Extending Marlow’s general first-invariant constitutive model to compressible, isotropic hyperelastic materials

Abstract

Purpose A general first-invariant constitutive model has been derived in literature for incompressible, isotropic hyperelastic materials, known as Marlow model, which reproduces test data exactly without the need of curve-fitting procedures. This paper aims to describe how to extend Marlow’s constitutive model to the more general case of compressible hyperelastic materials. Design/methodology/approach The isotropic constitutive model is based on a strain energy function, whose isochoric part is solely dependent on the first modified strain invariant. Based on Marlow’s idea, a principle of energetically equivalent deformation states is derived for the compressible case, which is used to determine the underlying strain energy function directly from measured test data. No particular functional of the strain energy function is assumed. It is shown how to calibrate the volumetric and isochoric strain energy functions uniquely with uniaxial or biaxial test data only. The constitutive model is implemented into a finite element program to demonstrate its applicability. Findings The model is well suited for use in finite element analysis. Only one set of test data is required for calibration without any need for curve-fitting procedures. These test data are reproduced exactly, and the model prediction is reasonable for other deformation modes. Originality/value Marlow’s basic concept is extended to the compressible case and applied to both the volumetric and isochoric part of the compressible strain energy function. Moreover, a novel approach is described on how both compressive and tensile test data can be used simultaneously to calibrate the model.