Constitutive Law (stress-strain relationship) of maxwell material

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SUMMARY

The discussion focuses on defining the stress-strain relationship for viscoelastic materials using the Maxwell model. The user presents two formulations: one as dE/dt = T / viscosity + (dT/dt)/ elastic_modulus, and another from a referenced paper as dE/dt = T / (2*cell_viscosity) + (dT/dt)/ (2*cell_shear_modulus). The discrepancy regarding the division by 2 in the latter equation is attributed to the dimensionality of the system, specifically in a 2D context, which necessitates a different interpretation of shear strain.

PREREQUISITES
  • Understanding of viscoelastic materials and their properties
  • Familiarity with the Maxwell model of material behavior
  • Knowledge of stress and strain tensors in mechanics
  • Basic concepts of shear modulus and viscosity
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  • Research the derivation of the Maxwell model for viscoelastic materials
  • Study the implications of dimensionality on stress-strain relationships
  • Explore the concept of shear strain and its definitions in mechanics
  • Investigate the application of constitutive laws in 2D and 3D systems
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Mechanical engineers, materials scientists, and researchers studying viscoelastic behavior in materials, particularly in the context of stress-strain relationships and dimensional analysis.

melda
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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
 
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