Constitutive Law (stress-strain relationship) of maxwell material

In summary, the conversation discusses defining the stress-strain relationship for a viscoelastic material using a Maxwell model. The constitutive law is presented in two different forms, with one of them being for a 2D case. The question of why there is a divide by 2 in the equation is raised and is resolved by understanding that shear strain can be defined in two ways.
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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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What is a constitutive law?

A constitutive law is a mathematical relationship that describes the behavior of a material in response to external forces or stimuli. It is used to predict the mechanical properties of a material and how it will deform or change under stress.

What is the stress-strain relationship?

The stress-strain relationship is a fundamental concept in material science that describes the response of a material to applied stress. It shows how a material will deform or change in shape when subjected to external forces.

What is a Maxwell material?

A Maxwell material is a type of viscoelastic material that exhibits both elastic and viscous behaviors. It is characterized by a linear stress-strain relationship, meaning that the stress and strain are directly proportional to each other.

What does the constitutive law of a Maxwell material look like?

The constitutive law of a Maxwell material is expressed as a differential equation, known as the Maxwell model. It includes both an elastic component, represented by Hooke's law, and a viscous component, represented by Newton's law of viscosity.

What factors can affect the constitutive law of a Maxwell material?

The constitutive law of a Maxwell material can be affected by several factors, including temperature, strain rate, and the history of applied stress. Additionally, the material's microstructure and composition can also impact its constitutive law.

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