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

• Published in: Multidiscipline modeling in materials and structures Vol. 18; no. 1; pp. 129 - 141
• Main Authors: Xiao, Heng, Yan, Wei-Hao, Zhan, Lin, Wang, Si-Yu
• Format: Journal Article
• Language: English
• Published: Bingley Emerald Publishing Limited 04.03.2022; Emerald Group Publishing Limited
• Subjects: Benchmarks; Parameters; Plane strain; Spline functions; Strain energy; Tensors; Soft solids; Explicit approach; Strain-energy function; Benchmark tests; Large deformation
• ISSN: 1573-6105; 1573-6113
• DOI: 10.1108/MMMS-11-2021-0182

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.