The enhanced assumed strain (EAS) method is one of the most frequently used methods to avoid locking in solid and structural finite elements. One issue of EAS elements in the context of geometrically nonlinear analyses is their lack of robustness in the Newton–Raphson scheme, which is characterized by the necessity of small load increments and large number of iterations. In the present work we extend the recently proposed mixed integration point (MIP) method to EAS elements in order to overcome this drawback in numerous applications. Furthermore, the MIP method is generalized to generic material models, which makes this simple method easily applicable for a broad class of problems. In the numerical simulations in this work, we compare standard strain‐based EAS elements and their MIP improved versions to elements based on the assumed stress method in order to explain when and why the MIP method allows to improve robustness. A further novelty in the present work is an inverse stress‐strain relation for a Neo‐Hookean material model.

中文翻译：

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提高非线性问题的假定假定应变单元的效率和鲁棒性

增强假定应变（EAS）方法是避免锁定在实体和结构有限元中的最常用方法之一。在几何非线性分析中，EAS元素的一个问题是它们在Newton-Raphson方案中缺乏鲁棒性，其特点是需要较小的载荷增量和大量的迭代。在当前的工作中，我们将最近提出的混合积分点（MIP）方法扩展到EAS元素，以克服许多应用中的这一缺点。此外，MIP方法被通用化为通用材料模型，这使得该简单方法可以轻松地应用于广泛的问题类别。在这项工作的数值模拟中，我们将基于应变的标准EAS元素及其MIP改进版本与基于假定应力方法的元素进行比较，以说明MIP方法何时以及为何能够提高鲁棒性。本研究的另一个新颖之处是新霍克材料模型的逆应力-应变关系。