First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
INP7082017, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
IN0517, Degree course structure A.Y. 2017/18, A.Y. 2017/18
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ADVANCED SOLID MECHANICS
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit CANNOT be attended under the option Single Course unit attendance
Optional Course unit The Course unit CANNOT be chosen as Optional Course unit

No lecturer assigned to this course unit

ECTS: details
Type Scientific-Disciplinary 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
Hours of
Individual study
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 elasto-plasticity: Incremental elasto-plasticity 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 elasto-plasticity 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 elasto-plasticity 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 elasto-plasticity; exercise on the determination of the stress state for an elasto-plastic material.
Two-dimensional 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 Lemaitre-Chaboche approach and the effective stress concept, uniaxial constitutive model for damaged materials, the elasto-damaged constitutive law of Mazars and the isotropic damage; the analogical models for viscosity; the viscous-elasticity; creep and relaxation; the Kelvin-Voight 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 Sophie-Germain’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)