【新文速递】2024年8月16日固体力学SCI期刊最新文章

今日更新：International Journal of Solids and Structures 2 篇，Journal of the Mechanics and Physics of Solids 4 篇，International Journal of Plasticity 1 篇，Thin-Walled Structures 3 篇International Journal of Solids and StructuresMixed variational formulation and finite-element implementation of second-order poro-elasticityHamza Khurshid, Elten Polukhov, Marc-André Keipdoi:10.1016/j.ijsolstr.2024.113055二阶孔隙弹性的混合变分公式及有限元实现We present a variational formulation of second-order poro-elasticity that can be readily implemented into finite-element codes by using standard Lagrangian interpolation functions. Point of departure is a two-field minimization principle in terms of the displacement and the fluid flux as independent variables. That principle is taken as a basis for the derivation of continuous and incremental saddle-point formulations in terms of an extended set of independent variables. By static condensation this formulation is then reduced to a minimization principle in terms of the displacement and fluid flux as well as associated higher-order fields. Once implemented into a finite-element code, the resulting formulation can be applied to the numerical simulation of porous media in consideration of second-order effects. Here, we analyze the model response by means of several example problems including two standard tests in poro-elasticity, namely the consolidation problems of Terzaghi and Mandel, and compare the results with those of a corresponding first-order model. As becomes clear, the second-order formulation can unleash its full potential when applied to the study of porous media having spatial dimensions comparable to the size of their microstructure. In particular, it is capable to regularize steep field gradients at external as well as internal surfaces and to describe material dilatation effects known from experiments.我们提出了一个二阶孔隙弹性的变分公式，它可以很容易地通过使用标准拉格朗日插值函数实现到有限元代码中。出发点是以位移和流体通量为自变量的双场最小化原理。这一原理被用来作为根据一组扩展的自变量推导连续和增量鞍点公式的基础。通过静态冷凝，该公式就位移和流体通量以及相关的高阶场而言被简化为最小化原则。一旦实现成有限元程序，所得公式可以应用于考虑二阶效应的多孔介质的数值模拟。在这里，我们通过几个例子问题来分析模型的响应，包括两个标准的孔隙弹性试验，即Terzaghi和Mandel固结问题，并将结果与相应的一阶模型的结果进行比较。随着越来越清楚，二阶公式可以释放其全部潜力，当应用于多孔介质的研究具有相当的空间尺寸，其微观结构的大小。特别是，它能够正则化外部和内部表面的陡场梯度，并描述从实验中已知的物质膨胀效应。Generalized prismatic tensegrity derived by dihedral symmetric linesLiheng Wu, Jianguo Caidoi:10.1016/j.ijsolstr.2024.113068由二面体对称线导出的广义棱柱张拉整体Classic prismatic tensegrity structures, characterized by dihedral symmetry with one orbit of nodes, are among the simplest and possibly the earliest spatial tensegrity structures invented. This paper introduces a generalized form of the prismatic tensegrity structures by converting a single-loop linkage into truss, and the joint axes of the linkages form a set of linear dependent lines with dihedral symmetry of one orbit. Consequently, the dihedral symmetry of resulting tensegrity structures is characterized by lines passing the nodes in pairs rather than the nodes themselves. The generated tensegrity structures are kinematically and statically indeterminate, generally, and are called dihedral-line tensegrity structures in this paper. A necessary condition for prestress stability of the generated tensegrity is presented using higher-order analysis of screws. Specifically, this paper focuses on symmetric dihedral-line tensegrity