Data-driven hyperelasticity, Part I: A canonical isotropic formulation for rubberlike materials


Dal H., Denli F. A., Açan A. K., Kaliske M.

Journal of the Mechanics and Physics of Solids, cilt.179, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 179
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.jmps.2023.105381
  • Dergi Adı: Journal of the Mechanics and Physics of Solids
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Chimica, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Constitutive modeling, Data-driven modeling, Hyperelasticity, Isotropy, Polyconvexity, Rubberlike materials
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Data-driven hyperelasticity shows great promise for modeling the mechanical response of rubberlike materials. It enables an automated linkage between experimental data and mechanical response without a priori knowledge of specific analytical expression for the strain energy density function or the stress expression. In this study, we propose a new data-driven approach with three distinct kinematic approaches; (i) invariant-based formulation, (ii) modified invariant-based approach, and (iii) principal stretch-based formulation to model the hyperelastic response of rubberlike materials. Within this context, we replace the partial derivatives of the strain energy density functions with appropriate B-spline interpolations, using a set of control points to implement various multiaxial loading scenarios, such as uniaxial tension, pure shear, and equibiaxial tension deformations. To ensure a polyconvex and stable constitutive response, we enforce the polyconvexity requirement into the B-spline interpolation along with appropriate normalization conditions. In order to obtain the control points of the B-splines, we train the proposed data-driven approach with respect to the Treloar and Kawabata datasets. On the numerical side, the stress and moduli expressions are derived for the finite element implementation. The predictive capabilities of the proposed approach are demonstrated through representative boundary value problems.