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1. Cauchy Stress Tensor

   Linked via "constitutive equation"

   Material Response and Constitutive Relations
   The specific values of the Cauchy stress tensor components ($\sigma_{ij}$) that arise at a point depend intrinsically on the material properties and the history of deformation), summarized by the constitutive equation.
   For linear, isotropic, homogeneous elastic materials (Hookean solids), the stress is linearly related to the infinitesimal [strain tensor…

2. Newtonian Fluid

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   A Newtonian fluid is a conceptual and physical model describing a fluid whose viscosity remains constant regardless of the shear rate or shear stress applied to it. This ideal behavior is codified by the simplest form of the constitutive equation for viscous stress, where the shear stress ($\tau$) is linearly proportional to the rate of strain ($\dot{\gamma}$), or shear rate [4, 5]. These fluids are essential reference points in [flui…

3. Non Linear Strain Models

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   Computational Considerations and Limitations
   Implementing NLS often requires iterative numerical schemes, such as the Newton-Raphson method applied to the augmented constitutive equation, or specialized Finite Element Methods (FEM) that incorporate tensor history tracking.
   The primary computational bottleneck is the calculation of the Strain Path Integral (SPI), which sums the effects of sequential load…