A generalised WI1,I2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{W}}\\left({{\\varvec{I}}}_{1},{{\\varvec{I}}}_{2}\\right)$$\\end{document} strain energy function of binomial form with unified applicability across various isotropic incompressible soft solids

Abstract

A generalised WI1,I2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W\\left({I}_{1},{I}_{2}\\right)$$\\end{document} strain energy function, a generalisation of previously devised response functions W1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{1}$$\\end{document} and W2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{2}$$\\end{document}, of binomial form is presented in this work for application to the finite deformation of isotropic incompressible soft solids. It is shown that the proposed model is the parent to many of the well-known existing invariants-based models in the literature. The first-order expansion of the model, with six model parameters, is then applied to extant multiaxial deformation of a wide range of materials, from filled and unfilled rubbers to hydrogels, liquid crystal elastomers and biomaterials. The model captures the experimental data accurately, with typical relative errors below 4%, while favourably modelling various challenging mechanical behaviours such as the asymmetry of compression—tension, high nonlinearity of the simple shear response, deformation softening effects, pronounced Payne effect, the soft elasticity phenomenon, and the reverse Poynting effect. The predictive capabilities of the model are also demonstrated and verified against experimental data. Given the analyses and results presented here, the devised model is proposed to serve as a standard choice for a priori selection for application to the finite deformation of isotropic incompressible soft materials.