多场耦合层合结构若干力学问题研究
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摘要
薄膜／基底结构在柔性电子器件、电子封装以及微／纳电子机械系统等集成系统中有着广泛的应用。在生产封装过程中,由于薄膜与基底的热学和力学参量失配引起的残余应力使结构产生变形和缺陷,这些变形和缺陷直接影响到系统的性能和寿命。精确地分析计算薄膜/基底结构中的残余应力一直以来是工程和理论界所关注的焦点。
针对两层及三层弹性薄膜/基底结构,基于Euler-Bernoulli梁理论,利用"Newmark模型”考察层间非完美界面,给出了由温度变化引起的残余应力、结构挠度及曲率和界面剪切应力及剥离应力的闭合形式解析解,建立了非完美界面的修正Stoney公式,将结果分析退化并与经典结果进行了比较。
利用状态空间理论分析多层弹性薄膜/基底结构,建立了多层结构的状态空间方程,得到了由温度变化产生的残余应力、结构变形和界面剪切应力的解析解,并进行了分析计算。
基于修正偶应力理论建立了能反映尺寸效应的Euler-Bernoulli梁理论,并用以分析了两层薄膜/基底结构,给出了修正偶应力理论框架下的Stoney公式,并推导了完美界面和非完美界面情形下具有尺寸效应的结构曲率和残余应力的解析解。利用状态空间理论对考虑尺寸效应的多层薄膜/基底结构的热响应进行了分析,给出了非完美界面时多层结构的状态方程及其解,分析表明尺寸效应和界面效应对小尺寸结构的残余应力和结构变形有着重要的影响。
针对两层压电薄膜/基底结构,建立了完美界面和非完美界面两种情况下薄膜应力和结构曲率的解析解。给出了多场耦合作用时磁-电-弹层合结构的状态空间列式,讨论了外加电场、磁场以及环境温度变化对残余应力和结构挠度的影响。
研究了考虑层间剪切效应的多层石墨烯纳米条带的静力弯曲问题,利用Newmark梁理论得到了考虑石墨烯面内延展性时悬臂梁弯曲问题的解析解,对比分子动力学模拟结果显示,面内延展性对多层石墨烯结构的连续力学模型有着重要的影响。利用状态空间法研究了多层石墨烯纳米条带的自由振动问题,得到了不同边界条件下的频散关系和相应的振动模态,考察了多层石墨烯纳米条带的动力学响应。
Film/substrate structures have been widely used in flexible electronics, electronic packaging, and Micro/Nano-Electro-Mechanical-Systems. During the processes of production and packaging, the thermal residual stresses are built up due to the mismatch of thermal and mechanical properties between the film and substrate, which can finally lead to deformations and defects. These deformations and defects usually provide the driving force for the mechanical failure of the structures. The thermal stresses in film/substrate structures play an important role in the design and service lifetime, and their distribution and magnitude is a subject of perennial interest.
Film/substrate bil-/trilayers with weak interface are investigated based on the Euler-Bernoulli beam theory, and the weak interfaces between the layers are examined by adopting the Newmark's model. The closed-form analytical solutions of thermal stresses, deflection, curvature and interfacial shear stresses are presented, which can be degenerated to the classical results when the interface stiffness tends to infinity.
The state space method is employed to analyze film/substrate multilayers. The state equation governing the multilayer structure subjected to a uniform temperature variation is obtained. The thermal stresses, deflection and interfacial shear stresses can be calculated based on the state equation exactly.
A new Bernoulli-Euler beam model based on the modified couple stress theory is developed and applied to the analysis of a nanosized film/substrate bi-/multilayer structure subject to temperature variation. A modified Stoney's formula for bilayer is obtained in the framework of the modified couple stress theory. The analytical solutions of the thermal stresses and curvature of the bilayer structure with perfect or weak interface are derived. A state-space formulation for the multilayer structure is presented, and the axial force, deflection and interfacial shear stress are predicted. The results show that nano-sized structures can exhibit a significant size-dependent phenomenon, and the presence of weak interfaces may alter strikingly the response of a layered structure.
A bilayer system composed of a piezoelectric thin film bonded to an elastomeric substrate is studied. Exact solutions for stress distribution with perfect or weak interface are derived. A state-space formulation for the magneto-electro-elastic laminated structures is developed considering the couplings among the elastic, electric, magnetic, and thermal fields.
The bending of multilayer graphene nanoribbons incorporating the effect of interlayer shear is analyzed. An improved beam theory is adopted and extended in which the in-plane extension of each layer is taken into account. Exact solutions for cantilever multilayer graphene nanoribbons are derived. Comparisons with the molecular dynamics (MD) simulations show that the current study provides a strong evidence to include the in-plane extension effect in the continuum modeling of multilayer graphene structures. The free vibration of multilayer graphene nanoribbons is investigated. The frequency equations for different boundary conditions are obtained via the state space method.
