基于有限元理论的木材机械性能建模与仿真研究
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摘要
木材是人民生活和经济建设的重要工程材料，随着现代化工业和科学技术的发展，木材作为一种具有优势性的建筑材料得到了广泛应用。尽管木材已经使用了上千年，但是对其机械性能还不是完全了解，如树种间机械性能差异，裂纹扩展，因含水率变化而引起的变形，在施加较大负载时木材表现出复杂的非线性力学特性等等。木材结构决定木材的性质，木材的性质又决定木材经济价值，并直接影响木材的加工和利用，因此，更好剖析木材的机械性能尤为重要。
本文在国内外有关木材机械性能研究的基础上，通过试验系统分析了木材微观构造和宏观构造不同构造级上的机械性能。通过微观结构观察得出木材早材、过渡材、晚材宽度按生长轮序号的分布关系；通过对木材逐个生长轮密度的测量，得出了密度随生长轮序号的分布关系；通过对木材逐个生长轮制取的薄小试件，测量了木材早、晚材的刚度随生长轮序号的分布关系；木材的机械性能与含水率紧密相关，试验测量了木材三个主方向的收缩系数与生长轮序号的分布关系。在木材机械性能建模的研究中，将有限元方法和均质化理论应用于生长轮模型的构建中，用等价的均匀连续体替代复杂的周期性微观结构材料的平均特性，建立宏观量场和微观量场之间的关系方程，最后根据均质化方法建立代表性单元的本构关系。模型仿真采用ANSYS实体模型单元SOLID46计算材料的有效性能。木材结构建模研究中应用了复合材料理论，研究了平面应力下单层材料的应力—应变关系，建立单层材料与总坐标间的刚度转换关系；木材宏观结构可以视为由各生长轮层合而成的复合结构，应用层合板的强度理论对木材进行了强度分析，采用HILL—蔡强度判别式来判断失效，同时进行理论计算和ANSYS仿真，以及木材顺纹抗拉强度试验加以验证，试验结果与理论计算结果是相符的。应用Hill—蔡屈服准则，对木材裂尖塑性区进行了分析研究，建立木材正交各向异性材料的裂尖应力场及屈服准则，讨论各向异性常数对塑性区及断裂性能的影响，以及木材生长轮间早材和晚材的不同强度比、刚度比对木材塑性区的影响，同时还从微观结构和ANSYS仿真验证了对塑性区的讨论。木材的强度、变形和破坏性能都与其内部结构、裂缝扩展以及断裂参数有关，考虑到裂纹尺寸的随机性，用随机有限元计算了木材强度因子的变化曲线，为验证其可行性，用帽儿山落叶松为材料加工的紧凑拉伸试件拟和了木材强度因子的测试曲线，两曲线具有相同的变化趋势，说明采用随机有限元方法对木材的断裂特性进行计算和预测是可行的。
本研究将有限元理论、均质化理论、复合材料理论和木材科学相结合，属于交叉和前沿的研究，是连接微观与宏观力学发展的桥梁，在工业加工等领域中有重要的潜在应用价值，对提高木材从微观到宏观的机械性能认识、扩大木材的适用范围、提高木材的利用水平和实现木材工业的可持续发展具有重要意义。
Wood is an important engineering material for people's life and economic construction.With the development of science and technology in industry field, it has been widely used as asuperior nature material. The material has been used for several thousand years, but itsmechanical properties, such as the difference of mechanical properties among species, crackpropagation, the deformation caused by changes in moisture content and the complex nonlinearmechanical performance with overload etc. is not yet fully understood by people. Timber'sstructure determines its mechanical properties, which estimate the value of timber andinfluence the processing and use of timber. Therefore, the detailed investigations and a betterunderstanding of timber's mechanical properties are very important.
