论文标题
使用新的低内存基于Broyden-Step的算法对超弹性复合材料的微弹性复合材料分析
Micromechanical analysis of hyperelastic composites with localized damage using a new low-memory Broyden-step-based algorithm
论文作者
论文摘要
为预测具有超弹性成分和嵌入局部损伤的复合材料的有限应变行为，提出了多尺度（微观到麦克罗）分析。假定复合材料具有周期性的微观结构，并受到远程字段。在微观尺度上，采用了基于（完整）复合材料的均匀化技术的有限晶体微力分析来预测有效变形。在宏观上，开发了基于代表性细胞法和相关的高阶理论的程序，用于确定受损复合材料中的弹性场。通过应用离散的傅立叶变换，将周期性复合材料离散为相同的细胞，然后通过应用离散的傅立叶变换来简化为单个单元的问题。傅立叶变换域中所得的管理方程，界面和边界条件可以通过使用高阶理论以及迭代程序来处理损害和材料非线性的影响来解决。迭代溶液的初始条件是使用弱非固定物质极限和自然固定点迭代获得的。然后采用了本地含量的低内存准牛顿求解器。提出了一种用于实现求解器的新算法，该算法允许直接存储在存储器中的矢量功能历史记录序列，这对于基于目标向量函数的特定组件的收敛控制可能是有利的。此处采用的强形式基于傅立叶变换的方法，与新求解器一起，可以将方法扩展到非线性材料上，并可能具有与标准方法相比的计算效率。
A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure and be subjected to a remote field. At the microscale, finite-strain micromechanical analysis based on the homogenization technique for the (intact) composite is employed for the prediction of the effective deformation. At the macroscale, a procedure, based on the representative cell method and the associated higher-order theory, is developed for the determination of the elastic field in the damaged composite. The periodic composite is discretized into identical cells and then reduced to the problem of a single cell by application of the discrete Fourier transform. The resulting governing equations, interfacial and boundary conditions in the Fourier transform domain, are solved by employing the higher-order theory in conjunction with an iterative procedure to treat the effects of damage and material nonlinearity. The initial conditions for the iterative solution are obtained using the weakly-nonlinear material limit and a natural fixed-point iteration. A locally-convergent low-memory Quasi-Newton solver is then employed. A new algorithm for the implementation of the solver is proposed, which allows storing in the memory directly the vector-function history-sequence, which may be advantageous for convergence-control based on specific components of the objective vector-function. The strong-form Fourier transform-based approach employed here, in conjunction with the new solver, enables to extend the application of the method to nonlinear materials and may have computational efficiency comparable or possibly advantageous to that of standard approaches.
