考虑材料的拉压模量不同及应变软化特性的柱形孔扩张问题

建立了拉压模量不同及应变软化特性材料的柱形孔扩张理论。对于岩土类材料,提出用a及b分别作为拉压模量不同和软化特征的控制参数,运用不同模量弹性理论及应力跌落软化模型推导了Tresca和Mohr-Coulomb材料柱形圆孔扩张问题的应力及位移解。分析了不同模量及软化特性材料对柱形孔扩张的影响,结果表明:圆孔极限扩张压力,塑性区的发展规律,应力场,位移场等均随着模量参数a和软化系数b的变化而变化,因此若采用经典的弹性理论及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。     

金属棒材拉丝应力统一解

材料拉压强度不相等时棒材拉丝问题的应力解答是研究材料成形工艺人员所关心的问题。根据统一强度理论,分析了棒材拉丝问题,得到考虑材料拉压比影响的棒材拉丝应力统一解和最大截面缩减率统一解。分析过程中引入一个反映棒材拉制和压制工艺的系数,将棒材拉丝问题的拉制解和压制解统一起来。当材料拉压强度相同时,棒材拉丝应力的Mises解答是棒材拉丝应力统一解的特例。在拉丝过程中,棒材拉丝问题的最大截面缩减率随材料拉压比变化而变化。当材料的拉压强度相等时,棒材拉丝最大截面缩减率的Mises解答是最大截面缩减率统一解的特例,也是它的最大值。     

不同拉压模量及软化特性材料的球形孔扩张问题的统一解

对于具有不同的拉压模量及软化特性的岩土类材料,提出了不同拉压模量及软化特性的控制参数,采用双剪统一强度理论推导了球形孔扩张问题的应力及位移的统一解。分析了模量、模型和软化等控制参数对球形孔扩张时的扩张压力、塑性区开展规律及应力场的影响。结果表明:圆孔极限扩张压力,塑性区的发展规律,应力场,位移场等均随着模量控制参数、模型参数及软化参数的变化而变化,因此若采用经典的弹性理论、单一的模型参数及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。     

不同拉压模量及软化特性材料的柱形孔扩张问题的统一解

对于具有不同的拉压模量及软化特性的岩土类材料,提出了不同拉压模量及软化特性的控制参数,采用双剪统一强度理论推导了柱形孔扩张问题的应力及位移的统一解。分析了模量、模型和软化等控制参数对柱形孔扩张时的扩张压力、塑性区开展规律及应力场的影响。结果表明:圆孔极限扩张压力、塑性区的发展规律、应力场、位移场等均随着模量控制参数、模型参数及软化参数的变化而变化,因此若采用经典的弹性理论、单一的模型参数及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。     

连续壁梁的弹性力学精确解

本文根据连续壁梁的不同支座宽度,用级数表示的应力函数给出了弹性力学的精确解。并和热莫奇金的解答作了比较,指出了热莫奇金解答中连续壁梁某些部分应力出现错误的原因。本文解答可用于连续壁梁设计。     

路基压实粉质黏土动态回弹模量的四参数预估模型及有限元实现

利用动三轴试验,研究路基压实粉质黏土动态回弹模量的影响因素,分析动态回弹模量对偏应力、体应力等因素的依赖关系,通过双因素回归分析,在AASHTO-N37A动态回弹模量预估模型的基础上引入k4项,提出了含四参数的改进模型。为了使该改进模型能有效运用于有限元计算中,基于广义Hooke定律推导了其精确一致切线刚度矩阵,通过编写用户自定义材料子程序(UMAT)将改进模型移植入有限元软件ABAQUS中,分别在单个土体单元和路基路面结构条件下对改进模型进行了计算验证。研究结果表明:四参数改进模型能更好预估粉质黏土在不同压实度下的动态回弹模量,利用二次开发的改进模型在有限元软件中计算得出的土体单元的应力—应变关系与解析解较为吻合,而将改进模型运用于路基路面结构分析可以体现因应力不同造成的回弹模量在路基各个位置的差异,同时能反映车辆荷载作用下回弹模量的演变,实现了模量与应力状态的动态耦合,从而路基路面结构设计提供了更为真实的数值模拟方法。     