In this paper, the mechanical properties of macro and microstructure were studiedsystematically with a great deal of tests based on the former researches in the field. Thedistribution relation of the width of early wood, transition wood and latewood versus thenumbers of growth ring was achieved by observing the microstructure. The density versus thenumber of growth ring was determined by measuring the density of growth ring one by one.Slip specimens measured the stiffness of early wood and latewood versus the number ofgrowth ring. Due to the mechanical properties closed related with moisture content, shrinkagecoefficients of three main directions of wood versus growth ring was detected by tests. Duringthe modeling of wood mechanical properties, FEM and heterogeneous theory were applied formodel of growth rings assumed as the continuum. The average performance of wood fiber withthe other organizations was considered synthetically whose geometric and material informationwere integrated into an equivalent body. The average property of complex periodic-microstructure- material was substituted by the equivalent uniform continuum. The relativeequations between micro vector fields and macro ones were established through the boundaryconditions of stress and displacement in the basic units where the field of strain and stress wasobtained by known macro vector fields, geometric and physical equations. Finally, constitutiveequation that is the relation between macro stress and strain of special units was achievedaccording to heterogeneous theory with SOLID46adopted as a model to calculate the efficientperformance in the simulation software of ANSYS. The composite material theory used for themodeling research to the wood composite laminated structure and the strain and stress relationof single layer material under plane stress w as studied. The stiffness conversion wasconstructed by monolayer material versus macro axis. The macro structure of wood wasregarded as composite laminated structure integrated by growth rings. The strength wasanalyzed by composite material theory and malfunction was evaluated by HILL-CAI criterion. The result of tests was consistent with theoretical calculation. Crack plastic zone of wood withanisotropy was studied by HILL-CAI criterion, crack tip stress fields and yield criteria were setup, the effect that constant of anisotropy material influence on the performance of plastic zoneand the different stiffness ratios of early wood and latewood in growth ring impact of theplastic zone were analyzed. Meanwhile, the research result on plastic zone was verifiedthrough the microphotograph of wood microstructure and ANSYS simulation software. Thestrength, deformation and failure of wood are related with parameters on its structure, crackpropagation and fracture. The size of crack with stochastic being taken into account, curve ofwood strength factors was calculated by stochastic FEM, which had been verified by relatedexperiments. The results show that the fracture properties of wood were calculated andpredicted by stochastic FEM is feasible and applicable.
In this study, finite element theory, homogenization theory, composite material theory andwood micro-mechanics are researched which are of cross-frontier research to improve theawareness on the mechanical properties of wood from micro to macro, expend the scope ofapplication, enhance the wood utilization level. The investigation is of great significance forsustainable development of wood industry.
本文在国内外有关木材机械性能研究的基础上，通过试验系统分析了木材微观构造和宏观构造不同构造级上的机械性能。通过微观结构观察得出木材早材、过渡材、晚材宽度按生长轮序号的分布关系；通过对木材逐个生长轮密度的测量，得出了密度随生长轮序号的分布关系；通过对木材逐个生长轮制取的薄小试件，测量了木材早、晚材的刚度随生长轮序号的分布关系；木材的机械性能与含水率紧密相关，试验测量了木材三个主方向的收缩系数与生长轮序号的分布关系。在木材机械性能建模的研究中，将有限元方法和均质化理论应用于生长轮模型的构建中，用等价的均匀连续体替代复杂的周期性微观结构材料的平均特性，建立宏观量场和微观量场之间的关系方程，最后根据均质化方法建立代表性单元的本构关系。模型仿真采用ANSYS实体模型单元SOLID46计算材料的有效性能。木材结构建模研究中应用了复合材料理论，研究了平面应力下单层材料的应力—应变关系，建立单层材料与总坐标间的刚度转换关系；木材宏观结构可以视为由各生长轮层合而成的复合结构，应用层合板的强度理论对木材进行了强度分析，采用HILL—蔡强度判别式来判断失效，同时进行理论计算和ANSYS仿真，以及木材顺纹抗拉强度试验加以验证，试验结果与理论计算结果是相符的。应用Hill—蔡屈服准则，对木材裂尖塑性区进行了分析研究，建立木材正交各向异性材料的裂尖应力场及屈服准则，讨论各向异性常数对塑性区及断裂性能的影响，以及木材生长轮间早材和晚材的不同强度比、刚度比对木材塑性区的影响，同时还从微观结构和ANSYS仿真验证了对塑性区的讨论。木材的强度、变形和破坏性能都与其内部结构、裂缝扩展以及断裂参数有关，考虑到裂纹尺寸的随机性，用随机有限元计算了木材强度因子的变化曲线，为验证其可行性，用帽儿山落叶松为材料加工的紧凑拉伸试件拟和了木材强度因子的测试曲线，两曲线具有相同的变化趋势，说明采用随机有限元方法对木材的断裂特性进行计算和预测是可行的。
本研究将有限元理论、均质化理论、复合材料理论和木材科学相结合，属于交叉和前沿的研究，是连接微观与宏观力学发展的桥梁，在工业加工等领域中有重要的潜在应用价值，对提高木材从微观到宏观的机械性能认识、扩大木材的适用范围、提高木材的利用水平和实现木材工业的可持续发展具有重要意义。
