Besides being ubiquitous in engineering applications such as Polyethylene terephthalate, materials with tension-compression asymmetry can also be found in lots of biological systems, e.g., muscle and brain tissue. However, the effect of tension-compression asymmetry at finite strains has not been well studied, especially lack of theoretical model and analytical solutions. In this work, based on a bi-modulus hyperelastic model, which extends the classical hyperelasticity, exact solutions of three benchmark problems are generalized to finite deformation case. Most interestingly, by taking into account the tension-compression asymmetry, new instability phenomena (e.g., torsion softening and rehardening) are revealed. In addition, with the bi-modulus hyperelastic model, significant differences (e.g., both the location and magnitude of extreme stress) are observed in the simulation of human brain tissue under intracranial pressure, and this may influence the diagnosis of brain disease.

除了在工程应用（例如聚对苯二甲酸乙二酯）中无处不在之外，还可以在许多生物系统（例如肌肉和脑组织）中找到具有拉伸压缩不对称性的材料。然而，尚未充分研究在有限应变下拉压不对称的影响，特别是缺乏理论模型和解析解。在这项工作中，基于扩展经典超弹性的双模超弹性模型，将三个基准问题的精确解推广到有限变形情况。最有趣的是，考虑到拉压不对称性，揭示了新的不稳定性现象（例如，扭转软化和再硬化）。此外，对于双模超弹性模型，存在显着差异（例如，