Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties lead to a significant increase in computational effort. Model order reduction aims to implement efficient methods for accelerating the simulation process while preserving a high degree of accuracy. Numerous studies have already demonstrated the benefits of this method for linear elastic material modeling. However, in the present work, we investigate a two-surface gradient-extended damage-plasticity model. We conducted complex simulations with this model, demonstrating both damage behavior and softening. The POD-based discrete empirical interpolation method (DEIM) is introduced and implemented. To accomplish simulations with DEIM and softening behaviour, we propose the implementation of a reduced form of the arc-length method. Existing research on calculating models with both damage and softening behavior using the DEIM and arc-length method is limited. To validate the methods, two numerical examples are thoroughly investigated in this study: a plate with a hole and an asymmetrically notched specimen. The results show that the proposed methods can create a reduced order model with high accuracy and a significant speedup of the simulation. For both examples, the analysis is conducted in three steps: first, plasticity without damage is examined, followed by damage without plasticity, and finally, the combination of plasticity and damage is investigated.

翻译：精确模拟对于工程应用至关重要，为此构建了复杂的连续介质力学材料模型。然而，材料模型和几何特性的日益复杂导致计算量显著增加。模型降阶旨在实现既能加速模拟过程又能保持高精度的有效方法。大量研究已证明该方法在线弹性材料建模中的优势。但本文中，我们研究了一个双面梯度扩展损伤-塑性模型。我们使用该模型进行了复杂模拟，展示了损伤行为和软化特性。引入并实现了基于POD的离散经验插值方法（DEIM）。为使用DEIM和软化行为完成模拟，我们提出了弧长法的简化形式实现。现有关于使用DEIM和弧长法计算同时具有损伤和软化行为的模型的研究有限。为验证这些方法，本文深入研究了两个数值算例：含孔洞板件和非对称缺口试件。结果表明，所提方法能够构建具有高精度且显著加速模拟的降阶模型。两个算例均按三步进行分析：首先研究无损伤塑性行为，其次研究无塑性损伤行为，最后研究塑性-损伤耦合行为。