In this paper, an asymptotic solution is obtained for mode I stress and solvent concentration fields around stationary planar sharp V-notches in polymer gels at equilibrium state via poroelasticity theory. To this end, the mechanical equilibrium equations are first solved by employing a proper Airy stress function and then the solvent concentration field is obtained accordingly. It is shown that the stress field is similar to its corresponding linear elasticity solution with both real and complex eigenvalues. Furthermore, it is found that the solvent concentration field, around the notch tip, possesses the same singularity as the stress field and exhibits cosine variations with respect to the angular coordinate. The asymptotic solution is given for both plane stress and plane strain conditions. Next, a numerical study was performed on single edge notched (SEN) specimens with notch opening angles of 30° and 60° to explore the accuracy of the obtained asymptotic solution. It is shown that there is a very good match between the numerical results and the predictions of the asymptotic solution which confirms the validity of the present solution. The comparative study indicates that the first two or three terms of the asymptotic solution calibrated with the finite element over deterministic (FEOD) method is enough to accurately capture the stress and concentration fields at radial distances of about r/a = 0.2 from the notch tip. It is further shown that thicker SEN specimens absorb more solvent molecules per volume around their notch tips for similar far field applied strains and hence have more propensity to brittle fracture.

本文通过多孔弹性理论获得了平衡状态下聚合物凝胶中稳态平面V形槽口周围的模式I应力和溶剂浓度场的渐近解。为此，首先通过采用适当的艾里应力函数来求解机械平衡方程，然后相应地获得溶剂浓度场。结果表明，应力场与其对应的线性弹性解具有相似的特征值和真实特征值。此外，发现在凹口尖端周围的溶剂浓度场具有与应力场相同的奇异性，并且相对于角坐标表现出余弦变化。给出了平面应力和平面应变条件的渐近解。下一个，对缺口开度为30°和60°的单边缺口（SEN）标本进行了数值研究，以探索所得渐近解的准确性。结果表明，数值结果与渐近解的预测之间有很好的匹配，证实了本解的有效性。对比研究表明，用确定性有限元法（FEOD）校准的渐近解的前两个或三个项足以精确地捕获径向距离为的应力场和集中场。结果表明，数值结果与渐近解的预测之间有很好的匹配，证实了本解的有效性。对比研究表明，用确定性有限元法（FEOD）校准的渐近解的前两个或三个项足以精确地捕获径向距离为的应力场和集中场。结果表明，数值结果与渐近解的预测之间有很好的匹配，证实了本解的有效性。对比研究表明，用确定性有限元法（FEOD）校准的渐近解的前两个或三个项足以精确地捕获径向距离为的应力场和集中场。 从缺口尖端开始，r / a = 0.2。进一步表明，对于相似的远场施加应变，较厚的SEN样品在其缺口尖端周围每体积吸收更多的溶剂分子，因此具有更大的脆性断裂倾向。