structures, in which the nodes also have dihedral symmetry in two orbits and members in seven orbits. It is found that there are at least N struts for the generated tensegrity with DN symmetry. Several examples illustrate how the classic prismatic tensegrity structures are recovered from these dihedral-line tensegrity structures by removing certain zero-force members. Symmetric-adapted force density matrices are also provided as well as the relation to that of the classic prismatic tensegrity. Given 4N+6 dimensional parameters inherent to these tensegrity structures, a rich variety of tensegrity structure family is presented.经典的棱柱式张拉整体结构具有二面对称的特点，节点为一轨道，是最简单也可能是最早发明的空间张拉整体结构之一。本文介绍了棱柱式张拉整体结构的广义形式，将单环连杆转换为桁架，连杆的连接轴形成一组线性隶属线，具有一轨道的二面对称性。因此，生成的张拉整体结构的二面对称性特征是成对通过节点的线，而不是节点本身。一般来说，生成的张拉实体结构在运动学和静力学上都是不确定的，本文将其称为二面体线张拉实体结构。本文利用螺钉的高阶分析提出了生成的张拉整体预应力稳定性的必要条件。具体而言，本文重点研究对称二面体线张拉整体结构，其中节点在两个轨道上也具有二面体对称性，而构件在七个轨道上也具有二面体对称性。研究发现，生成的具有 DN 对称性的张拉整体至少有 N 个支柱。几个例子说明了如何通过移除某些零力构件，从这些二面线张拉结构中恢复出经典的棱柱张拉结构。此外，还提供了经对称调整的力密度矩阵以及与经典棱柱型张拉整体结构的关系。考虑到这些张弦结构固有的 4N+6 维参数，呈现了丰富多样的张弦结构族。Journal of the Mechanics and Physics of SolidsAdhesive and Cohesive Fracture of Blood Clots: Experiments and ModelingShiyu Liu, Aram Bhamani, Gabriella Paige Sugerman, Zhen Yang, Manuel Rausch, Farshid Ghezelbash, Jianyu Lidoi:10.1016/j.jmps.2024.105858血凝块的黏附性和内聚性骨折:实验和模型Blood clots represent living materials composed of a polymer network and an abundance of cells. They might fracture within the bulk material of the clot (cohesive fracture), at the interface between the clot and surrounding tissue (adhesive fracture), or through a combination of both modes (hybrid fracture). The clot fracture within vascular systems and injury sites could lead to life-threatening conditions. Despite the significance, understanding and modeling the fracture behaviors of blood clots, including their dependence on mechanical loading and cellular components, remain in a nascent stage. In this study, we employ an integrated experimental-computational approach to comprehensively investigate the fracture behaviors of bovine blood clots. We explore various mechanical factors, substrates, and cellular components such as red blood cells (RBCs) and platelets. Our findings reveal that among various tissue substrates, blood clots exhibit the highest interfacial adhesion energy with muscle, and the lowest to the inner arterial lining, consistent with their biological function. Both interfacial and bulk fracture energies are rate-dependent, although they exhibit different dependencies. Also, RBCs and platelets have different effects on clot fracture. An increase in RBC content tends to toughen both adhesion and fracture of blood clots. However, an increase in platelet content enhances interfacial adhesion energy but lowers the bulk fracture energy. The platelet content also governs the shift from adhesive fracture to hybrid fracture. To model clot fracture, we developed two finite element models incorporating a coupled cohesive-zone and Mullins-effect approach to simulate pure shear fracture and peeling of blood clots. These models, validated through experimental data, elucidate the interplay between intrinsic fracture toughness, interfacial strength, and bulk energy dissipation during clot fracture. This study significantly advances our understanding of clot mechanics, providing valuable insights into the mechanics of similar living materials and the management of clot-related disorders such as hemorrhage and thrombosis.