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...

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...

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

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...

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

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...

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...

 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...

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...

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

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

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...

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...

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...

(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...

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...

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...

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...

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

{\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...

area expansion modulus Ka, a bending modulus Kb and an edge energy Λ {\displaystyle \Lambda } . For fluid bilayers the shear modulus is by definition...

dotate di modulo" [On the geometric representation of double algebras with modulus]. Atti della Reale Accademia delle Scienze e Belle-Lettere di Napoli. 3...

taken to be internally tangent at a point, and if a point is taken on the smaller circle—and let it be at the point of tangency—and if the two circles...