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27 relations: Acceleration, Anisotropy, Cartesian coordinate system, Cauchy stress tensor, Chain rule, Constitutive equation, Continuum mechanics, Coordinate vector, Deformation (engineering), Displacement (vector), Euclidean space, Finite strain theory, Hypoelastic material, Identity matrix, Isotropy, Lagrangian and Eulerian specification of the flow field, Objective stress rate, Position (vector), Principle of material objectivity, Rotation matrix, Scalar field, Skew-symmetric matrix, Stress (mechanics), Symmetric matrix, Tensor, Tensor field, Velocity.
Acceleration
In physics, acceleration is the rate of change of velocity of an object with respect to time.
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Anisotropy
Anisotropy, is the property of being directionally dependent, which implies different properties in different directions, as opposed to isotropy.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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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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Chain rule
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.
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Constitutive equation
In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces.
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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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Coordinate vector
In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular ordered basis.
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Deformation (engineering)
In materials science, deformation refers to any changes in the shape or size of an object due to-.
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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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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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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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Hypoelastic material
In continuum mechanics, a hypoelastic material is an elastic material that has a constitutive model independent of finite strain measures except in the linearized case.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Isotropy
Isotropy is uniformity in all orientations; it is derived from the Greek isos (ἴσος, "equal") and tropos (τρόπος, "way").
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Lagrangian and Eulerian specification of the flow field
In classical field theory the Lagrangian specification of the field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
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Objective stress rate
Predictions from three objective stress rates under shear In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference.
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Position (vector)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.
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Principle of material objectivity
Principle of material objectivity is an obsolete term and should be replaced by principle of material frame-indifference.
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Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
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Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.
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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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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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Symmetric matrix
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.
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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 field
In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).
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Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
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References
[1] https://en.wikipedia.org/wiki/Objectivity_(frame_invariance)