血凝块是由聚合物网络和大量细胞组成的活物质。它们可能在血块的大块材料内断裂(内聚性断裂)，也可能在血块与周围组织的界面处断裂(粘连性断裂)，或者通过两种模式的结合(混合型断裂)。血管系统和损伤部位的血栓破裂可能导致危及生命的情况。尽管具有重要意义，但对血凝块断裂行为的理解和建模，包括它们对机械载荷和细胞成分的依赖，仍处于初级阶段。在这项研究中，我们采用了一种综合的实验计算方法来全面研究牛血凝块的断裂行为。我们探讨了各种机械因素，底物和细胞成分，如红细胞(rbc)和血小板。我们的研究结果表明，在各种组织基质中，血凝块与肌肉的界面粘附能最高，与动脉内壁的界面粘附能最低，这与它们的生物学功能一致。界面和整体断裂能都是速率相关的，尽管它们表现出不同的依赖关系。此外，红细胞和血小板对凝块骨折的影响也不同。红细胞含量的增加会使血栓的粘连和破裂变得更韧。然而，血小板含量的增加增加了界面粘附能，但降低了整体断裂能。血小板含量也决定了粘连骨折向混合型骨折的转变。为了模拟血块断裂，我们开发了两个有限元模型，结合了耦合黏结区和mullins效应方法来模拟纯剪切断裂和血块剥离。这些模型通过实验数据验证，阐明了凝块断裂过程中固有断裂韧性、界面强度和块能量耗散之间的相互作用。这项研究显著地推进了我们对凝块机制的理解，为类似生物材料的机制和凝块相关疾病(如出血和血栓形成)的管理提供了有价值的见解。Fracture and size effect in mechanical metamaterialsJ. Ulloa, M.P. Ariza, J.E. Andrade, M. Ortizdoi:10.1016/j.jmps.2024.105860机械超材料的断裂与尺寸效应We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of freedom, but exhibits linear-elastic fracture mechanics scaling and therefore no size effect. To higher order, the overall energetics of the metastructure can be characterized explicitly in terms of the solution of the zeroth-order continuum problem by the method of Γ-expansion. We present explicit expressions of the second-order correction for octet frames. As an application, we evaluate the compliance of double-cantilever octet specimens to second order and use the result to elucidate the dependence of the apparent toughness of the specimen on cell size. The analysis predicts the discreteness of the metamaterial lattice to effectively shield the crack-tip, a mechanism that we term lattice shielding. The theory specifically predicts anti-shielding, i. e., coarser is weaker, in agreement with recent experimental observations.我们采用变分法来评估精细超材料的渐近行为与细胞尺寸的函数关系。在零阶，超材料表现为具有位移和旋转自由度的微极性连续体，但表现出线性弹性断裂力学缩放，因此没有尺寸效应。在更高阶的情况下，超材料结构的整体能量学可以通过Γ-展开方法对零阶连续性问题的求解进行明确表征。我们提出了八面体框架二阶修正的明确表达式。作为应用，我们评估了双悬臂八面体试样的二阶顺应性，并利用该结果阐明了试样表观韧性与单元尺寸的关系。分析预测超材料晶格的离散性可有效屏蔽裂纹尖端，我们称之为晶格屏蔽机制。该理论特别预测了反 屏蔽，即越粗则越弱，这与最近的实验观察结果一致。Stress–strain hysteresis during hydrostatic loading of porous rocksAlvin T. Biyoghé, Yves M. Leroy, Lucas Pimienta, Robert W. Zimmermandoi:10.1016/j.jmps.2024.105861多孔岩石静水加载过程中的应力-应变滞后现象A micro-mechanical model is proposed to predict the stress–strain hysteresis during the cyclic hydrostatic loading of fluid-saturated rocks under drained or undrained conditions. A spherical pore is surrounded by a multi-cracked shell where local deviatoric stress develops despite the remote hydrostatic loading. The effective properties of the material composing the shell are constructed assuming an isotropic distribution of cracks with no interaction, and the overall properties thanks to the spherical assemblage approach. The fluid pressure in drained and undrained conditions is assumed to be uniform throughout the assemblage. A new analytical solution is proposed, assuming all cracks are closed and slipping either forwardly or reversely. It is shown with numerical simulations for drained conditions that this assumption is indeed respected for sufficiently small values of the crack friction angle. However, for reasonable values, the closed cracks during the unloading phase could slip in either direction: reversely close to the pore and still