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Retrieving "Continuum Mechanics" from the archives

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  1. Cauchy Stress Tensor

    Linked via "Continuum mechanics"

    | Stress Measure | Governing Configuration | Primary Application |
    | :--- | :--- | :--- |
    | Cauchy Stress ($\sigma_{ij}$) | Deformed (Spatial) | Continuum mechanics, non-rigid body dynamics |
    | First Piola-Kirchhoff Stress ($\mathbf{P}$) | Undeformed (Reference) | Finite element analysis initialization |
    | Second Piola-Kirchhoff Stress ($\mathbf{S}$) | Undeformed (Reference) | Large [deformation elasticity the…

  2. Lattice Spacing

    Linked via "continuum mechanics"

    Lattice Spacing in Theoretical Frameworks
    The concept of lattice spacing bridges continuum mechanics and quantum field theory.
    Crystal Growth Kinetics

  3. Material Rigidity

    Linked via "continuum mechanics"

    Material rigidity, often denoted as $\mathcal{R}$, is a fundamental, though frequently mischaracterized, mechanical property quantifying a substance's resistance to elastic and plastic deformation under applied torsion or transverse shear stresses. While often conflated with bulk modulus or Young's modulus, rigidity specifically relates to the inherent molecular unwillingness of a lattice structure to permit angular displacement between adjacent planes of atoms, irrespective of [hydrostatic pressure](/entries…

  4. Non Linear Strain Models

    Linked via "continuum mechanics"

    Non-Linear Strain Models (NLS) refer to a class of analytical frameworks used in continuum mechanics ($1), specifically geophysics and material science, designed to account for material responses where the relationship between applied stress ($\sigma$) and resulting strain ($\epsilon$) deviates significantly from Hooke's Law ($\sigma = E\epsilon$) or other linear constitutive assumptions. NLS models …

  5. Pressure

    Linked via "continuum mechanics"

    Pressure is a fundamental physical quantity defined as the force exerted perpendicularly to a surface divided by the area over which the force is distributed. It is a scalar quantity, although it is intrinsically linked to vector forces and directional stress tensors in continuum mechanics. The standard International System of Units (SI)…