Generalized continuum modeling of 2-D periodic cellular solids

A generalized continuum representation of two-dimensional periodic cellular solids is obtained by treating these materials as micropolar continua. Linear elastic micropolar constants are obtained using an energy approach for square, equilateral triangular, mixed triangle and diamond cell topologies. The constants are obtained by equating two different continuous approximations of the strain energy function. Furthermore, the effects of shear deformation of the cell walls on the micropolar elastic constants are also discussed. A continuum micropolar finite element approach is developed for numerical simulations of the cell structures. The solutions from the continuum representation are compared with the “exact” discrete simulations of these cell structures for a model problem of elastic indentation of a rectangular domain by a point force. The utility of the micropolar continuum representation is illustrated by comparing various cell structures with respect to the stress concentration factor at the root of a circular notch.     

A simple plasticity model for prediction of non-coaxial flow of sand

A bounding surface plasticity model for non-coaxiality, another aspect of anisotropic behavior of sands under rotation of principal stress axes; is developed in the critical state framework. Numerous experimental evidences exist that corroborate dependence of plastic shear strain rate direction on inherent fabric anisotropy. At first, general expressions for plastic strain rate with respect to possible emerge of non-coaxial flow are obtained. Consequently, using an anisotropy state parameter that is specially developed for this model and accounts for the interaction between imposed loading and soil fabric; effect of anisotropy on plastic flow direction is taken into account. Besides, novel circumstances are proposed for plastic modulus and dilatancy under rotation of principal stress axes. Finally, it is shown that the model is able to simulate successfully the non-coaxial behavior of sands subjected to principal stress axes rotation.     

低成本基板倒装焊底充胶分层裂缝扩展研究

采用MIL-STD-883C热循环疲劳加载标准，通过电学检测方法测定了B型和D型两种倒装焊封装焊点寿命。并使用无损声学C-SAM高频超声显微镜技术观测这两种倒装焊封装在焊点有无断裂两种情况时芯片／底充胶界面的分层和扩展，计算得到分层裂缝扩展速率。在有限元模拟中采用粘塑性和时间相关模量描述了SnPb焊点和底充胶的力学行为。使用裂缝尖端附近小矩形路径J积分方法作为断裂力学参量得到不同情况下的界面分层裂缝顶端附近的能量释放率。然后由实验裂缝扩展速率和有限元模拟给出的能量释放率得到可作为倒装焊封装可靠性设计依据的Par—is半经验方程。     

板壳有限变形精确理论及有限元列式

以位移型退化壳理论为基础,提出了板壳模型的有限变形精确理论,该理论引入转动伪矢量概念,充分发挥刚性线段的运动学模型和有限转动矩和作用,精确表达非线性位移－应变关系,抛弃以往的小位移、小应变、小转动增量乃至小加载小长等各种简化假设,并严格遵循能量共轭关系建立有限元平衡方程,能够可靠和有效地用于板壳结构的大位移、大转动分析。算例表明,该文列式在弹性范围内具明显的平方收敛效率,并且计算结果与加载步长无关。由于不受小加载步长、小转动增量等的限制,实现了板壳几何非线性问题的大步长加载。     

Locking-Free Degenerated Isoparametric Shell Element

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Numerical simulation for the simple shear test in amorphous glassy polymers

In this paper, a driving stress finite element method of elastic-plastic large deformation based on implicit time integrating algorithm and an eight-chain molecular network model is used for the numerical simulation of the simple shear test of polycarbonate (PC) materials. The simulated results are compared with experimental ones. The strain localization propagation for the shear band deformation for simple shear deformation is investigated numerically. The effects of microstructure parameters in the model on strain softening and orientation hardening of the PC are discussed in detail. Supported by the National Natural Science Foundation of China.     

Plastic spin associated with a non-normality theory of plasticity

A plasticity model using a vertex-type plastic flow rule on a smooth yield surface for an anisotropic solid has been proposed recently. This model is here completed by incorporating the effect of plastic spin. Simple shear with a large shear strain is one of the hardest tests on finite strain anisotropic plasticity models, and it is here shown which plastic spin expression is needed to avoid unrealistic oscillatory behavior of the shear stress under large shear strains. The idea of using non-normality with a smooth yield surface originates from a recent proposal of using an abrupt strain path change to determine the subsequent yield surface shape. For this method both polycrystal plasticity calculations and experiments have shown a vertex-type response on the apparently smooth yield surface.     

