我国地下化石能源丰富, 如煤、页岩油气等, 与工业和民生发展息息相关. 我国已探明的页岩气储量居世界第一, 拥有巨大的开采价值. 由于长年的板块移动等地质构造过程, 地壳中存在地应力 (原岩应力), 即初始应力场. 在地应力这一初始应力的作用下, 岩体材料的变形行为表现出有限变形的几何非线性、应力和应变关系的物理非线性, 对地下应力场和应变场重新分布的估计大多采用的经典线弹性模型不再适用. 为了更好的保存和利用地下资源, 在理论上建立有效的具有初始应力场的有限变形弹性理论, 这是对岩体材料变形行为研究的基本难题, 也是工业生产其他应用领域解决初始应力场问题急需的理论基础. 从力学角度出发, 建立具有初始应力场的弹性理论是弹性力学和连续介质力学重要内容, 是进一步针对特定问题发展有限元法等数值计算方法的基础.
本学位论文正是在此背景下, 采用理论分析辅助以实验研究的手段,围绕建立具有初始应力场的弹性理论展开,主要针对两个核心关键学术问题: 具有初始应力场的弹性材料的力学性能问题、初始应力场与其他场耦合的力学问题, 开展研究工作.
针对具有初始应力场 (初始应变场) 的弹性体上叠加小变形问题, 通过引入中间构形和中间应力, 将描述在不同构形上的本构关系进行对比和统一, 并厘清各弹性系数张量之间的关系, 讨论和分析初始应力场对弹性体的力学性能的影响. 建立了具有初始应力场的线弹性理论并讨论该弹性理论的适定性, 为具有初始应力的线弹性理论的应用提供理论依据.
对于有机质等软物质所发生的有限变形, 在一般有限变形弹性理论的基础上, 建立具有初始应力场的本构关系. 通过张量表示理论和连续有限变形分析, 构建初始给定变形和初始应力场表示的自由能函数, 得到具有初始应力场的有限变形弹性理论, 为分析有机质等软材料的力学性能奠定理论基础.
基于多场耦合的线弹性理论, 探索热-化-力耦合作用下具有初始应力场的弹性理论. 从连续介质力学基本方程和热力学基本定律出发, 考虑化学扩散与化学反应、温度变化以及发生有限变形时初始应力场对自由能函数的影响, 建立热-化-力耦合场下的弹性本构关系, 研究弹性材料在复杂环境下的原位力学性能.
研究初始应力诱导的沉积膜/硬基底系统的干裂物理行为. 通过稀释蛋白质溶液的液滴在硅表面蒸发沉积薄膜的实验, 形成具有残余应力场的附着在硬基底上的有机薄膜. 在液滴蒸发过程, 液滴表面张力对沉积过程起主要作用; 在薄膜蒸发过程中, 残余应力场对薄膜干裂行为的控制作用, 最终形成多样的且具有高度规律性的图案. 通过残余应力释放, 研究薄膜裂纹图案扩展以及转化规律的力学机制.
本论文探索了具有初始应力场的有限变形弹性理论, 并实验讨论了残余应力作用下固-液界面沉积膜的变形和干裂物理行为. 为初始应力场下材料的力学性能、软物质的有限变形力学行为以及当前应力于应变场更精准估计的研究提供理论依据.
Fossil energy is closely related to the development of industry and people’s livelihood in China, whose resources is rich in coal but poor in natural gas. The proven shale gas reserves rank first in the world which have great mining value. The earth’s crust is always under a state of in-situ stress, which is a result of the gravitational force and the tectonic force due to long-term geological process like plate tectonics. The initial stress is acting as rock material is deformed, while the nonlinearities of finite deformation and the stress-strain relationship should be considered. For local in-situ stress and strain estimates, the classical theory of elasticity commonly used is no longer applicable. In order to better preserve and utilize the resources and for accurately predictive estimates of the stress field, constructing an effective constitutive equation for finite deformation of an initially stressed material is a basic problem, which also provides theoretical guidance for materials with initial stress in other fields like industrial production. In view of mechanics, the establishment of the elastic theory with an initial stress field is an important part of elasticity and continuum mechanics, which is also a theoretical basis of further development of numerical calculation methods such as finite element method for specific problems.
In this context, adopting theoretical analysis and assisted by experimental methods, this dissertation is aimed at the establishment of linear and nonlinear theories of elasticity with initial stress field, focusing on two key academic issues: elastic theory with initial stress and the mechanical properties of initially stressed materials; constitutive laws with finite deformation under multi-field coupling.
Based on the small deformation superimposed on the body with initial stress, the constitutive laws described on different configurations are clarified and unified by introducing intermediate configuration. The elastic coefficient tensors are also clarified. The mechanical properties of the initially stressed material are discussed and analyzed. Methods for the construction of constitutive equations for materials with initial stress are formulated. The well-posedness of elastic problem with initial stress is discussed, which provides a theoretical basis for the application of the linear elastic theory with the initial stress.
On the basis of the finite deformation theory of elasticity, nonlinear constitutive relationships with initial stress field are developed for finite deformation of soft materials like organic matter. Using the tensor representation theory and continuous finite deformation analysis, the free energy function represented by the given deformation and the initial stress field is constructed. This theory lays a theoretical foundation for analyzing themechanical properties of soft materials and the overall mechanical properties of rocks.
The mechanical-chemo-thermal constitutive laws with initial stress field are explored. From the perspective of the basic equations of continuum mechanics and the basic laws of thermodynamics, the chemical diffusion and chemical reactions, temperature changes, and initial stress fields are considered in the free energy function. The constitutive laws under multi-field coupling with initial stress fields are discussed, while the in-situ mechanical properties of Kerogen are studied.
Based on experiments, the physical behavior of cracking from dryness of the deposited-film/hard-substrate system induced by surface tension and residual stress is explored. By colloidal droplets evaporating on a Si wafer, a thin film with residual stress field attached to a solid substrate is formed. In the evaporation process of the droplet, the effect of surface tension is discussed, while during the evaporation of the thin film, the residual stress field controls the film's cracking which finally forms a variety of highly regular patterns. The mechanical mechanisms of the crack propagation and pattern transformation are analyzed.
This dissertation explores the theory of elasticity with an initial stress field, and experimentally discusses the deformation and cracking of the deposited film on the solid-liquid interface caused by residual stress. It provides a theoretical basis for the study of the mechanical properties of materials under the initial stress field, the finite deformation of soft materials, and more accurate estimation of underground stress and strain fields.