Soft materials are known for their plethora of biomedical applications, intricate structure–property correlation and nonlinear mechanical response. Multiple length–time scale phenomena and hierarchical structure results in their nonlinearity. Phenomenological and continuum mechanical models have been developed to predict their mechanics, which have mostly been very material-specific with inability to predict the mechanics of different types of soft materials simultaneously. This shortcoming has been addressed in the present work, wherein a generic nonlinear viscoelastic model has been proposed to predict the mechanical response of hydrogels, sponges, and xerogels. A fractal derivative viscoelastic model is proposed considering a fractal Maxwell model in parallel with a nonlinear spring. In particular, this model is chosen to qualitatively mimic the material nonlinearity inherent in soft materials. The fractal dashpot in combination with the nonlinear spring accounts for the power law time-dependent rheology of generic soft materials. These two different aspects in the form of nonlinear stiffness and non-Newtonian rheology account for mechanics of most soft materials. The present model is shown to fit well the existing literature results for mechanical response of a multitude of soft material classes with different test conditions and loading rates, which is one of the salient features of the model, apart from its simplistic mathematical framework. Further, a parametric study is reported on the mechanics of nanocellulose loaded poly(vinyl alcohol) xerogel. The model predictions are observed to be in conjunction with the experimental observations.

软材料以其大量的生物医学应用，复杂的结构-特性关联和非线性机械响应而闻名。多个时标尺度现象和层次结构导致其非线性。已开发出现象学和连续力学模型来预测其力学，这些模型大多是非常特定于材料的，无法同时预测不同类型的软材料的力学。在当前的工作中已经解决了这个缺点，其中提出了一种通用的非线性粘弹性模型来预测水凝胶，海绵和干凝胶的机械响应。提出了分形麦克斯韦模型与非线性弹簧并行的分形导数粘弹性模型。特别是，选择该模型以定性地模拟软材料固有的材料非线性。分形阻尼器与非线性弹簧的组合说明了通用软材料的幂律时间相关的流变性。非线性刚度和非牛顿流变学形式的这两个不同方面解释了大多数软材料的力学。结果表明，该模型与现有的文献结果非常吻合，具有不同测试条件和加载速率的多种软材料类别的机械响应，这是该模型的重要特征之一，除了其简单的数学框架外。此外，关于载有纳米纤维素的聚乙烯醇干凝胶的力学性能的参数化研究已有报道。