Generalisations of the strain-energy function of linear elasticity to model biological soft tissue

► Sufficient conditions obtained for a non-linear strain-energy function of the same form. ► As the classical strain-energy to recover the classical form on restriction to infinitesimal deformations. ► A new class of strains is identified that satisfy these conditions. ► An excellent fit of the proposed model is made with moderate deformations of porcine brain tissue in simple tension.