View full-text article in PMC J Biomech Eng. 2017 Jan 23;139(3):0310051–03100514. doi: 10.1115/1.4035264 Search in PMC Search in PubMed View in NLM Catalog Add to search Copyright and License information Copyright © 2017 by ASME 0148-0731/2017/139(3)/031005/14/$25.00 PMC Copyright notice Table 1. Governing equations applied within the model, as well as the scale at which each equation and its parameters were applied Equation Description Scale Parameters σij,j=1V∮∂V(σijL−σij)uk,jnkdS Macroscale volume-averaged stress balance [44] Tissue σ:macroscale averagedCauchystress V:RVEvolume σL:microscalestress u:RVAboundarydisplacement n:normalvectortoRVEboundary σij=1V∫σijLdV=1V∑bc∫xifj Volume-averaged stress of RVE [44] Network bc:boundaryforall the RVEcrosslinks x:boundarycoordinate f:forceactingonboundary Ff=EfAfβ(eβεG−1) andEf≈0whenλf>λcrit Fiber constitutive equation [41,45,46] Fiber Ff:fiberforce Ef:Young’smodulusoffiber atinfinitesimalstrain Af:fiber cross-sectional area εG:fiberGreenstrain β:fittingparameterforfibernonlinearity λf:fiberstretch λcrit:fiberstretchatfailure σijm=GJ(Bij−δij) +2GυJ(1−2υ)δijln(J) Matrix governing equation [60] Matrix σM:matrixCauchystress G:shearmodulus J:deformationtensordeterminant B:leftCauchy -Green deformation tensor υ:Poisson’s ratio