局部损伤超弹性复合材料细观力学分析的低记忆Broyden步长算法
Micromechanical analysis of hyperelastic composites with localized damage using a new low-memory Broyden-step-based algorithm
摘要：
提出了一种多尺度（微观到宏观）分析方法，用于预测含超弹性组分和嵌入局部损伤的复合材料的有限应变行为。复合材料被假定为具有周期性的微观结构，并受到远程场。在微观尺度上，基于均匀化技术的（完整的）复合材料的有限应变细观力学分析用于预测的有效变形。在宏观尺度上，一个程序，基于代表性的细胞方法和相关的高阶理论，开发的损伤复合材料中的弹性场的确定。将周期性复合材料离散成相同的单元，然后通过应用离散傅里叶变换将其简化为单个单元的问题。由此产生的控制方程，界面和边界条件的傅里叶变换域，解决了采用高阶理论结合迭代过程来处理损伤和材料非线性的影响。利用弱非线性材料极限和自然不动点迭代法，得到了迭代解的初始条件。然后采用局部收敛的低内存拟牛顿求解器。提出了一种新的算法的求解器的实现，它允许直接存储在存储器中的向量函数的历史序列，这可能是有利的收敛控制的目标向量函数的特定组件的基础上。这里采用的强形式的傅立叶变换为基础的方法，结合新的求解器，使该方法的应用扩展到非线性材料，并可能具有可比的计算效率或可能有利于标准的方法。
英文摘要：
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.
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