何时能从应力强度分布中识别组合载荷？关于SIFBench有限元数据的正向-逆向耦合研究

中文摘要 AI 辅助

本研究利用公开的SIFBench有限元数据，探讨从裂纹前沿的应力强度因子分布恢复作用于裂纹的拉伸、弯曲和承载载荷相对大小的反问题。核心并非现场案例的载荷恢复，而是严格刻画组合载荷何时可识别，并给出在不可识别区域精确返回校准不确定性的估计器。对于已知几何形状，从载荷到分布的正向映射是线性的，可识别性归结为一个几何问题：三个基本载荷分布沿前沿作为函数是否线性独立。当它们接近相关时，反问题不适定，分析表明不适定程度由固有稳定性裕度控制，而非仅由条件数决定。一个裂纹前沿算子既作为结构化正向代理，又作为单纯形约束、集值反估计器所需的可微映射。在SIFBench角裂纹场景中，经验行为与理论相符：典型几何形状适定，少数确实不适定，因此多数情况下点估计可靠，其余情况则无信息。验证基于受控合成噪声，未使用或声称真实断裂案例。

英文摘要

This work studies the inverse problem of recovering the relative magnitudes of the tension, bending, and bearing loads acting on a crack from its stress-intensity-factor profile along the crack front, using the public SIFBench finite-element data. The central claim is not forensic load recovery on field cases, but a rigorous characterization of when the combined load is identifiable at all, together with an estimator that returns calibrated uncertainty precisely in the regimes where it is not. For a known geometry the forward map from loads to profile is exactly linear, and identifiability reduces to a single geometric question: whether the three elementary load profiles are linearly independent as functions along the front. When they are nearly dependent, many different load combinations produce almost the same profile and the inverse problem is illposed; the analysis shows that the degree of ill-posedness is controlled by an intrinsic stability margin, not by the conditioning number alone. A single crack-front operator serves both as a structured forward surrogate and as the differentiable map required by a simplex-constrained, set-valued inverse estimator. On the SIFBench corner-crack scenario the empirical behaviour matches the theory: the typical geometry is well posed while a sizable minority is genuinely ill-posed, so a point estimate is reliable on the majority and provably uninformative on the rest. Validation is on controlled synthetic noise; no real fracture cases are used or claimed.

发表机构

• Université de Picardie Jules Verne（皮卡第儒勒·凡尔纳大学）

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