In solid mechanics, Maxwell stresses are known to be induced if a body is exposed to magnetic and, in the case of dielectrics, electric fields. Acting as tractions at outer or inner surfaces as well as volume forces, they are superimposed with tractions and stresses due to mechanical loads and provide a more or less significant contribution, depending on loading, material properties and geometric aspects. The Maxwell stress tensor, constituting the physical and mathematical basis, however, is controversially discussed to date. Several formulations are known, most of them having been suggested more than 100 years ago. Being equivalent in vacuum, they differ qualitatively just as quantitatively in solid or fluidic matter. In particular, the dissimilar effect of body forces, emanating from a choice of established Maxwell stress tensor approaches, on crack tip loading in dielectric solids is investigated theoretically in this paper. Due to the singularity of fields involved, their impact is basically non-negligible compared to external mechanical loading. The findings obtained indicate that fracture mechanics could be the basis of an experimental validation of Maxwell stress tensors.

在固体力学中，如果物体暴露在磁场中，如果是电介质，则暴露在电场中，就会产生麦克斯韦应力。它们充当外表面或内表面的牵引力以及体积力，与机械载荷产生的牵引力和应力叠加，并根据载荷、材料特性和几何方面提供或多或少的重要贡献。然而，构成物理和数学基础的麦克斯韦应力张量迄今为止仍存在争议。有几种已知的配方，其中大多数是在 100 多年前就被提出的。它们在真空中是等价的，但在固体或流体物质中，它们在质量上有所不同，在数量上也有所不同。特别是，本文从理论上研究了由于选择已建立的麦克斯韦应力张量方法而产生的体力对电介质固体中裂纹尖端载荷的不同影响。由于涉及领域的奇异性，与外部机械载荷相比，它们的影响基本上是不可忽略的。获得的结果表明断裂力学可以成为麦克斯韦应力张量实验验证的基础。