Tension-compression asymmetry at finite strains: A theoretical model and exact solutions

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. (c) 2020 Elsevier Ltd. All rights reserved.