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40 relations: Adhémar Jean Claude Barré de Saint-Venant, Cauchy stress tensor, Compatibility (mechanics), Concrete, Continuum mechanics, Cylindrical coordinate system, Deformation (mechanics), Density, Digital image correlation and tracking, Dislocation, Displacement (vector), Eigendecomposition of a matrix, Einstein notation, Elasticity (physics), Finite strain theory, Hooke's law, Infinitesimal, Infinitesimal strain theory, Levi-Civita symbol, Orthonormal basis, Particle, Plane stress, Plasticity (physics), Poisson's ratio, Saint-Venant's compatibility condition, Skew-symmetric matrix, Solid mechanics, Spherical coordinate system, Steel, Stiffness, Strain gauge, Strain rate, Stress (mechanics), Stress–strain analysis, Stress–strain curve, Structural load, Tensor, Tensor derivative (continuum mechanics), Trace (linear algebra), Von Mises.
Adhémar Jean Claude Barré de Saint-Venant
Adhémar Jean Claude Barré de Saint-Venant (23 August 1797, Villiers-en-Bière, Seine-et-Marne – 6 January 1886, Saint-Ouen, Loir-et-Cher) was a mechanician and mathematician who contributed to early stress analysis and also developed the unsteady open channel flow shallow water equations, also known as the Saint-Venant equations that are a fundamental set of equations used in modern hydraulic engineering.
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Cauchy stress tensor
In continuum mechanics, the Cauchy stress tensor \boldsymbol\sigma, true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy.
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Compatibility (mechanics)
In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that unique tensor field that is obtained when the body is subjected to a continuous, single-valued, displacement field.
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Concrete
Concrete, usually Portland cement concrete, is a composite material composed of fine and coarse aggregate bonded together with a fluid cement (cement paste) that hardens over time—most frequently a lime-based cement binder, such as Portland cement, but sometimes with other hydraulic cements, such as a calcium aluminate cement.
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Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
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Cylindrical coordinate system
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.
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Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration.
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Density
The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume.
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Digital image correlation and tracking
Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in images.
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Dislocation
In materials science, a dislocation or Taylor's dislocation is a crystallographic defect or irregularity within a crystal structure.
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Displacement (vector)
A displacement is a vector whose length is the shortest distance from the initial to the final position of a point P. It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point.
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Eigendecomposition of a matrix
In linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.
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Einstein notation
In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.
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Elasticity (physics)
In physics, elasticity (from Greek ἐλαστός "ductible") 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.
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Finite strain theory
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory.
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Hooke's law
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
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Infinitesimal strain theory
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.
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Levi-Civita symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.
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Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
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Particle
In the physical sciences, a particle (or corpuscule in older texts) is a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass.
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Plane stress
In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular surface.
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Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a (solid) material undergoing non-reversible changes of shape in response to applied forces.
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Poisson's ratio
Poisson's ratio, denoted by the Greek letter 'nu', \nu, and named after Siméon Poisson, is the negative of the ratio of (signed) transverse strain to (signed) axial strain.
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Saint-Venant's compatibility condition
In the mathematical theory of elasticity the strain \varepsilon is related to a displacement field \ u by where 1\le i,j \le 3.
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Skew-symmetric matrix
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition In terms of the entries of the matrix, if aij denotes the entry in the and; i.e.,, then the skew-symmetric condition is For example, the following matrix is skew-symmetric: 0 & 2 & -1 \\ -2 & 0 & -4 \\ 1 & 4 & 0\end.
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Solid mechanics
Solid mechanics is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.
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Spherical coordinate system
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
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Steel
Steel is an alloy of iron and carbon and other elements.
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Stiffness
Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force.
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Strain gauge
A strain gauge is a device used to measure strain on an object.
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Strain rate
Strain rate is the change in strain (deformation) of a material with respect to time.
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Stress (mechanics)
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.
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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.
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Stress–strain curve
The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve.
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Structural load
Structural loads or actions are forces, deformations, or accelerations applied to a structure or its components.
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Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
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Tensor derivative (continuum mechanics)
The derivatives of scalars, vectors, and second-order tensors with respect to second-order tensors are of considerable use in continuum mechanics.
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Trace (linear algebra)
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.
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Von Mises
von Mises may refer to.
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Cauchy strain tensor, Infinitesimal strain, Infinitesimal strain tensor, Plane strain, Small strain theory, Strain tensor, Volumetric strain.
References
[1] https://en.wikipedia.org/wiki/Infinitesimal_strain_theory
