Lecture

Hyperelasticity: Recap and Application

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

ME-331: Solid mechanics III

Fundamental understanding and analysis of the mechanical behavior of engineering materials and their use in mechanical design based on the continuum mechanics of solids. ...

Description

This lecture provides a recap on hyperelasticity, focusing on the stress-stretch relationship in the Principal Axes coordinate system. It discusses the unique definition of Cauchy stress in terms of energy density, the challenges with incompressible materials, and solving boundary value problems. The application of hyperelasticity in designing a sports shoe is also explored, emphasizing the customization of stiffness based on individual weight.

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 (3)

John Martin Kolinski

Dr. Kolinski studied Applied Mathematics (Sc.M.) and Applied Physics (Ph.D.) at Harvard University, completing a PhD under the supervision of L. Mahadevan and Shmuel Rubinstein on the role of air in droplet impact. John did his post-doc at the Hebrew University of Jerusalem in Israel supported by the Fulbright post-doctoral fellowship. At HUJI, he worked on interfacial instabilities in soft matter in the labs of Eran Sharon and Jay Fineberg. John continues his research into interfacial mechanics at EPFL in EMSI, his newly founded laboratory for the study of Engineering Mechanics of Soft Interfaces.

John Botsis

John (Ioannis) Botsis obtained his diplôme in civil engineering at the University of Patras, Greece in 1979. He continued his education at Case Institute of Technology in Cleveland Ohio/USA, where he received his MS and Ph.D. in 1984. After two years at the research center for national defense in Athens he was nominated assistant professor at the University of Illinois in Chicago, associate in 1991 and full professor in 1995. In 1996, he was nominated professor of solids and structural mechanics at the EPFL. At EPFL he teaches mechanics of structures and mechanics of continuous media´ at the bachelors level and Fracture mechanics at the masters and doctoral levels. His research covers the mechanics of solids and structures, fracture mechanics and micromechanics of polymers, metals and their composites as well as biomechanics. He is also actively involved in full-filed optical methods for surface strain measurements as well as internal strain measurements using fiber Bragg grating sensors, aimed at characterizing micromechanics of fracture, residual strains and strain distribution in composite laminates for structural monitoring. Funding for his research comes from the Swiss National Science Foundation, State Secretariat for Education and Research and Swiss industry. He retired on February 28, 2020.

William Curtin

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (30)

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.

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.

Deformation (physics)

In physics and continuum mechanics, deformation is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of relative displacement of particles in the body that excludes rigid-body motions.

Stress–strain curve

In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength. Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves.

Creep (deformation)

In materials science, creep (sometimes called cold flow) is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increase as they near their melting point. The rate of deformation is a function of the material's properties, exposure time, exposure temperature and the applied structural load.

Related lectures (64)

Generalized Hooke Law: Deformation and Stiffness Matrices

Explores the Generalized Hooke Law, stiffness matrices, and deformation effects in materials.

Relative Deformation in 3D: Strain Matrix

Explores relative deformation in 3D through strain matrix and displacement gradient, emphasizing constraints, stress-strain relations, and equilibrium equations.

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Geometrically Necessary Dislocations in Materials

Explains geometrically necessary dislocations in materials and their role in reducing work hardening.

Deformation and Strain Tensors