Soft materials such as rubber and hydrogels are commonly used in industry for their excellent hyperelastic behaviour. There are various types of constitutive models for soft materials, and phenomenological models are very popular for finite element method (FEM) simulations. However, it is not easy to construct a model that can precisely predict the complex behaviours of soft materials. In this paper, we suggest that the strain energy density functions should be expressed as functions of ordered principal stretches, which have more flexible expressions and are capable of matching various experimental curves. Moreover, the feasible region is small, and simple experiments, such as uniaxial tension/compression and hydrostatic tests, are on its boundaries. Therefore, strain energy density functions can be easily constructed by the interpolation of experimental curves, which does not need initial guessing in the form of the strain energy density function as most existing phenomenological models do. The proposed strain energy density functions are perfectly consistent with the available experimental curves for interpolation. It is interesting to find that for incompressible materials, a 3D constitutive relation can be obtained from single uniaxial stress–strain experimental curve (from compression to tension) via interpolation, which can predict other experimental curves reasonably well. To further improve the accuracy, additional experiments can be used in the interpolation.

橡胶和水凝胶等软材料因其出色的超弹性性能而常用于工业。软材料有多种类型的本构模型，现象学模型在有限元法 (FEM) 模拟中非常流行。然而，构建一个能够精确预测软材料复杂行为的模型并不容易。在本文中，我们建议应变能密度函数应表示为有序主拉伸的函数，其具有更灵活的表达方式并且能够匹配各种实验曲线。此外，可行区域小，单轴拉伸/压缩和静水压试验等简单实验在其边界上。所以，应变能密度函数可以通过实验曲线的插值轻松构建，不需要像大多数现有现象学模型那样以应变能密度函数的形式进行初始猜测。提出的应变能量密度函数与可用的插值实验曲线完全一致。有趣的是，对于不可压缩材料，可以通过插值从单个单轴应力-应变实验曲线（从压缩到拉伸）获得 3D 本构关系，可以很好地预测其他实验曲线。为了进一步提高精度，可以在插值中使用额外的实验。它不需要像大多数现有的现象学模型那样以应变能密度函数的形式进行初始猜测。提出的应变能量密度函数与可用的插值实验曲线完全一致。有趣的是，对于不可压缩材料，可以通过插值从单个单轴应力-应变实验曲线（从压缩到拉伸）获得 3D 本构关系，可以很好地预测其他实验曲线。为了进一步提高精度，可以在插值中使用额外的实验。它不需要像大多数现有的现象学模型那样以应变能密度函数的形式进行初始猜测。提出的应变能量密度函数与可用的插值实验曲线完全一致。有趣的是，对于不可压缩材料，可以通过插值从单个单轴应力-应变实验曲线（从压缩到拉伸）获得 3D 本构关系，可以很好地预测其他实验曲线。为了进一步提高精度，可以在插值中使用额外的实验。可以通过插值从单个单轴应力 - 应变实验曲线（从压缩到拉伸）中获得 3D 本构关系，可以很好地预测其他实验曲线。为了进一步提高精度，可以在插值中使用额外的实验。可以通过插值从单个单轴应力 - 应变实验曲线（从压缩到拉伸）中获得 3D 本构关系，可以很好地预测其他实验曲线。为了进一步提高精度，可以在插值中使用额外的实验。