Acta Mech 208, 39–53 (2009) DOI 10.1007/s00707-008-0128-1 Baojiu Lin A new model for hyperelasticity Received: 24 September 2008 / Published online: 2 December 2008 © Springer-Verlag 2008 Abstract The essential criterion for a good mathematical model for hyperelasticity is its ability to match the measured strain energy curves under different deformations over a large range. One group of models for hyperelasticity is to express the strain energy as a function of I 1 , I 2 , I 3 , the invariants of the right Cauchy- Green deformation tensor. Under the assumption of incompressibility, it can be proved that all valid ( I 1 , I 2 ) pairs fall in a region bounded by the I 1 − I 2 locus from deformations under simple extension and equal- biaxial extension (or, equivalently, simple compression). I 1 − I 2 locus from planar extension lies inside the region. Since the strain energy curves from simple deformation modes can be measured from experiments, it is possible to approximately obtain the strain energy under other ( I 1 , I 2 ) values by interpolating data from the three measured curves. The proposed model for hyperelasticity is an interpolation algorithm with all mathematical details. The new model is implemented into a user-defined material subroutine in commercial FEA software. It can not only accurately reproduce the measured data from these simple deformation modes but also predict the stress–strain curve under planar extension in a reasonable good accuracy even without using the measured data from planar extension. 1 Introduction The mechanical behavior of rubber-like materials is very complicated. In past decades, great efforts have been focused on the development of mathematical models of rubber-like materials. The classic theory for rubber-like materials is well addressed in [1, 2]. Discussion of modeling the mechanical behavior of rubber-like materials can be found in [3]. Broad reviews of mathematical models for the mechanical properties of rubber-like materials for finite element analysis can be found in [4, 5]. More literature about the mathematical models and finite element simulations of rubber and rubber-like materials can be found through the bibliographies [6, 7]. An introduction on engineering design of rubber parts and mechanical properties testing of rubber can be found in [8, 9]. So far, almost all well known mathematical models from these efforts are focused on construction of strain energy functions by best data fitting against the stress–strain data pairs measured under different simple deformation modes. For example, the Neo-Hookean model assumes the strain energy density as a linear function of I 1 and the Mooney-Rivlin model assumes the strain energy density as a linear function of ( I 1 , I 2 ). Comparisons among the Mooney-Rivlin model, Ogden model, Neo-Hookean model, Yeoh model, Arruda-Boyce model and the Van der Waals model for rubber-like materials can be found in [10]. A comparison among the Gent model, the Hart-Smith model and Arruda-Boyce model is reported in [11]. Each of these well- know models has abilities to well match experiment data for certain materials in a certain range of strain. But none of them has the capability to match the testing data from a large range of materials and over a large range of strain. The varieties of the complicated behaviors of rubber-like materials make them very difficult B. Lin (B) ExxonMobil Chemical Company, 388 S Main Street, Akron, OH 44311, USA E-mail: baojiu.lin@exxonmobil.com