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An adaptive sub-incremental strategy for the solution of homogenization-based multi-scale problems

机译：求解均质化多尺度问题的自适应亚增量策略

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摘要

In this contribution, several schemes for the solution of homogenization-based multi-scale constitutive problems undergoing finite strains with inelastic material behavior are investigated. These schemes are aimed at improving the robustness and efficiency of the Newton-Raphson method in the multilevel finite element (ML-FEM) framework. An adaptive sub-incremental strategy is proposed for the discrete representative volume element (RVE) boundary value problem. The procedure is able to ensure the convergence of the solution algorithm, in the presence of several sources of non-linearity, and obtains improved initial guesses for the Newton-Raphson scheme in the ML-FEM framework. The enlargement of the convergence bowl of the Newton-Raphson procedure at the micro-scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ML-FEM analyses. The proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the Newton-Raphson scheme at the macroscopic level. Numerical examples of both micro-scale and two-scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed.
机译：在此贡献中，研究了几种解决方案的解决方案，该方案基于均质化的多尺度本构问题，这些问题在有限应变下具有非弹性材料行为。这些方案旨在在多层有限元（ML-FEM）框架中提高Newton-Raphson方法的鲁棒性和效率。针对离散代表体元（RVE）边值问题，提出了一种自适应的亚增量策略。在存在多个非线性源的情况下，该过程能够确保求解算法的收敛性，并且可以在ML-FEM框架中获得针对Newton-Raphson方案的改进的初始猜测。牛顿-拉夫森过程的收敛碗在微观尺度上的扩大允许规定较大的宏观变形梯度，并显着降低了ML-FEM分析的总体计算成本。所提出的策略在宏观水平上保留了代表牛顿-拉夫森方案的渐进收敛的二次速率。给出了微观尺度和两尺度有限元模拟的数值示例，以证明所提出的求解程序的改进的鲁棒性和效率。

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