Stress analysis is an all-pervasive practice in engineering design. With displacement-based finite element analysis, directly-calculated stress fields are obtained in a post-processing step by computing the gradient of the displacement field—therefore less accurate. In enriched finite element analysis (EFEA), which provides unprecedented versatility by decoupling the finite element mesh from material interfaces, cracks, and structural boundaries, stress recovery is further aggravated when such discontinuities get arbitrarily close to nodes of the mesh; the presence of small area integration elements often yields overestimated stresses, which could have a detrimental impact on nonlinear analyses (e.g., damage or plasticity) since stress concentrations are just a nonphysical numerical artifact. In this article, we propose a stress recovery procedure for enhancing the stress field in problems where the field gradient is discontinuous. The formulation is based on a stress improvement procedure (SIP) initially proposed for low-order standard finite elements. Although generally applicable to all EFEA, we investigate the technique with the Interface-enriched Generalized Finite Element Method and compare the procedure to other post-processing smoothing techniques. We demonstrate that SIP for EFEA provides an enhanced stress field that is more accurate than directly-calculated stresses—even when compared with standard FEM with fitted meshes.

中文翻译：

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不连续梯度场非拟合有限元分析的改进应力恢复技术

应力分析是工程设计中普遍存在的实践。使用基于位移的有限元分析，在后处理步骤中通过计算位移场的梯度获得直接计算的应力场，因此精度较低。在丰富的有限元分析 (EFEA) 中，通过将有限元网格与材料界面、裂缝和结构边界解耦，提供前所未有的多功能性，当这些不连续性任意靠近网格节点时，应力恢复会进一步加剧；小面积积分单元的存在通常会产生高估的应力，这可能对非线性分析产生不利影响（例如.，损坏或可塑性），因为应力集中只是一种非物理的数值伪影。在本文中，我们提出了一种应力恢复程序，用于在场梯度不连续的问题中增强应力场。该公式基于最初为低阶标准有限元提出的应力改进程序 (SIP)。虽然普遍适用于所有 EFEA，但我们使用富接口广义有限元方法研究该技术，并将该过程与其他后处理平滑技术进行比较。我们证明了 EFEA 的 SIP 提供了一个增强的应力场，它比直接计算的应力更准确——即使与带有拟合网格的标准 FEM 相比也是如此。