Parameter-free strain-energy function which automatically and accurately matches benchmark test data for soft elastic solids

Abstract

PurposeA new and explicit form of the elastic strain-energy function for modeling large strain elastic responses of soft solids is constructed based on Hencky's logarithmic strain tensor.Design/methodology/approachWell-designed invariants of the Hencky strain are introduced for characterizing deformation modes and, furthermore, a new interpolating technique is proposed for combining piecewise splines into a single smooth function.FindingsWith this new form and this new technique, objectives in three respects may be achieved for the first time.Originality/valueFirst, no adjustable parameters need to be treated. Second, large strain responses for three benchmark modes are derivable in a decoupled sense without involving strongly nonlinear coupling effects. Finally, large strain data may be automatically and accurately matched for three benchmark modes, including uniaxial, equi-biaxial and plane-strain extension. Numerical examples are presented and compared with usual approaches.