Lecture

Hyperelasticity: Basic Theory and Applications

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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 introduces the concept of hyperelasticity, focusing on the basic theory and applications. It covers topics such as non-linear but reversible stress-strain response, energy density per unit mass, and the constructive law for stress. The lecture explains the relationship between the internal stored energy and the current state of deformation, emphasizing the use of stretch ratio instead of the Green-Lagrange strain. It also discusses isotropic hyperelastic materials and the importance of principal invariants in determining the energy function. The presentation concludes with a detailed examination of hyperelastic materials in the Principal Axes coordinate system.

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Instructors (3)

William Curtin

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.

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (32)

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.

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.

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.

Elasticity (physics)

In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.

Stress–strain analysis

Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. In simple terms we can define stress as the force of resistance per unit area, offered by a body against deformation.

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