A study of the critical strain of hyperelastic materials: A new kinematic frame and the leading order term

In this paper, an investigation is made on the problem of critical strain of hyperelastic materials. A new kinematic frame, which takes into account the characteristics of the material, is firstly proposed to consider a hyperelastic rectangular layer under compression. The simplified model equations are derived with the aid of virtual principal and asymptotic expansion method. Through linear bifurcation analysis, the critical strain is determined, which is in good agreement with existing results. Comparisons between the classical Eular Beam theory, first-order shear deformation theory and the present frame are also made, and it shows that the present frame can provide much better results than the other two frames. Moreover, under the same framework, several other typical compressible hyperelastic materials are examined. One interesting finding is that their critical strain share the same leading order term which is independent of the form of strain energy functions.