linear elastic regime) the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is...

Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is...

of the tangent modulus of elasticity, Et, which is less than the elastic modulus, in place of the elastic modulus of elasticity. The tangent is equal...

most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant...

Dynamic modulus (sometimes complex modulus) is the ratio of stress to strain under vibratory conditions (calculated from data obtained from either free...

ratio of the longest half sine wave to the actual column length, Et = tangent modulus at the stress Fcr, and KL = effective length (length of an equivalent...

complex modulus. The temperature of the sample or the frequency of the stress are often varied, leading to variations in the complex modulus; this approach...

polymer. While HDPE and PEX both display increases in the initial tangent modulus and yield stress under temperature or strain-rate increases when undergoing...

tending to lengthen an object. Tensile modulus Young's modulus E {\displaystyle E} , the Young modulus, or the modulus of elasticity in tension, is a mechanical...

results in a characteristic three-phase behavior of stiff-soft-stiff tangent modulus. Phase I corresponds to the small-deformation regime during which the...

state is identical to that of the Murnaghan equation of state. The tangent bulk modulus predicted by the MacDonald–Tait model is K = K 0 ( V 0 V ) n . {\displaystyle...

acid)/poly(N,N'-dimethyl acrylamide) or PAMPS/PDMAAm ultimate stress and tangent modulus increased. However, when using bacterial cellulose and gelatin, it...

(Supplier Isola) Loss Tangent (tanδ) 0.02 – 0.03, 0.030 @ 1 GHz Glass transition temperature Can vary, but is over 120 °C Young's modulus – LW 3.5×10^6 psi...

us define the angle θ between a vector that is tangent to the polymer at position 0 (zero) and a tangent vector at a distance L away from position 0, along...

{q}}} is the squared modulus, and ⁠ q ¯ {\displaystyle {\bar {q}}} ⁠ is the complex conjugate. The resulting spheres are tangent for pairs of Gaussian...

 is the fluid tangent bulk modulus; M = K f N / ( K f + N ϕ ) {\displaystyle M={K_{f}}N/\left({{K_{f}}+N\phi }\right)}   is Biot modulus; K u = K + b 2...

Retrieved 2020-08-31. "Modulus and Argument". mas-coursebuild.ncl.ac.uk. Newcastle University. Retrieved 2025-01-05. "Modulus and Argument of a Complex...

manifold M: any holomorphic function on it is constant by the maximum modulus principle. Now if we had a holomorphic embedding of M into Cn, then the...

logistic curve. The logistic function is an offset and scaled hyperbolic tangent function: f ( x ) = 1 2 + 1 2 tanh ⁡ ( x 2 ) , {\displaystyle f(x)={\frac...

endomorphisms in a certain precise sense, roughly that the action on the tangent space at the identity element of A is a direct sum of one-dimensional modules...

distinguished: If a differentiable map f on M has a hyperbolic structure on the tangent bundle, then it is called an Anosov map. Examples include the Bernoulli...

numbers can be expressed more easily in polar coordinates: the magnitude or modulus of the product is the product of the two absolute values, or moduli, and...

non-negative real number. This allows to define the absolute value (or modulus or magnitude) of z to be the square root | z | = x 2 + y 2 . {\displaystyle...

a metric tensor g {\displaystyle g} implies that the modulus of a vector defined on the tangent bundle to a certain point p {\displaystyle p} of the manifold...

wheel is depicted as two concentric circles. The larger, outer circle is tangent to a horizontal line (e.g. a road that it rolls on), while the smaller...

published until 1693 (in his Traité des Indivisibles). Constructing the tangent of the cycloid dates to August 1638 when Mersenne received unique methods...

n-dimensional differentiable manifold has a tangent space. This is an n-dimensional Euclidean space consisting of the tangent vectors of the curves through the...

insulators. Structures are classified as tangent suspension, angle suspension, tangent strain, angle strain, tangent dead-end and angle dead-end. Where the...

{\displaystyle {\tfrac {d}{dx}}e^{x}=e^{x}} means that the slope of the tangent to the graph at each point is equal to its height (its y-coordinate) at...

shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful...