theoretical analyses under the same process as that for flexible piezoelectric devices have been carried out on commercial piezoelectric devices, which validates the universality of the present results.

In order to improve the output power per unit area, flexible piezoelectric devices can be designed with a laminated structure. In this thesis, several typical bending mechanical behaviors of the laminated structures consisting of both hard and soft layers of flexible piezoelectric devices are studied via the energy method. For the problem of premature failure of the outer layers, the buckling mechanical behavior is studied, and the analytical expressions of the displacements and strains are given. An optimized design for splitting of the neutral mechanical plane is proposed to avoid the premature failure of the outer layers. The loading condition of bending on a cylinder is often adopted to measure the bendability of flexible electronic devices. For this reason, the analytical model of the laminated structure that is bent on a cylinder is studied, and the analytical expressions of the strains and positions of the neutral mechanical plane are given. It is found that the length of the structure has an important influence on splitting of the neutral mechanical plane. In view of the controversy that whether the deformation of the soft layers in the laminated structures is dominated by shear strain or normal strain, three analytical models of small deformation under pure bending are studied, i.e., that only taking into account the normal strain-induced deformation of the soft adhesive layers, that only taking into account the shear deformation, and that incorporating both the shear deformation and the normal strain-induced deformation; the results show that shear deformation dominates in the soft layers during bending, which quantitatively clarifies the above-mentioned controversy.

Comprehensive theoretical analyses, finite element modeling and experimental verifications have been adopted in this study. An accurate characterization of the electrical properties is realized for piezoelectric devices, and some important design guidelines are provided for the laminated structure-based flexible piezoelectric devices.