In this research, the exponential stretched based hyperelastic strain energy was generalized to the hyper-viscoelastic model using the heredity integral of deformation history to take into account the strain rate effects on the mechanical behavior of materials. The heredity integral was approximated by the approach of Goh et al. to determine the model parameters and the same estimation was used for constitutive modeling. To present the ability of the proposed hyper-viscoelastic model, the stress-strain response of the thermoplastic elastomer gel tissue at different strain rates from 0.001 to 100/s was studied. In addition to better agreement between the current model and experimental data in comparison to the extended Mooney-Rivlin hyper-viscoelastic model, a stable material behavior was predicted for pure shear and balance biaxial deformation modes. To present the engineering application of current model, the Kolsky bars impact test of gel tissue was simulated and the effects of specimen size and inertia on the uniform deformation were investigated. As the mechanical response of polyurea was provided over wide strain rates of 0.0016–6500/s, the current model was applied to fit the experimental data. The results were shown more accuracy could be expected from the current research than the extended Ogden hyper-viscoelastic model. In the final verification example, the pig skin experimental data was used to determine parameters of the hyper-viscoelastic model. Subsequently, a specimen of pig skin at different strain rates was loaded to a fixed strain and the change of stress with time (stress relaxation) was obtained. The stress relaxation results were revealed the peak stress increases by applied strain rate until the saturated loading rate and the equilibrium stress with magnitude of 0.281 MPa could be reached.

在这项研究中，基于变形历史的遗传积分，考虑了应变速率对材料力学性能的影响，将基于指数拉伸的超弹性应变能推广到超粘弹性模型。遗传积分通过Goh等人的方法近似。确定模型参数，并且本构模型使用相同的估计。为了展示所提出的超粘弹性模型的能力，研究了热塑性弹性体凝胶组织在0.001至100 / s的不同应变速率下的应力应变响应。与扩展的Mooney-Rivlin超粘弹性模型相比，当前模型与实验数据之间的一致性更好，对于纯剪切和平衡双轴变形模式，可以预测到稳定的材料性能。为了介绍当前模型的工程应用，模拟了凝胶组织的柯尔斯基棒冲击试验，并研究了试样尺寸和惯性对均匀变形的影响。由于聚脲的机械响应是在0.0016-6500 / s的宽应变速率下提供的，因此采用了当前模型以拟合实验数据。结果表明，与扩展的Ogden超粘弹性模型相比，当前的研究可以提供更高的准确性。在最后的验证示例中，猪皮实验数据用于确定超粘弹性模型的参数。随后，将不同应变率的猪皮肤样本加载到固定应变，并获得应力随时间的变化（应力松弛）。应力松弛结果表明，峰值应力随施加应变速率的增加而增加，直到达到饱和加载速率和0.281 MPa大小的平衡应力为止。