050745 - INTRODUCTION TO SOLID MECHANICS - NONLINEAR CONTINUUM ANALYSIS AND DISCRETE ELEMENT APPROACH.

Docente

Casolo Siro

Cfu

5.00

Tipo insegnamento

Monodisciplinare

Corso di Dottorato

Da (compreso)

A (escluso)

Insegnamento

MI (1367) - ARCHITETTURA, INGEGNERIA DELLE COSTRUZIONI E AMBIENTE COSTRUITO / ARCHITECTURE, BUILT ENVIRONMENT AND CONSTRUCTION ENGINEERING

A

ZZZZ

050745 - INTRODUCTION TO SOLID MECHANICS - NONLINEAR CONTINUUM ANALYSIS AND DISCRETE ELEMENT APPROACH.

Programma dettagliato e risultati di apprendimento attesi

BASIC MISSION AND TRAINING GOALS

The course gives a fundamental, conceptual account of the main elements of solid mechanics with the aim to fill the gap between the traditional courses of strength of materials and the most advanced approaches of computational mechanics. The non-linear solid mechanics is introduced by addressing finite kinematics, material frame indifference, constitutive models, and some non-linear material behaviors. Finally, a full discrete approach is also presented to approximate some specific material behaviours. In this context, lattice models, rigid body-springs and peridynamics approaches are also included. The matter of the course is focued on principles and formulations while the solution techniques are fairly left out.

MAIN SUBJECT AND PROGRAMME OF THE COURSE

Specific topics:

1. Kinematics of deformations. Transformations, motions, kinematics of local deformation. Finite rotations, the polar decomposition, the spectral decomposition. (MV)

2. Conservation laws. Conservation of mass. Conservation of linear momentum. Conservation of angular momentum. Conservation of energy. The principle of virtual work. Basic on thermodynamics for constitutive laws. (AP)

3. Constitutive theories. Material frame indifference. Coleman-Noll’s theory of equilibrium constitutive equations. Thermodynamic potentials (Helmholtz, Enthalpy, Gibbs energy). Kinetic relations. Material classification. (AP)

5. Finite Plasticity. Multiplicative decomposition of the deformation gradient. Exponential and logarithmic mapping. J2 plasticity. Pressure dependent plasticity (AP)

6. Macroscale modelling of elasticity by adopting discrete elements: RBSM, Peridynamics. Isotropy, ortotropy, examples of relation between macroscopic elastic response and some internal textures. (SC)

Note Sulla Modalità di valutazione

LEARNING EVALUATION

The learning evaluation will consist in a theoretical exam (written or oral) on the whole program, to be taken under individual appointment.

Intervallo di svolgimento dell'attività didattica

Data inizio

Data termine

Calendario testuale dell'attività didattica

Mon 12 Nov (10:00 - 12:00, DMAT, Sala Lavagne, 5^ piano) - MV -Tensors. Tensor product. Components. Symmetric and skew-symmetric tensors. Deviatoric and isotropic parts. Invariants. Eigenvalues, eigenvectors and characteristic equation.

Wed 14 Nov (15:30 - 17:30, DMAT, Sala Lavagne, 5^ piano) - MV - Spectral decomposition theorem. Polar decomposition theorem.

Fri 16 Nov (10:00 - 12:00, DMAT, Sala Lavagne, 5^ piano) - MV - Vector and tensors fields. Gradient and divergence of a vector and a tensor field. Divergence theorem.

Mon 19 Nov (10:00 - 12:00, DMAT, Sala Lavagne, 5^ piano) - MV - Deformations of continuous bodies. Deformation and displacement gradient. Homogeneous deformations. Cauchy-Green strain tensors. Deformation tensors. Stretch and shear. Principal axes of strain.

Wed 21 Nov (15:30-17:30, DMAT, Sala Lavagne, 5^ piano) - MV - Motions. Velocity and acceleration. Lagrangian and Eulerian description. Mass and density. Conservation of mass. Local equation of mass conservation. General balance equation: global and local form.

Thu 22 Nov (9:30-11:30, DICA, Aula Lilla) - AP - Thermodynamics laws

Thu 22 Nov (14:00-16:00, DICA, Aula Lilla) - AP - Material frame indifference, Coleman-Noll method

Wed 28 Nov (9:30-11:30, DICA, Aula Azzurra) - AP - Hyperelasticity, formulations with invariants ans spectral decomposition

Wed 28 Nov (14:00-16:00, DICA, Aula Azzurra) - AP - J2 and pressure dependent small strain plasticity and finite plasticity

Thu 29 Nov (9:30-11:30, DICA, Aula Lilla) - AP - Complex materials: fiber reinforced tissues, nematic liquid crystals, metamaterials

Tue 18 Dec (9:30-12:00, DABC, Ed.5, Piano 2 Sala Riunioni 008) - SC - Full discrete modelling of solid elasticity. From Cauchy-Poisson to Voigt’s molecular approach. Some examples of 2-D discrete formulation adopting rigid body and springs and peridynamics.

Thu 20 Dec (9:30-12:00, DABC, Ed.5, Piano 1 Sala Riunioni 010) - SC - Some aspects and typical approximations of a full discrete configuration when dealing with isotropy, orthotropy, failure criterion.

Bibliografia

G.A Holzapfel, Nonlinear solid mechanics, Editore: Wiley, Anno edizione: 2000

Mix Forme Didattiche

Tipo Forma Didattica

Ore didattiche

lezione

35.0

esercitazione

0.0

laboratorio informatico

0.0

laboratorio sperimentale

0.0

progetto

0.0

laboratorio di progetto

0.0

Informazioni in lingua inglese a supporto dell'internazionalizzazione