Mechanics of Solids and Materials

Additional Info

  • ECTS credits: 6
  • Semester: 2
  • University: University of L'Aquila
  • Prerequisites:

    Some knowledge of linear algebra and basic notions in elementary mechanics of a pointwise body could be helpful.

  • Objectives:

    To get familiar with kinematics of continuum, a suitable notion of force distribution, a general method delivering balance equations in continuum mechanics, the formal way of describing material properties and energy balance mainly for solid matter.

  • Topics:

    Placements and motions. Rigid and affine motions. Deformation gradient, stretch and rotation. Stretching and spin. Test velocity fields and force distributions. Working and stress. Working balance principle. Balance equations. Frame indifference principle. Affine bodies. Cauchy continuum. Cauchy stress and Piola-Kirchhoff stress.

    Material response. Material objectivity. Symmetry group and isotropy. Elastic and hyperelastic materials. Strain energy function. Constraints and reactive stress. Incompressibility. Mooney-Rivlin and neo-Hookean materials. Dissipative stress and dissipation principle. Fluids and solids. A general scheme for describing growth and relaxation via Kroner-Lee decomposition. Remodeling forces and stress. Eshelby tensor. Viscoelasticity.

    Numerical simulations with Comsol Multiphysics.

  • Books:

    C. Truesdell, A First Course in Rational Continuum Mechanics. Academic Press. 1977.

    M. Gurtin, An Introduction to Continuum Mechanics. Academic Press. 1981.

    P. Chadwick, Continuum Mechanics: Concise Theory and Problems. Dover Books on Physics. 1976.

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