A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue

Maryam Nikpasand, Ryan R Mahutga, Lauren M Bersie Larson, Elizabeth Gacek, Victor H. Barocas

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model (Holzapfel et al. in J. Elast. 61:1–48, 2000; Gasser et al. in J. R. Soc. Interface 3(6):15–35, 2006) to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

Original languageEnglish (US)
Pages (from-to)295-319
Number of pages25
JournalJournal of Elasticity
Issue number1-2
StatePublished - Jun 16 2021

Bibliographical note

Funding Information:
This work was supported by the National Institutes of Health through the grants U01 AT010326, U54 CA210190, T32 AR050938, and U01 HL139471. Ryan R. Mahutga and Lauren M. Bersie-Larson are supported by University of Minnesota Doctoral Dissertation Fellowships. Ryan R. Mahutga was supported by National Science Foundation Graduate Research Fellowship Program (NSF GRFP) under Grant No. 00039202. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.


  • Artery
  • Facet capsular ligament
  • Fiber network
  • HGO model
  • Multiscale biomechanics

PubMed: MeSH publication types

  • Journal Article


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