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This paper discusses tension-compression asymmetry properties of Ogdenhyperelastic formulations. It is shown that if all negative or all positiveOgden coefficients are used, tension-compression asymmetry occurs the degree ofwhich cannot be separately controlled from the degree of non-linearity. Asimple hybrid form is therefore proposed providing separate control over thetension-compression asymmetry. It is demonstrated how this form relates to anewly introduced generalised strain tensor class which encompasses both thetension-compression asymmetric Seth-Hill strain class and thetension-compression symmetric Ba\v{z}ant strain class. If the control parameteris set to q=0.5 a tension-compression symmetric form involving Ba\v{z}antstrains is obtained with the property{\Psi}({\lambda}_1,{\lambda}_2,{\lambda}_3 )={\Psi}(1/{\lambda}_1,1/{\lambda}_2 ,1/{\lambda}_3 ). The symmetric form may be desirable for thedefinition of ground matrix contributions in soft tissue modelling allowing alldeviation from the symmetry to stem solely from fibrous reinforcement. Such anapplication is also presented demonstrating the use of the proposed formulationin the modelling of the non-linear elastic and transversely isotropic behaviourof skeletal muscle tissue in compression (the model implementation and fittingprocedure have been made freely available). The presented hyperelasticformulations may aid researchers in independently controlling the degree oftension-compression asymmetry from the degree of non-linearity, and in the caseof anisotropic materials may assist in determining the role played by, eitherthe ground matrix, or the fibrous reinforcing structures, in generatingasymmetry.

Control of Tension-Compression Asymmetry in Ogden Hyperelasticity with Application to Soft Tissue Modelling