Last updated An inclusion in a linear elastic body. The stiffness tensor of the body is C0 and that of the inclusion is Ci. When the body and the inclusion have different elastic properties the inclusion is called an inhomogeneity. A transformation strain changes the shape and size of the inclusion.
Eshelby started with a thought experiment on the possible stress, strain, and displacement fields in a linear elastic body containing an inclusion. In particular, he considered the situation in which the inclusion has undergone a transformation (such as twinning or localized thermal expansion) but its change in shape and size are restricted because of the surrounding material. In that situation, the inclusion and the surrounding material remains in a stressed state. Also the strain states in the body and the inclusion are potentially inhomogeneous and complicated.
Eshelby found that the resulting elastic field can be found using a "sequence of imaginary cutting, straining and welding operations."[1] Eshelby's finding that the strain and stress field inside the ellipsoidal inclusion is uniform and has a closed-form solution, regardless of the material properties and initial transformation strain (also called the eigenstrain), has spawned a large amount of work in the mechanics of composites.
The results find their applications in the effective medium theory for heterogeneous elastic materials.
In continuum mechanics, stress is a physical quantity that describes the magnitude of forces that cause deformation. Stress is defined as force per unit area. When an object is pulled apart by a force it will cause elongation which is also known as deformation, like the stretching of an elastic band, it is called tensile stress. But, when the forces result in the compression of an object, it is called compressive stress. It results when forces like tension or compression act on a body. The greater this force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Therefore, stress is measured in newtons per square meter (N/m2) or pascal (Pa).
Yuan-Cheng "Bert" Fung was a Chinese-American bioengineer and writer. He is regarded as a founding figure of bioengineering, tissue engineering, and the "Founder of Modern Biomechanics".
George Barker Jeffery FRS was a leading mathematical physicist in the early twentieth century. He is probably best known to the scientifically literate public as the translator of papers by Albert Einstein, Hendrik Lorentz, and other fathers of relativity theory.
Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly bonded to each other. The surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane.
Samuel Francis (Frank) Boys was a British theoretical chemist.
John Douglas Eshelby FRS was a scientist in micromechanics. His work has shaped the fields of defect mechanics and micromechanics of inhomogeneous solids for fifty years and provided the basis for the quantitative analysis of the controlling mechanisms of plastic deformation and fracture.
Micromechanics is the analysis of composite or heterogeneous materials on the level of the individual constituents that constitute these materials.
A rigid line inclusion, also called stiffener, is a mathematical model used in solid mechanics to describe a narrow hard phase, dispersed within a matrix material. This inclusion is idealised as an infinitely rigid and thin reinforcement, so that it represents a sort of ‘inverse’ crack, from which the nomenclature ‘anticrack’ derives.
Mechanical metamaterials are artificial structures with mechanical properties defined by their structure rather than their composition. They can be seen as a counterpart to the rather well-known family of optical metamaterials. They are often also termed elastodynamic metamaterials and include acoustic metamaterials as a special case of vanishing shear. Their mechanical properties can be designed to have values which cannot be found in nature.
Platonic crystals are periodic structures which are designed to guide flexural wave energy through thin elastic plates.
In continuum mechanics an eigenstrain is any mechanical deformation in a material that is not caused by an external mechanical stress, with thermal expansion often given as a familiar example. The term was coined in the 1970s by Toshio Mura, who worked extensively on generalizing their mathematical treatment. A non-uniform distribution of eigenstrains in a material leads to corresponding eigenstresses, which affect the mechanical properties of the material.
George G. Adams is an American mechanical engineer specializing in tribology, contact mechanics, dynamics, and microelectromechanical systems (MEMS). He is a distinguished professor in the Mechanical and Industrial Engineering department at Northeastern University, Boston. Together with João Arménio Correia Martins, he discovered the frictional dynamic instabilities or Adams-Martins instabilities. Adams has published more than 120 papers in peer-reviewed journals, presenting new mathematical solutions of fundamental problems of mechanics, such as the dynamics of elastic structures subjected to moving loads, the contact of elastic plates with account to the adhesion force, as well as his studies of adhesion in MEMS microswitches and of contact mechanics. He has had many government and industry contracts and research grants.
The Ogden–Roxburgh model is an approach which extends hyperelastic material models to allow for the Mullins effect. It is used in several commercial finite element codes, and is named for R.W. Ogden and D. G. Roxburgh.
Eli Sternberg was a researcher in solid mechanics and was considered to be the "nation's leading elastician" at the time of his death. He earned his doctorate in 1945 under Michael Sadowsky at the Illinois Institute of Technology with a dissertation entitled Non-Linear Theory of Elasticity and Applications. He made contributions widely in elasticity, especially in mathematical analysis, the theory of stress concentrations, thermo-elasticity, and visco-elasticity.
Thomas Benjamin Britton is a materials scientist and engineer based at The University of British Columbia. He is a specialist in micromechanics, electron microscopy and crystal plasticity. In 2014 he was awarded the Silver Medal of the Institute of Materials, Minerals and Mining (IOM3), a society of which he then became a Fellow in 2016.
The fracture of soft materials involves large deformations and crack blunting before propagation of the crack can occur. Consequently, the stress field close to the crack tip is significantly different from the traditional formulation encountered in the Linear elastic fracture mechanics. Therefore, fracture analysis for these applications requires a special attention. The Linear Elastic Fracture Mechanics (LEFM) and K-field are based on the assumption of infinitesimal deformation, and as a result are not suitable to describe the fracture of soft materials. However, LEFM general approach can be applied to understand the basics of fracture on soft materials. The solution for the deformation and crack stress field in soft materials considers large deformation and is derived from the finite strain elastostatics framework and hyperelastic material models.
Alain Goriely is a Belgian mathematician, currently holding the statutory professorship (chair) of mathematical modelling at the University of Oxford, Mathematical Institute. He is director of the Oxford Centre for Industrial Mathematics (OCIAM), of the International Brain and Mechanics Lab (IBMTL) and Professorial Fellow at St Catherine's College, Oxford. At the Mathematical Institute, he was the director of external relations and public engagement, from 2013 until 2022, initiating the Oxford Mathematics series of public lectures. In 2022, he was elected to the Royal Society.
Max Born was a widely influential German physicist and mathematician who was awarded the 1954 Nobel Prize in Physics for his pivotal role in the development of quantum mechanics. Born won the prize primarily for his contributions to the statistical interpretation of the wave function, though he is known for his work in several areas of quantum mechanics as well as solid-state physics, optics, and special relativity. Born's entry in the Biographical Memoirs of Fellows of the Royal Society included thirty books and 330 papers.
Slip bands or stretcher-strain marks are localized bands of plastic deformation in metals experiencing stresses. Formation of slip bands indicates a concentrated unidirectional slip on certain planes causing a stress concentration. Typically, slip bands induce surface steps and a stress concentration which can be a crack nucleation site. Slip bands extend until impinged by a boundary, and the generated stress from dislocation pile-up against that boundary will either stop or transmit the operating slip.
Fionn Patrick Edward Dunne is a Professor of Materials Science at Imperial College London and holds the Chair in Micromechanics and the Royal Academy of Engineering/Rolls-Royce Research Chair. Professor Dunne specialises in computational crystal plasticity and microstructure-sensitive nucleation and growth of short fatigue cracks in engineering materials, mainly Nickel, Titanium and Zirconium alloys.
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