基于LM算法的粘弹性材料剪切松弛模量的拟合

在对粘弹性材料进行有限元计算时,需要材料的剪切松弛模量,必须对经验公式或实验数据进行转换。根据KWW经验公式与广义Maxwell剪切松弛函数的对应关系,列出了求解松弛时间与剪切松弛模量的超定非线性方程组,用LM优化算法得到了方程组的最优解。初步讨论了初值的选取方法。根据此方法得到的松弛时间与剪切松弛模量的拟合曲线的拟合度达到了0.99以上。所提出的方法也适用于用实验数据(随时间变化的应力应变)求解材料的剪切松弛模量。     

黏弹-塑性岩体中锚注与衬砌联合支护的解析解EI北大核心CSCD

针对黏弹-塑性岩体中深埋圆形隧洞锚注、衬砌联合支护问题,导出开挖、锚注加固和衬砌支护阶段位移、应力的解析解。在开挖段,用随时间变化的半径函数模拟扩孔式断面开挖过程,并同时考虑纵向开挖的空间效应,给出黏弹区和塑性区应力、位移及塑性区半径随时间变化的解答。某时刻施加锚注支护后,将锚注岩体等效为弹塑性材料,用圆柱型正交各向异性体现锚杆对径向刚度加强,用强度指标的增强体现锚注的加固作用,分别对锚注区完全弹性和部分达到塑性的情况导出了锚注和衬砌支护阶段应力、位移的解答,并给出判断再次出现塑性的条件和塑性区半径的表达式。根据解答,分析了不同位置应力和位移随时间变化情况;不同加固程度、锚注时刻对洞口应力、位移的影响。该文的解答可用于相似条件下隧洞初步设计。     

黏弹-塑性岩体中锚注与衬砌联合支护的解析解

针对黏弹-塑性岩体中深埋圆形隧洞锚注、衬砌联合支护问题,导出开挖、锚注加固和衬砌支护阶段位移、应力的解析解。在开挖段,用随时间变化的半径函数模拟扩孔式断面开挖过程,并同时考虑纵向开挖的空间效应,给出黏弹区和塑性区应力、位移及塑性区半径随时间变化的解答。某时刻施加锚注支护后,将锚注岩体等效为弹塑性材料,用圆柱型正交各向异性体现锚杆对径向刚度加强,用强度指标的增强体现锚注的加固作用,分别对锚注区完全弹性和部分达到塑性的情况导出了锚注和衬砌支护阶段应力、位移的解答,并给出判断再次出现塑性的条件和塑性区半径的表达式。根据解答,分析了不同位置应力和位移随时间变化情况;不同加固程度、锚注时刻对洞口应力、位移的影响。该文的解答可用于相似条件下隧洞初步设计。     

拉伸环向周期裂纹管的应力强度因子

利用裂纹非自发扩展的能量释放率,即G*-积分理论分析求解了拉伸周期裂纹管应力强度因子问题,给出了周期裂纹管应力强度因子的系列解答。该解亦可作为开裂曲板应力强度因子的近似解。     

Investigations into the fracture mechanics of acetylsalicylic acid and lactose monohydrate

The fracture mechanics of acetylsalicylic acid (ASS) and lactose monohydrate (LM) were studied using three-point beam bending experiments and compared with conventional tabletting performance. ASS was found to have an unusual behaviour in terms of its Young's modulus and tensile strength when determined with beams of different porosities. The Young's modulus as a function of beam porosity showed two exponential parts separated by a constant region and the tensile strength as a function of the porosity followed a non-exponential law. Tabletting experiments revealed that ASS undergoes different deformation mechanisms at the different compaction pressures associated with the porosity ranges covering the different regions. The different deformation mechanisms might have caused different crack and flaw patterns or different crack lengths, in particular at the beam surfaces, which are under maximum tensile stress during the tests. The unusual findings were, however, not reflected in experiments to determine the critical stress intensity factor as a function of beam porosity, because here crack propagation is controlled via a notch introduced into the beams. In contrast to ASS, LM behaved like the majority of materials i.e. Young's modulus, tensile strength and critical stress intensity factor were found to relate to the beam porosity exponentially.     

Surface effect on the elastic behavior of static bending nanowires

The surface effect from surface stress and surface elasticity on the elastic behavior of nanowires in static bending is incorporated into Euler-Bernoulli beam theory via the Young-Laplace equation. Explicit solutions are presented to study the dependence of the surface effect on the overall Young's modulus of nanowires for three different boundary conditions: cantilever, simply supported, and fixed-fixed. The solutions indicate that the cantilever nanowires behave as softer materials when deflected while the other structures behave like stiffer materials as the nanowire cross-sectional size decreases for positive surface stresses. These solutions agree with size dependent nanowire overall Young's moduli observed from static bending tests by other researchers. This study also discusses possible reasons for variations of nanowire overall Young's moduli observed.     