Wood is an important engineering material for people's life and economic construction.With the development of science and technology in industry field, it has been widely used as asuperior nature material. The material has been used for several thousand years, but itsmechanical properties, such as the difference of mechanical properties among species, crackpropagation, the deformation caused by changes in moisture content and the complex nonlinearmechanical performance with overload etc. is not yet fully understood by people. Timber'sstructure determines its mechanical properties, which estimate the value of timber andinfluence the processing and use of timber. Therefore, the detailed investigations and a betterunderstanding of timber's mechanical properties are very important.
In this paper, the mechanical properties of macro and microstructure were studiedsystematically with a great deal of tests based on the former researches in the field. Thedistribution relation of the width of early wood, transition wood and latewood versus thenumbers of growth ring was achieved by observing the microstructure. The density versus thenumber of growth ring was determined by measuring the density of growth ring one by one.Slip specimens measured the stiffness of early wood and latewood versus the number ofgrowth ring. Due to the mechanical properties closed related with moisture content, shrinkagecoefficients of three main directions of wood versus growth ring was detected by tests. Duringthe modeling of wood mechanical properties, FEM and heterogeneous theory were applied formodel of growth rings assumed as the continuum. The average performance of wood fiber withthe other organizations was considered synthetically whose geometric and material informationwere integrated into an equivalent body. The average property of complex periodic-microstructure- material was substituted by the equivalent uniform continuum. The relativeequations between micro vector fields and macro ones were established through the boundaryconditions of stress and displacement in the basic units where the field of strain and stress wasobtained by known macro vector fields, geometric and physical equations. Finally, constitutiveequation that is the relation between macro stress and strain of special units was achievedaccording to heterogeneous theory with SOLID46adopted as a model to calculate the efficientperformance in the simulation software of ANSYS. The composite material theory used for themodeling research to the wood composite laminated structure and the strain and stress relationof single layer material under plane stress w as studied. The stiffness conversion wasconstructed by monolayer material versus macro axis. The macro structure of wood wasregarded as composite laminated structure integrated by growth rings. The strength wasanalyzed by composite material theory and malfunction was evaluated by HILL-CAI criterion. The result of tests was consistent with theoretical calculation. Crack plastic zone of wood withanisotropy was studied by HILL-CAI criterion, crack tip stress fields and yield criteria were setup, the effect that constant of anisotropy material influence on the performance of plastic zoneand the different stiffness ratios of early wood and latewood in growth ring impact of theplastic zone were analyzed. Meanwhile, the research result on plastic zone was verifiedthrough the microphotograph of wood microstructure and ANSYS simulation software. Thestrength, deformation and failure of wood are related with parameters on its structure, crackpropagation and fracture. The size of crack with stochastic being taken into account, curve ofwood strength factors was calculated by stochastic FEM, which had been verified by relatedexperiments. The results show that the fracture properties of wood were calculated andpredicted by stochastic FEM is feasible and applicable.
In this study, finite element theory, homogenization theory, composite material theory andwood micro-mechanics are researched which are of cross-frontier research to improve theawareness on the mechanical properties of wood from micro to macro, expend the scope ofapplication, enhance the wood utilization level. The investigation is of great significance forsustainable development of wood industry.
引文
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