A novel high-order three-scale reduced homogenization (HTRH) approach is introduced for analyzing the nonlinear heterogeneous materials with multiple periodic microstructure. The first-order, second-order and high-order local cell solutions at microscale and mescoscale gotten by solving the distinct multiscale cell functions are derived at first. Then, two kinds of homogenized parameters are calculated, and the nonlinear homogenization equations defined on global structure are evaluated, successively. Further, the displacement and stress fields are established as high-order multiscale approximate solutions by assembling the various unit cell solutions and homogenization solutions. The significant characteristics of the presented approach are an efficient reduced model form for solving high-order nonlinear local cell problems, and hence reducing the computational cost in comparison to direct computational homogenization. Besides, the new asymptotic high-order nonlinear homogenization does not need higher order continuities of the coarse-scale (or macroscale) solutions. Finally, by some representative examples, the efficiency and accuracy of the presented algorithms are verified. The numerical results clearly illustrate that the HTRH approach reported in this work is effective and accurate to predict the macroscopic nonlinear properties, and can capture the microscale and mesoscale behavior of the composites accurately.

提出了一种新颖的高阶三尺度缩减均质化（HTRH）方法，用于分析具有多个周期性微观结构的非线性异质材料。首先推导了通过求解不同的多尺度细胞函数得到的微观和中尺度的一阶，二阶和高阶局部细胞解。然后，计算了两种均匀化参数，并依次评估了在全局结构上定义的非线性均匀化方程。此外，通过组合各种晶胞溶液和均质溶液，将位移场和应力场建立为高阶多尺度近似解。提出的方法的显着特征是用于解决高阶非线性局部像元问题的有效简化模型形式，因此，与直接计算同质化相比，降低了计算成本。此外，新的渐近高阶非线性均匀化不需要粗糙尺度（或宏观尺度）解的更高阶连续性。最后，通过一些代表性的例子，验证了所提出算法的效率和准确性。数值结果清楚地表明，这项工作中报道的HTRH方法能够有效，准确地预测宏观非线性性质，并且可以准确地捕获复合材料的微观和中尺度行为。通过一些代表性的例子，验证了所提算法的效率和准确性。数值结果清楚地表明，这项工作中报道的HTRH方法能够有效，准确地预测宏观非线性性质，并且可以准确地捕获复合材料的微观和中尺度行为。通过一些代表性的例子，验证了所提算法的效率和准确性。数值结果清楚地表明，这项工作中报道的HTRH方法能够有效，准确地预测宏观非线性性质，并且可以准确地捕获复合材料的微观和中尺度行为。