针对两层及三层弹性薄膜/基底结构,基于Euler-Bernoulli梁理论,利用"Newmark模型”考察层间非完美界面,给出了由温度变化引起的残余应力、结构挠度及曲率和界面剪切应力及剥离应力的闭合形式解析解,建立了非完美界面的修正Stoney公式,将结果分析退化并与经典结果进行了比较。
利用状态空间理论分析多层弹性薄膜/基底结构,建立了多层结构的状态空间方程,得到了由温度变化产生的残余应力、结构变形和界面剪切应力的解析解,并进行了分析计算。
基于修正偶应力理论建立了能反映尺寸效应的Euler-Bernoulli梁理论,并用以分析了两层薄膜/基底结构,给出了修正偶应力理论框架下的Stoney公式,并推导了完美界面和非完美界面情形下具有尺寸效应的结构曲率和残余应力的解析解。利用状态空间理论对考虑尺寸效应的多层薄膜/基底结构的热响应进行了分析,给出了非完美界面时多层结构的状态方程及其解,分析表明尺寸效应和界面效应对小尺寸结构的残余应力和结构变形有着重要的影响。
针对两层压电薄膜/基底结构,建立了完美界面和非完美界面两种情况下薄膜应力和结构曲率的解析解。给出了多场耦合作用时磁-电-弹层合结构的状态空间列式,讨论了外加电场、磁场以及环境温度变化对残余应力和结构挠度的影响。
研究了考虑层间剪切效应的多层石墨烯纳米条带的静力弯曲问题,利用Newmark梁理论得到了考虑石墨烯面内延展性时悬臂梁弯曲问题的解析解,对比分子动力学模拟结果显示,面内延展性对多层石墨烯结构的连续力学模型有着重要的影响。利用状态空间法研究了多层石墨烯纳米条带的自由振动问题,得到了不同边界条件下的频散关系和相应的振动模态,考察了多层石墨烯纳米条带的动力学响应。
Film/substrate structures have been widely used in flexible electronics, electronic packaging, and Micro/Nano-Electro-Mechanical-Systems. During the processes of production and packaging, the thermal residual stresses are built up due to the mismatch of thermal and mechanical properties between the film and substrate, which can finally lead to deformations and defects. These deformations and defects usually provide the driving force for the mechanical failure of the structures. The thermal stresses in film/substrate structures play an important role in the design and service lifetime, and their distribution and magnitude is a subject of perennial interest.
Film/substrate bil-/trilayers with weak interface are investigated based on the Euler-Bernoulli beam theory, and the weak interfaces between the layers are examined by adopting the Newmark's model. The closed-form analytical solutions of thermal stresses, deflection, curvature and interfacial shear stresses are presented, which can be degenerated to the classical results when the interface stiffness tends to infinity.
The state space method is employed to analyze film/substrate multilayers. The state equation governing the multilayer structure subjected to a uniform temperature variation is obtained. The thermal stresses, deflection and interfacial shear stresses can be calculated based on the state equation exactly.
A new Bernoulli-Euler beam model based on the modified couple stress theory is developed and applied to the analysis of a nanosized film/substrate bi-/multilayer structure subject to temperature variation. A modified Stoney's formula for bilayer is obtained in the framework of the modified couple stress theory. The analytical solutions of the thermal stresses and curvature of the bilayer structure with perfect or weak interface are derived. A state-space formulation for the multilayer structure is presented, and the axial force, deflection and interfacial shear stress are predicted. The results show that nano-sized structures can exhibit a significant size-dependent phenomenon, and the presence of weak interfaces may alter strikingly the response of a layered structure.
A bilayer system composed of a piezoelectric thin film bonded to an elastomeric substrate is studied. Exact solutions for stress distribution with perfect or weak interface are derived. A state-space formulation for the magneto-electro-elastic laminated structures is developed considering the couplings among the elastic, electric, magnetic, and thermal fields.
The bending of multilayer graphene nanoribbons incorporating the effect of interlayer shear is analyzed. An improved beam theory is adopted and extended in which the in-plane extension of each layer is taken into account. Exact solutions for cantilever multilayer graphene nanoribbons are derived. Comparisons with the molecular dynamics (MD) simulations show that the current study provides a strong evidence to include the in-plane extension effect in the continuum modeling of multilayer graphene structures. The free vibration of multilayer graphene nanoribbons is investigated. The frequency equations for different boundary conditions are obtained via the state space method.
引文
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