自旋张量的绝对表示及其在有限变形理论中的应用

基于对一类线性张量方程的一般解法,导出了任一对称张量所对应的自旋张量的绝对表示。该结果可以很自然地用于研究左和右伸长张量的自旋并研讨在连续介质力学中常见到的各种转动率张量间的关系。一个重要的公式,即Hill意义下广义应变的共轭应力和Cauchy应力之间的关系,从功共轭原理建立了起来。尤其是详细讨论了对数应变的时间变率及相应的共轭应力。无疑,上述结果对有限变形条件下本构理论的研究是颇为重要的。     

Drapage géométrique des compositesGeometrical draping of composite fabrics

This paper presents a study devoted to the composite fabric shaping simulation in finite strain analysis. We introduce a new geometrical approach based on the fishnet method for which the deformation of a fabric mesh element consists in a pure trellis effect. Such a fabric mesh element is then defined by a curved quadrilateral whose edges are geodesic lines with the same length plotted onto the surface to drape. Given three vertices of the fabric mesh element on the surface, we propose an optimization algorithm to define the fourth vertex of the fabric mesh element. This algorithm allows us to drape the surface using an advancing front approach from the data of an initial impact point between the fabric and the surface and the initial fibre directions at this point. A numerical draping simulation example using this approach is given. To cite this article: H. Borouchaki, A. Cherouat, C. R. Mecanique 331 (2003).     

Large deflection of rectangular sandwich plates

The governing differential equations and the boundary conditions for the large deflection of rectangular sandwich plates are derived using the principle of the complementary energy. The governing differential equations are transformed into systems of nonlinear algebraic equations using the finite difference method, and solved by successive iteration. For the purpose of illustration, deflection behavior of simply supported rectangular plates under uniform load is presented. The deflection behavior of plates with various values of shear rigidities and intensity of applied loads is studied. The change in the stress patterns of the face layers of the plate is also discussed.     

Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids

The diffuse mode bifurcation of elastoplastic solids at finite strain is investigated. The multiplicative decomposition of deformation gradient and the hyperelasto-plastic constitutive relationship are adapted to the numerical bifurcation analysis of the elastoplastic solids. First, bifurcation analyses of rectangular plane strain specimens subjected to uniaxial compression are conducted. The onset of the diffuse mode bifurcations from a homogeneous state is detected; moreover, the post-bifurcation states for these modes are traced to arrive at localization to narrow band zones, which look like shear bands. The occurrence of diffuse mode bifurcation, followed by localization, is advanced as a possible mechanism to create complex deformation and localization patterns, such as shear bands. These computational diffuse modes and localization zones are shown to be in good agreement with the associated experimental ones observed for sand specimens to ensure the validity of this mechanism. Next, the degradation of horizontal sway stiffness of a rectangular specimen due to plane strain uniaxial compression is pointed out as a cause of the bifurcation of the first antisymmetric diffuse mode, which triggers the tilting of the specimen. Last, circular and punching failures of a footing on a foundation are simulated.     

Strain localization and fabric evolution in sand

Strain localization is frequently observed in sand and is considered an important precursor related to major geohazards such as landslides, debris flow and failure of relevant geo-structures. This paper presents a numerical study on strain localization in sand, with a special emphasis on the influence of soil fabric and its evolution on the initiation and development of shear band. In particular, a critical state sand plasticity model accounting for the effect of fabric and its evolution is used in the finite element analysis of plane strain compression tests. It is found that the initiation of shear band is controlled by the initial fabric, while the development of shear band is governed by two competing physical mechanisms, namely, the structural constraint and the evolution of fabric. The evolution of fabric generally makes the sand response more coaxial with the applied load, while the structural constraint induced by the sample ends leads to more inhomogeneous deformation within the sand sample when the initial fabric is non-coaxial with the applied stress. In the case of smooth boundary condition, structural constraint dominates over the fabric evolution and leads to the formation of a single shear band. When the boundary condition is rough, the structural constraint may play a comparable role with fabric evolution, which leads to symmetric cross-shape shear bands. If the fabric is prohibited from evolving in the latter case, a cross-shape shear band pattern is found with the one initiated first by the structural constraint dominating over the second one. In all cases, significantly larger dilation and fabric evolution are observed inside the shear band than outside. The simulated shear band orientation coincides with the Roscoe’s angle for cases with high confining pressure and lies in between the Roscoe’s angle and Arthur’s angle for the low confining pressure cases.     