Discretized peridynamics for linear elastic solids

Peridynamics is a theory of continuum mechanics employing a nonlocal model that can simulate fractures and discontinuities (Askari et?al. J Phys 125:012–078, 2008; Silling J Mech Phys Solids 48(1):175–209, 2000). It reformulates continuum mechanics in forms of integral equations rather than partial differential equations to calculate the force on a material point. A connection between bond forces and the stress in the classical (local) theory is established for the calculation of peridynamic stress, which is calculated by summing up bond forces passing through or ending at the cross section of a node. The peridynamic stress and the constitutive law in elasticity are used for the derivation of one- and three-dimensional numerical micromoduli. For three-dimensional discretized peridynamics, the numerical micromodulus is larger than the analytical micromodulus, and converges to the analytical value as the horizon to grid spacing ratio increases. A comparison of material responses in a three-dimensional discretized peridynamic model using numerical and analytical micromoduli, respectively, is performed for different horizons. As the horizon increases, the boundary effect is more conspicuous, and the errors increase in the back-calculated Young’s modulus and strains. For the simulation of materials of Poisson’s ratios other than 1/4, a pairwise compensation scheme for discretized peridynamics is proposed. Compared with classical (local) elasticity solutions, the computational results by applying the proposed scheme show good agreement in the strain, the resultant Young’s modulus and Poisson’s ratio.     

层内混杂复合材料断裂纤维附近的应力重分布

研究了层内混杂复合材料的高模量纤维断裂引起的邻近各层应力重分布问题。通过建立适当的计算模型,利用二维弹性力学精确解和付氏变换法,建立问题的奇异积分方程组,通过求解方程组,计算高、低模量层和基体层的应力集中因子,计算结果对"混杂效应"作出了理论解释,并与一般采用的Shear-Lag理论计算结果作了比较,本文结果更精确、合理,可应用于层内混杂复合材料的设计。     

Bewertung von Spannungszuständen bei der experimentellen Bestimmung des Schubmoduls an zellularen Materialien

Evaluation of stress states for the experimental determination of the shear modulus of cellular materials The experimental determination of the shear modulus of materials proves to be problematic in practice. The different methods do not only preduce the desired pure shear stress state. In this paper, starting from several experimental implementations of the shear test, possible sources of errors in determination of the shear modulus are discussed. An estimation of the possible error is calculated by numerical simulations. Two examples from the field of cellular metals are given to illustrate the effect of just an approximate realization of the pure shear stress state.     

材料力学性能对液力胀接过程的影响分析

为寻求装配式空心凸轮轴结构设计和材料选择的理论依据,应用弹塑性力学分析了弹性模量和流动应力对液力胀接的影响.将内外管的变形过程简化为平面应变问题,根据典型点应力-应变曲线分析了液力胀接过程,并给出了不同材质套管的连接条件.研究结果表明:影响液力胀接的主要因素是内外管弹性模量和流动应力,这两个材料参数决定胀后内外管弹性回复量的大小;实现液力胀接内外管应满足的条件是:内外管弹性模量的比值大于内外管流动应力的比值.     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

Bestimmung des Elastizitätsmoduls aus der Nachgiebigkeit angerissener Bruchmechanik-Proben

Determining the moduls of elasticity from the compliance of precracked specimens . A new method is described which allows the determination of the modulus of elasticity of solid materials. Compliance tests with precracked fracture mechanics specimens in a simple tensile test machine yield accurate measurements of the modulus of elasticity in the orientation and material condition desired for fracture mechanics calculations.     

The stress analysis method for three-dimensional composite materials

This study proposes a stress analysis method for three-dimensionally fiber reinforced composite materials. In this method, the rule-of mixture for composites is successfully applied to 3-D space in which material properties would change 3-dimensionally. The fundamental formulas for Young's modulus, shear modulus, and Poisson's ratio are derived. Also, we discuss a strength estimation and an optimum material design technique for 3-D composite materials. The analysis is executed for a triaxial orthogonally woven fabric, and their results are compared to the experimental data in order to verify the accuracy of this method. The present methodology can be easily understood with basic material mechanics and elementary mathematics, so it enables us to write a computer program of this theory without difficulty. Furthermore, this method can be applied to various types of 3-D composites because of its general-purpose characteristics.