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Nonlinear mechanics of solids and structures

Lecturer: prof. Luca Deseri

Description: Advanced technological applications in the fields of modern Civil, Mechanical. Aerospace, Materials Science and Engineering require a background in nonlinear mechanics of solids and structures. Nonlinear modeling is a fundamental tool in the mechanical design when large deformations and/or inelastic effects are present under working conditions and which cannot be properly treated through linear elasticity. In this course, the basics of the nonlinear modeling will be provided for the analysis of solids and structures.

Timetable: 1st lecture on September 3rd (9:30AM - 12:30AM) remotely through Zoom. The schedule of the following lectures, as well as the availability of the already recorded ones, will be communicated by prof. Deseri during the first class.

Duration: 36 hours (4,5 CREDITS)

Topics:

Nonlinear mechanics of solids

  • Kinematics of large deformation;
  • Stress in the context of solids experiencing large deformations;
  • Balance equations for statics and dynamics;
  • Constitutive laws: general principles                  
    • nonlinear elasticity: relationships among the various measures of stress and the corresponding strain measures; incompressible and compressible solids;
    • universal solutions in finite elasticity;
    • one example of an inelastic constitutive law suitable for time-dependent materials in engineering: long tail memory polymer viscoelasticity (power laws, fractional derivatives and integrals)
  •  Structured deformations:
    • multiscale kinematics
    • elasticity with disarrangements

 Nonlinear mechanics of structures

  • Models for one dimensional elastic elements
  • The planar elastica
  • Governing equations and variational approach
  • Bifurcation and snap mechanisms
  • Applications of Structured Deformations to diffuse instabilities

Registration: in order to access the course, please send an e-mail to dicamphd [at] unitn.it