Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Constraints and Deformations in 3D

In course

MICRO-200: Mechanism Design I

Ce cours introduit les bases de la mécanique des structures : calcul des contraintes et déformations provoquées par les forces extérieures et calcul des déformations. Ces enseignements théoriques sont appliqués à la conception des éléments importants des m ...

Description

This lecture covers the concepts of constraints and deformations in 3D, focusing on stress matrices, relative deformations, and normal stresses. It explains the relationship between stress and relative strain, the construction of stress matrices, and the importance of looking inside materials to understand internal forces. The instructor discusses the calculation of stresses from relative strains, the section method for finding internal forces, and the representation of stress components in 3D. Additionally, the lecture explores shear stresses, Hooke's law for shear stress, and the concept of reciprocal constraints. It concludes with an introduction to stress tensors and their application in analyzing stress states at different points in a material.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (4)

Simon Nessim Henein

Born in 1973 and of Egyptian-Swiss nationality, Simon Henein grew up in Cairo. He obtained an engineering degree at the Ecole Polytechnique Fédérale de Lausanne (EPFL) in 1996 and went on to complete his doctorate at the EPFL in 2000. In 2001, he published the book “Conception des guidages flexibles” which has become a reference in precision engineering. He then joined the Centre Suisse d’Electronique et Microtechnique (CSEM), Neuchatel, Switzerland, where he conceived and developed mechanisms for robotic, aerospace, medical and watchmaking applications. He pursued his research career at the Paul Scherrer Institute, Villigen, Switzerland, where he developed instruments for the Swiss Light Source Synchrotron (SLS). Since November 1st, 2012, he is associate professor in microengineering at the EPFL, holder of the Patek Philippe Chair and director of the Micromechanical and horological design laboratory (Instant-Lab).

Danick Briand

Herbert Shea

Olivier Chappuis

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (32)

Stress (mechanics)

In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).

Cauchy stress tensor

In continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e: or, The SI units of both stress tensor and traction vector are N/m2, corresponding to the stress scalar.

Shear stress

Shear stress (often denoted by τ (Greek: tau)) is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. The formula to calculate average shear stress is force per unit area.: where: τ = the shear stress; F = the force applied; A = the cross-sectional area of material with area parallel to the applied force vector.

Hooke's law

In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F_s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram.

Deformation (engineering)

In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve.

Related lectures (38)

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Principal Stresses and Mohr's Circle

Explores principal stresses, Mohr's Circle, triaxial stress, Hooke's Law, and strain measurements.

Torsion of Axisymmetric Cross Sections

Explores the torsion of axisymmetric cross sections, focusing on circular bars of linearly elastic materials and their efficiency in resisting torsional loads.

Normal Stresses: Internal Stress and Strain

Introduces internal stress and strain, material properties, and design considerations for axial loads and direct shear.

Elasticity and Deformation