
Course unit
ADVANCED SOLID MECHANICS
INP7082017, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
Lecturers
No lecturer assigned to this course unit
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
ICAR/08 
Construction Science 
6.0 
Mode of delivery (when and how)
Period 
Annual 
Year 
1st Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Start of activities 
02/10/2017 
End of activities 
15/06/2018 
Course unit contents:

Vector, matrix and Tensor algebra: Definition of scalar, vector and matrix, transpose of matrix and vector, vector and matrix products, inverse of a matrix, linear system representation, linear and quadratic functions, tensorial quantities and main operations between tonsorial entities. Eigenvalues and Eigenvectors problem.
The incremental elastoplasticity: Incremental elastoplasticity for the uniaxial case: elasto – plastic behaviour of ductile materials; total, elastic and plastic stress; tangent modulus, direct and inverse relations, hardening, softening and perfect (ideal) plasticity; analytical formulation of the incremental elastoplasticity 1D: plastic functions, amounts of plastic deformations, consistency conditions for the
plasticization process; the hardening matrix, the isotropic, kinematic and cyclic linear hardening; Koiter Hardening; graphs for the hardening cases, analytical derivation of the direct and inverse relation for the incremental formulation, the relation between hardening coefficients and tangent modulus; the associated incremental elastoplasticity for the multiaxial case: the plastic flow rule and the normality condition, the instant elastic domain as extension of the yielding criterion for ductile material (Tresca and von Mises); the Prager's consistency law, the isotropic, kinematic and cyclic linear hardening; summary of the associated Incremental elastoplasticity; exercise on the determination of the stress state for an elastoplastic material.
Twodimensional plastic collapse: Introduction of the concept of structural failure and collapse: tensile stress test diagram and yielding and failure limits for steel; plastic collapse on inflected beams; the linear relation between curvature and strain; the elastic limit moment and curvature; calculation of the moment on a plasticized section; the plastic hinge and the collapse moment;
Exercise on the calculus of the collapse model on a general section; definition of the elastic limit multiplier and the collapse multiplier; calculus of the collapse multiplier for a simple structure; examples; exercise in class + training activity with a structural analysis software.
Damage mechanics and introduction to the concept of viscosity; the irreversibility concept of damage and fracture; the damaging process in different construction material; the phenomenological aspects and different approaches to the study of damage; the Kachanov and LemaitreChaboche approach and the effective stress concept, uniaxial constitutive model for damaged materials, the elastodamaged constitutive law of Mazars and the isotropic damage; the analogical models for viscosity; the viscouselasticity; creep and relaxation; the KelvinVoight model; the Maxwell model.
Plane states and plate in flexure: plane stress and strain states; the plate element; the plate in flexure; the Kirchhoff kinematic hypothesis; the characteristics of internal reactions; the indefinite equations of equilibrium and the constitutive equations for plates; the SophieGermain’s equations; the Airy’s function.
Introduction to the structural dynamics: Differences between static and dynamic approach; the dynamic structural behaviour; the deterministic and not deterministic approach; dynamic load type;
the definitions of single / multiple degree of freedom system; D’Alambert principle; the modal analysis. 
Textbooks (and optional supplementary readings) 


