This article describes a numerical method to reconstruct the stress field starting from strain data in elastoplasticity. Usually, this reconstruction is performed using the radial return algorithm, commonly implemented also in finite element codes. However, that method requires iterations to converge and can bring to errors if applied to experimental strain data affected by noise. A different solution is proposed here, where an approximated numerical method is used to derive the stress from the strain data with no iterations. The method is general and can be applied to any plasticity model with a convex surface of the yield locus in nonproportional loading. The theoretical basis of the method is described and then it is implemented on two constitutive models of anisotropic plasticity, namely, Hill48 and Yld2000‐2D. The accuracy of the proposed method and the advantage in terms of computational time with respect to the classical radial‐return algorithm are discussed. The possibility of using such method to reconstruct the stress field in case of few temporal data and noisy strain fields is also investigated.

中文翻译：

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大应变可塑性下快速应力重建的一种近似计算方法

本文介绍了一种从应变数据出发以弹塑性重建应力场的数值方法。通常，使用径向返回算法执行此重构，该算法通常也以有限元代码实现。但是，该方法需要迭代才能收敛，并且如果应用于受噪声影响的实验应变数据，可能会导致误差。这里提出了一种不同的解决方案，其中采用了近似的数值方法，无需迭代即可从应变数据得出应力。该方法是通用的，可应用于非比例加载中具有屈服轨迹凸表面的任何塑性模型。描述了该方法的理论基础，然后在两个各向异性塑性本构模型Hill48和Yld2000-2D上实现了该方法。讨论了所提方法的准确性以及相对于经典径向返回算法的计算时间优势。还研究了在时间数据较少和应变场嘈杂的情况下使用这种方法重建应力场的可能性。