forwardly away from the pore. Moreover, at critical radii, the slip could occur in either direction depending on the crack orientation. A similar micro-structural response is observed for undrained conditions, although the remote confining stress required to close the cracks is much larger. The model’s predictions compare favourably with recent experimental data on dry sandstones and carbonates, which were presented in a study on the influence of strain amplitude on the transition between static and dynamic properties. The crack density and matrix elasticity modulus are sufficient fitting parameters to accurately predict the hysteresis loops, especially for porosity levels above 10%.提出了一种细观力学模型来预测排水和不排水条件下饱和流体岩石在循环静水加载过程中的应力-应变滞后现象。一个球形孔是由一个多裂纹壳包围，局部偏应力发展，尽管远静水加载。构成壳体的材料的有效性能是在假设裂纹的各向同性分布而没有相互作用的情况下构建的，而整体性能则是通过球面组合方法构建的。假定在排水和不排水条件下的流体压力在整个组合中是均匀的。提出了一种新的解析解，假设所有裂缝都是闭合的，并且正向或反向滑动。排水条件下的数值模拟表明，当裂纹摩擦角值足够小时，这一假设确实得到了尊重。然而，在合理的数值范围内，卸载阶段闭合的裂缝可以向两个方向滑动:反向靠近孔隙，仍然向前远离孔隙。此外，在临界半径处，滑移可能发生在任何方向，这取决于裂纹的方向。在不排水条件下也观察到类似的微观结构响应，尽管闭合裂缝所需的远端围应力要大得多。该模型的预测与最近关于干砂岩和碳酸盐岩的实验数据相比较有利，这些数据是在一项关于应变幅值对静态和动态性质之间转换的影响的研究中提出的。裂纹密度和基体弹性模量是能够准确预测迟滞回线的拟合参数，特别是在孔隙率大于10%的情况下。Free Energy and Extension of Stiff Polymer Chains Confined in Nanotubes with Diverse Cross-Sectional ShapesYihan Zhao, Jizeng Wangdoi:10.1016/j.jmps.2024.105862不同截面形状纳米管中刚性聚合物链的自由能和延伸The statistical mechanics of stiff polymer chains confined within narrow tubes is a foundational topic in polymer physics, extensively analyzed in prior research. For cylindrical, rectangular, and slit-like confinements, the chains’ free energy and extension adhere to a scaling law consistent with the Odijk theory. While this scaling law may not apply to tubes with different cross-sectional geometries, there is a lack of research examining the behavior of stiff chains in tubes with intricate cross-sectional shapes. In this study, we investigate the partition function of a stiff chain confined within an elliptic tube using the path integral approach, deriving a deflection length in a concise closed form through dimensional analysis. This length scale facilitates straightforward expressions for the chain's free energy and extension. Notably, we discover a shape-independent property of these expressions applicable to tubes with a wide variety of cross-sectional geometries. Extensive numerical simulations are conducted using a biased chain-growth Monte Carlo method, incorporating the Pruned and Enriched Rosenbluth algorithm, to validate the theoretical predictions on the confinement free energy and extension of chains in tubes with differing shapes.窄管内刚性聚合物链的统计力学是聚合物物理学的一个基础问题，在以往的研究中得到了广泛的分析。对于圆柱形、矩形和裂隙状约束，链的自由能和延伸遵循与Odijk理论一致的标度定律。虽然该标度定律可能不适用于具有不同横截面几何形状的管，但缺乏对具有复杂横截面形状的管中刚性链行为的研究。在本研究中，我们使用路径积分方法研究了限制在椭圆管内的刚性链的配分函数，通过量纲分析得出了简洁封闭形式的挠度长度。这个长度标度便于直接表示链的自由能和延伸。值得注意的是，我们发现这些表达式适用于具有各种截面几何形状的管的形状无关性质。采用偏置链生长蒙特卡罗方法进行了大量的数值模拟，并结合了修剪和充实的Rosenbluth算法，以验证不同形状管中约束自由能和链延伸的理论预测。