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In homogeneous and isotropic materials, these define Hooke's law in 3D, = + (), where σ is the stress tensor, ε the strain tensor, I the identity matrix and tr the trace function. Hooke's law may be written in terms of tensor components using index notation as σ i j = 2 μ ε i j + λ δ i j ε k k , {\displaystyle \sigma _{ij}=2\mu ...
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The Rüchardt experiment, [1] [2] [3] invented by Eduard Rüchardt, is a famous experiment in thermodynamics, which determines the ratio of the molar heat capacities of a gas, i.e. the ratio of (heat capacity at constant pressure) and (heat capacity at constant volume) and is denoted by (gamma, for ideal gas) or (kappa, isentropic exponent, for real gas).
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
Poisson's ratio of a material defines the ratio of transverse strain (x direction) to the axial strain (y direction)In materials science and solid mechanics, Poisson's ratio (symbol: ν ()) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading.
A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
A two-dimensional flow that, at the highlighted point, has only a strain rate component, with no mean velocity or rotational component. In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e., the relative deformation) of a material in the neighborhood of a certain point, at a certain moment of time.
Using ideal gas equation of state for constant temperature process (i.e., / is constant) and the conservation of mass flow rate (i.e., ˙ = is constant), the relation Qp = Q 1 p 1 = Q 2 p 2 can be obtained. Over a short section of the pipe, the gas flowing through the pipe can be assumed to be incompressible so that Poiseuille law can be used ...