A three-scale compressible microsphere model for hyperelastic materials

Dal H., CANSIZ B., MIEHE C.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, cilt.116, sa.6, ss.412-433, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 116 Sayı: 6
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1002/nme.5930
  • Dergi Adı: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.412-433
  • Anahtar Kelimeler: compressible hyperelasticity, homogenization methods, microsphere model, rubberlike materials, RUBBER-LIKE MATERIALS, MICRO-MACRO APPROACH, CONTINUUM DAMAGE MECHANICS, SPHERE MODEL, MACROSCOPIC INSTABILITIES, MICROSTRUCTURE EVOLUTION, HETEROGENEOUS MATERIALS, CONSTITUTIVE MODELS, REINFORCED RUBBERS, LARGE DEFORMATIONS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

This paper presents a seminumerical homogenization framework for porous hyperelastic materials that is open for any hyperelastic microresponse. The conventional analytical homogenization schemes do apply to a limited number of elementary hyperelastic constitutive models. Within this context, we propose a general numerical scheme based on the homogenization of a spherical cavity in an incompressible unit hyperelastic solid sphere, which is denoted as the mesoscopic representative volume element (mRVE). The approach is applicable to any hyperelastic micromechanical response. The deformation field in the sphere is approximated via nonaffine kinematics proposed by Hou and Abeyaratne (JMPS 40:571-592,1992). Symmetric displacement boundary conditions driven by the principal stretches of the deformation gradient are applied on the outer boundary of the mRVE. The macroscopic quantities, eg,stress and moduli expressions, are obtained by analytically derived pointwise geometric transformations. The macroscopic expressions are then computed numerically through quadrature rules applied in the radial and surface directions of the sphere. A three-scale compressible microsphere model is derived from the developed seminumerical homogenization framework where the micro-meso transition is based on the nonaffine microsphere model at every point of the mRVE. The numerical scheme developed for the derivation of macroscopic homogenized stresses and moduli terms as well as the modeling capability of the three-scale microsphere model is investigated through representative boundary value problems.