International Journal of PlasticityRevealing the fatigue strengthening and damage mechanisms of surface-nanolaminated gradient structureYong Zhang, Chen-Yun He, Xiaogang Wang, Takayuki HAMA, Binhan Sun, Yun-Fei Jia, Xian-Cheng Zhang, Shan-Tung Tudoi:10.1016/j.ijplas.2024.104128揭示了表面纳米层状梯度结构的疲劳强化和损伤机理Extending the fatigue life of metals is a critical concern for maintaining material and component integrity in engineering systems. The integration of gradient structures within materials represents a highly promising approach to enhance the fatigue properties in metallic materials, while a detailed mechanistic understanding of the fatigue damage evolution of such structures is yet to be developed. Here, we report that the surface-nanolaminated gradient structure comprised of nanolaminates and hierarchical twins imparts remarkable resistance to both low-cycle and high-cycle fatigue. A dislocation-based strain gradient crystal plasticity model is developed to investigate the strengthening and damage mechanisms of our gradient structure. The size dependence of the initial dislocation density, its evolution and back stress hardening are taken into account and verified by the experimental data. The simulation results reveal that the strain delocalization and back stress hardening induced by the structure gradient significantly mitigate the fatigue damage accumulation. Additionally, in contrast to conventional gradient structures, the mechanical stability of the present structure enables these strengthening mechanisms to persist until crack initiation. These effects, combined with the sequential toughening mechanisms activated in the surface-nanolaminated gradient structure, ensure a marked life extension under low-cycle fatigue (by a factor of four), outperforming conventional gradient and other microstructural design strategies. Finally, a multiscale anti-fatigue design principal for damage homogenization is given based on the prior quantitative analysis.延长金属的疲劳寿命是保持工程系统中材料和部件完整性的关键问题。材料内部梯度结构的集成是提高金属材料疲劳性能的一种非常有前途的方法，但对这种结构疲劳损伤演变的详细机制理解尚未得到发展。在这里，我们报道了由纳米层合物和分层孪晶组成的表面纳米层化梯度结构对低周和高周疲劳具有显著的抵抗力。建立了基于位错的应变梯度晶体塑性模型，研究了梯度结构的强化和损伤机理。考虑了初始位错密度、位错演化和背应力硬化的尺寸依赖性，并用实验数据进行了验证。模拟结果表明，结构梯度引起的应变离域和背应力硬化显著减缓了疲劳损伤的积累。此外，与传统的梯度结构相比，当前结构的机械稳定性使这些强化机制能够持续到裂纹萌生。这些效应，再加上在表面纳米层化梯度结构中激活的顺序增韧机制，确保了在低周疲劳下的显著寿命延长(四倍)，优于传统的梯度和其他微结构设计策略。最后，在先前定量分析的基础上，给出了损伤均匀化的多尺度抗疲劳设计原则。Thin-Walled StructuresPrediction of sectional collapse of thin-walled structure under pure bending by nonlinear composite beam theoryFang Jiang, Wenbin Yudoi:10.1016/j.tws.2024.112414用非线性组合梁理论预测薄壁结构在纯弯曲作用下的截面倒塌Brazier (1927) found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper studies the Brazier effect by the nonlinear Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. Nonlinear VABS reduces three-dimensional (3D) continuum to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler–Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws regarding nonlinear elasticity and progressive damage. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.Brazier(1927)发现，当梁截面的一个维度相对小于其他维度时，即使应变可以保持很小，截面上也可能发生较大的面内位移。在这种情况下，所谓的火盆效应是指截面椭圆化，导致非线性弯曲屈曲和破坏。本文采用考虑有限截面变形的非线性变分渐近梁截面分析(VABS)理论研究了火盆效应。非线性VABS将三维(3D)连续体简化为一维(1D)梁分析和二维(2D)截面分析，具有几何和材料非线性，无需不必要的运动学假设。本理论是用通用梁截面分析工具VABS代码中的有限元方法实现的。利用欧拉-伯努利梁理论，采用迭代法求解经典型模型的有限翘曲场。变形梯度张量直接用于处理有限变形、各种应变定义以及几种关于非线性弹性和渐进损伤的材料规律。数值算例验证了VABS预测薄壁结构在纯弯曲作用下截面倒塌的能力。