Shear measurement using strain gages under large deformation and rotation

The measurement of shear strain under finite deformation and large rotation by using electrical-resistance metallic foil strain gages is studied both analytically and experimentally. Equations for calculating shear strain and axial and circumferential stretches are derived based on the kinematics of general tension-torsion deformation mode. These equations are applied to analyzing pure torsion experimental data. Comparison is made between results obtained with strain gages and a rotary transducer. It is shown that, in case of large rotation, one simple equation can be used to calculate the shear strain up to 30 percent with adequate accuracy.     

Digital volume correlation including rotational degrees of freedom during minimization

Digital volume correlation is a new experimental technique that allows the measurement of the full-field strain tensor in three dimensions. We describe the addition of rotational degrees of freedom into the minimization problem for digital volume correlation in order to improve the overall performance of the strain measurement. A parameterization of rotations that is particularly suited to the minimization problem is presented, based on the angle-axis representation of finite rotations. The partial derivative of both a normalized cross-correlation coefficient and the sum-of-squares correlation coefficient are derived for use with gradient-based minimization algorithms. The addition of rotation is shown to greatly reduce the measurement error when even small amounts of rigid body rotation are present in an artificially rotated test volume. In an aluminum foam sample loaded in compression, including rotational degrees of freedom produced smoother contours of minimum principal strain. Renderings of the aluminum foam architecture in areas of low, medium and high rotation showed material deformation pattern in detail.     

采用有限单元法计算梁任意形状截面特性

采用将梁截面离散化的方式,用数值积分计算截面的几何特性,并根据梁剪切变形和扭转理论,利用变分原理建立截面的有限元法方程,求解任意形状截面的扭转常数、剪切中心以及剪切面积修正系数等特性.本方法适用于各种形式的截面,具有计算精度高及适应性强的特点.根据上述理论编制了相应程序,按照不同的单元划分方式,分别计算出矩形截面截面特性,与理论解进行比较;又对舟山市定海长峙至岙山预应力混凝土连续箱梁截面进行了计算,并与Ansys结果进行比较,均证明采用本文的计算方法能得到满意的结果,且该方法适用于各种形状的截面形式.     

Finite strain analysis of wood species under compressive failure due to kinking

Finite element analysis of kink band formation in wood is carried out using an anisotropic failure criterion. The criterion is capable of describing the mixed mode I/mode II crack development observed in the kinked region. The evolution of cracking is simulated with the help of the so-called smeared crack approach. As for the finite rotation of the fibers in the kinked material, it is implemented in the finite element code through a hypo-elastic law characterized by an objective derivate using the rotation of the fibers. This formulation enables to follow strictly the matter under finite strain; which means that the evolution of the orthotropic directions is correctly described.Numerical results, such as the predicted load carrying capacity of wood under compression and its post-cracking behavior, prove to have a good agreement with the experimental observations. Further, the applicability of softening orthotropic plasticity under finite strain conditions for simulating compressive failure modes in wood is established.     

INCREMENTAL MICRO-MECHANICAL MODEL OF PLAIN WOVEN FABRIC

I. INTRODUCTION Previous research on woven fabric ignored the micro-weaving structures in fabric and modeled thewoven fabric as a ?exible orthotropic plate[1??3]. However, such a model is unable to predict certainbuckling phenomena of fabric commonly ob…     

Torsional damage of concrete beams with softening behaviour

Analysed in this paper is the torsional damage of concrete beam with softening behaviour. Change in the local stiffness and dissipated strain energy density are determined as the torsional load or rotation is increased. The idealized stress-strain curve is bilinear with a positive and negative slope. Use is made of the equations of elasticity for torsion and isoparameric mapping with finite difference. Numerical results are obtained for the pure torsion of a rectangular beam and combined torsion/compression of an I-beam. Determined are the critical torques which tend to agree well with the test data.