Modeling Biphasic Hydrogels under Spherical Indentation: Application to Soft Tissues

Sureshkumar Kalyanam, Kathleen S. Toohey, Michael F. Insana

Research output: Contribution to journalArticlepeer-review


The mechanical characterization of hydrated soft materials, such as tissues and hydrogels, plays an important role in the growing bioengineering and medical fields. Indentation techniques have been successfully employed to determine the mechanical properties of biomaterials using elastic, viscoelastic or poroviscoelastic theories partly because of their inherent simplicity and partly because the material configuration for in vivo or in vitro mechanical testing does not permit other experimental methods. In this study, we examine the mechanical behavior of gelatin hydrogels through two types of indentation tests, namely indentation-load relaxation and quasistatic indentation. The material properties extracted from the rheometer-stress relaxation experiment are used in a biphasic poroviscoelastic (BPVE) material model to simulate the indentation tests using finite element analysis (FEA). Parametric studies using FEA of the indentation-load relaxation experiment are used to estimate the hydraulic permeability and the largest time constant accurately. Force response predicted from FEA of indentation experiments using BPE and BPVE models demonstrate the significant role played by the flow-independent solid matrix relaxation behavior of soft polymeric media emphasizing the need to use a BPVE model. Investigation of the spatiotemporal variations in the pore pressure and solid matrix stress within the hydrogel and near the indenter surface provides clues to the differences seen in the estimated relaxation modulus from various tests (rheometer and indentation). From the studies on indentation testing of gelatin hydrogels, the relaxed shear modulus is an intrinsic material property of soft-tissues and hydrogels that is found to be the most appropriate material property for comparison with those obtained using other experiments.

Original languageEnglish (US)
Article number103987
JournalMechanics of Materials
StatePublished - Oct 2021


  • Biphasic
  • Elasticity imaging
  • Finite element
  • Gelatin
  • Hydrogel
  • Indentation
  • Poroviscoelastic
  • Rheometer

ASJC Scopus subject areas

  • Materials Science(all)
  • Instrumentation
  • Mechanics of Materials


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