A new and explicit form of the multi-axial elastic potential for elastic soft materials is constructed by means of two invariants of the Hencky strain. The new elasticity model with this form can bypass coupling complexities and uncertainties usually involved in parameter identification. Namely, exact closed-form solutions of decoupled nature are obtainable for stress responses under multiple benchmark modes. Unlike usual solutions with numerous coupled parameters, such new solutions are independent of one another and, as such, data sets for multiple benchmark modes can be separately matched with mutually independent single-variable functions. A comparative study is presented between a few well-known models and the new model. Results show that predictions from the former agree well with uniaxial and biaxial data, as known in the literature, but would be at variance with data for the constrained stress response in the plane-strain extension. In contrast, predictions from the new model agree accurately with all data sets. Furthermore, exact solutions for the Poynting effect of freely twisted elastic thin-walled tube are obtained from the new model.

通过亨基应变的两个不变量构建了弹性软材料多轴弹性势的新的明确形式。这种形式的新弹性模型可以绕过参数识别中通常涉及的耦合复杂性和不确定性。即，对于多种基准模式下的应力响应，可以获得解耦性质的精确封闭式解。与具有众多耦合参数的通常解决方案不同，这种新解决方案是彼此独立的，因此，多个基准模式的数据集可以分别与相互独立的单变量函数进行匹配。对一些知名模型和新模型进行了比较研究。结果表明，前者的预测与文献中已知的单轴和双轴数据非常吻合，但与平面应变延伸中约束应力响应的数据不一致。相比之下，新模型的预测与所有数据集都准确一致。此外，新模型还获得了自由扭转弹性薄壁管坡印廷效应的精确解。