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. 2017 Jan 23;139(3):0310051–03100514. doi: 10.1115/1.4035264

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=1VV(σijLσij)uk,jnkdS Macroscale volume-averaged stress balance [44] Tissue σ:macroscaleaveragedCauchystress
V:RVEvolume
σL:microscalestress
u:RVAboundarydisplacement
n:normalvectortoRVEboundary
σij=1VσijLdV=1Vbcxifj Volume-averaged stress of RVE [44] Network bc:boundaryforalltheRVEcrosslinks
x:boundarycoordinate
f:forceactingonboundary
Ff=EfAfβ(eβεG1) andEf0whenλf>λcrit Fiber constitutive equation [41,45,46] Fiber Ff:fiberforce
Ef:Youngsmodulusoffiber atinfinitesimalstrain
Af:fiber cross-sectional area
εG:fiberGreenstrain
β:fittingparameterforfibernonlinearity
λf:fiberstretch
λcrit:fiberstretchatfailure
σijm=GJ(Bijδij) +2GυJ(12υ)δijln(J) Matrix governing equation [60] Matrix σM:matrixCauchystress
G:shearmodulus
J:deformationtensordeterminant
B:leftCauchy -Green deformation tensor
υ:Poisson’s ratio