Vibration analysis of rotating variable-angle-tow composite cylindrical structures via high-fidelity shell modelsR. Azzara, M. Filippi, E. Carreradoi:10.1016/j.tws.2024.112446基于高保真壳模型的旋转变角-拖拽复合圆柱结构振动分析The paper focuses on rotordynamics analyses of various rotating variable-angle-tow (VAT) composite cylindrical structures using both low- and high-fidelity structural models. To model the spatially varying composite shell structures, the Carrera Unified Formulation (CUF) is employed. The CUF provides a hierarchical and automated approach for developing shell finite element models. Various shell models are created using different kinematics models based on Taylor or Lagrange expansion functions. The linearized equations of motion include the Coriolis and initial stress contributions. Several VAT composite curved panels and thin and thick cylinders have been analyzed to validate the presented approach and provide benchmark solutions. The results are discussed and compared with commercial software solutions. The results demonstrate the good accuracy and reliability of the proposed numerical methodology.本文采用高保真和低保真两种结构模型对各种旋转变角拖缆(VAT)复合圆柱结构进行了旋转动力学分析。为了模拟空间变化的复合材料壳结构，采用了Carrera统一公式(CUF)。CUF为开发壳体有限元模型提供了一种分层和自动化的方法。使用基于泰勒或拉格朗日展开函数的不同运动学模型创建各种壳模型。线性化的运动方程包括科里奥利和初始应力贡献。对几种VAT复合材料曲面板和厚、薄圆柱体进行了分析，验证了所提出的方法，并提供了基准解决方案。对结果进行了讨论，并与商业软件解决方案进行了比较。结果表明，所提出的数值方法具有较高的精度和可靠性。Optimizing microstructure and strength of CMT-wire arc additive manufactured WE43 Mg alloy through a novel active cooling techniqueKun Li, Benxiang Li, Liang Zhu, Xuru Hou, Ziche Li, Lawrence E. Murr, Bing Jiang, Fusheng Pandoi:10.1016/j.tws.2024.112453采用新型主动冷却技术优化cmt电弧添加剂制备WE43镁合金的组织和强度Cold metal transfer (CMT)-Wire arc additive manufacturing (WAAM) has been widely utilized in the production of large Magnesium (Mg) alloy components. However, the thermal cycling and heat input inherent in the CMT-WAAM process can adversely affect the microstructure and properties of Mg-Rare earth (RE) alloys. Currently, there is a lack of effective, low-cost, and easy-to-implement methods to mitigate these issues. In this study, an active cooling technique (ACT) comprising base cooling and bypass cooling was proposed. The ACT facilitates in-situ cooling of CMT-WAAMed WE43 components through uninterrupted water flow in the substrate and bypass plate, offering advantages in cost-effectiveness, safety, and ease of implementation. It was found that the CMT-WAAMed WE43 alloy thin wall component manufactured with the ACT assistance had fewer hard-brittle eutectic phases and finer grains due to the accelerated cooling rate. ACT effectively reduced the heat accumulation and peak temperatures in the component. Furthermore, it inhibited the transformation of the β1 phase to the β phase and suppressed the coarsening of the β1 phase. ACT also improved the ultimate tensile strength (UTS), yield strength (YS), and elongation (EL) of the CMT-WAAMed WE43 component by 11.7%, 5.8%, and 72.3%, respectively. This study provides a novel approach for the microstructure optimization of CMT-WAAMed Mg-RE alloy, which is crucial for the production of high-performance and large-size components in the aerospace industry.冷金属转移-电弧增材制造技术在大型镁合金部件的生产中得到了广泛的应用。然而，CMT-WAAM过程中固有的热循环和热输入会对mg -稀土(RE)合金的组织和性能产生不利影响。目前，缺乏有效、低成本和易于实现的方法来缓解这些问题。在本研究中，提出了一种由基础冷却和旁路冷却组成的主动冷却技术(ACT)。ACT通过基板和旁通板中不间断的水流，促进CMT-WAAMed WE43组件的原位冷却，具有成本效益，安全性和易于实施的优势。结果表明，在ACT辅助下制备的CMT-WAAMed WE43合金薄壁件由于冷却速度加快，其硬脆共晶相减少，晶粒细化。ACT有效地降低了组件的热积累和峰值温度。抑制β1相向β相转变，抑制β1相粗化。ACT还使CMT-WAAMed WE43构件的极限抗拉强度(UTS)、屈服强度(YS)和伸长率(EL)分别提高了11.7%、5.8%和72.3%。该研究为CMT-WAAMed Mg-RE合金的微观结构优化提供了一种新的方法，这对于航空航天工业中高性能和大尺寸部件的生产至关重要。来源：复合材料力学仿真Composites FEM