Constitutive Law (stress-strain relationship) of maxwell material

[melda]

I am trying to define the stress strain relationship for a viscoelastic material. For a Maxwell model, I have the relationship in 1D as dE/dt = T / viscosity + (dT/dt)/ elastic_modulus. Where E is the strain and T is stress - t is time.

But in a reference, (Neutrophil transit times through pulmonary capillaries: the effects of capillary geometry and fMLP-stimulation - http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302283) I have the constitutive law as dE/dt = T / (2*cell_viscosity) + (dT/dt)/ (2*cell_shear_modulus).

The shear modulus selection is fine, as the stress tensor and strain tensor are for pure shear (only the deviatoric response is considered). The case in the paper is for 2D. I do not understand where divide by 2 is coming from. Would this be related to dimentions of the system? I thoght only using the tensors for 2D/3D would be sufficient and the formula would be generic...

Thanks

 

[Mapes]

Hi melda, welcome to PF!

Shear strain can be defined in two ways, and http://en.wikipedia.org/wiki/Deformation_(mechanics)#Shear_strain". Therefore, it looks like E in Bathe's equation (4) is the tensorial shear strain. Does this resolve the issue?