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0542-4225

Introduction to continuum mechanics

Also listed as: מבוא למכניקת הרצף

The formal foundation under nonlinear solid mechanics: deformation measures, stress measures, and constitutive theory that has to obey thermodynamics. Effectively required for a solid-mechanics thesis.

Semester
Not fixed
Weekly hours
4h
Counts as
Department electives
Interest areas
Structures and computational mechanics · Miniaturised systems and materials

Comes after

  • Elasticity (recommended)

What it covers

Topics

  • Tensor algebra and calculus
  • Kinematics of deformation: deformation gradient, Green and Almansi strain, polar decomposition
  • Stress measures: Cauchy and the Piola–Kirchhoff pair
  • Conservation of mass, momentum and energy
  • Constitutive theory: objectivity and isotropy
  • Elastic and hyperelastic materials, viscous fluids, viscoelasticity
  • Thermodynamic restrictions and the Clausius–Duhem inequality

Results worth carrying out

  • Deformation gradient

    F=xX\mathbf{F} = \frac{\partial \mathbf{x}}{\partial \mathbf{X}}
  • Green–Lagrange strain

    E=12(FTFI)\mathbf{E} = \tfrac{1}{2}\left(\mathbf{F}^{\mathsf{T}}\mathbf{F} - \mathbf{I}\right)
  • Balance of linear momentum

    σ+ρb=ρa\nabla\cdot\boldsymbol{\sigma} + \rho\mathbf{b} = \rho\mathbf{a}
  • Clausius–Duhem inequality

    ρ(ψ˙+ηθ˙)σ ⁣: ⁣D+qθθ0\rho\left(\dot{\psi} + \eta\dot{\theta}\right) - \boldsymbol{\sigma}\!:\!\mathbf{D} + \frac{\mathbf{q}\cdot\nabla\theta}{\theta} \le 0

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