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Mechanical property that measures stiffness of a solid material
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
Young's_modulus
Topics referred to by the same term
Look up modulus in Wiktionary, the free dictionary. Modulus is the diminutive from the Latin word modus meaning measure or manner. It, or its plural moduli
Modulus
Slope of the stress-strain curve in solid mechanics
linear elastic regime) the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most
Tangent_modulus
Ratio of shear stress to shear strain
In solid mechanics, the shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material
Shear_modulus
Resistance of a material to uniform pressure
(strain) to other kinds of stress: the shear modulus describes the response to shear stress and Young's modulus describes the response to normal (lengthwise
Bulk_modulus
Geometric property of a structural member
shape in question. There are two types of section modulus, elastic and plastic: The elastic section modulus is used to calculate a cross-section's resistance
Section_modulus
Physical property that measures stiffness of material
deformation region; a stiffer material will have a higher elastic modulus. An elastic modulus has the form: δ =def stressstrain where stress is the force causing
Elastic_modulus
Computational operation
remainder of a division of one number by another, the latter being called the modulus of the operation. Given two positive numbers a and m, a modulo m (often
Modulo
Ratio used in material engineering
Dynamic modulus (sometimes complex modulus) is the ratio of stress to strain under vibratory conditions (calculated from data obtained from either free
Dynamic_modulus
Simple checksum formula
Luhn formula (creator: IBM scientist Hans Peter Luhn), also known as the "modulus 10" or "mod 10" algorithm, is a simple check digit formula used to validate
Luhn_algorithm
Topics referred to by the same term
Complex modulus may refer to: Modulus of complex number, in mathematics, the norm or absolute value, of a complex number: | x + i y | = x 2 + y 2 {\displaystyle
Complex_modulus
intermediate values. Fineness modulus of combined aggregates is always between the Fineness modulus of aggregates and combined modulus coarse aggregate have intermediate
Fineness_modulus
Intensive property in mechanics
In mechanics, the flexural modulus, bending modulus, or modulus of rigidity is an intensive property that is computed as the ratio of stress to strain
Flexural_modulus
Dimensionless number used in journal bearing design
Bearing modulus is a modulus used in journal bearing design. It is a dimensionless number. Bearing Modulus (C) is C = (Zn/p) where Z = oil viscosity n
Bearing_modulus
SI derived unit of pressure
or magnetic resonance imaging, and often displays the Young's modulus or shear modulus of tissue in kilopascals. In materials science and engineering
Pascal_(unit)
Computation modulo a fixed integer
by m. This means that every non-zero integer m may be taken as a modulus. In modulus 12, one can assert that: 38 ≡ 14 (mod 12) because the difference
Modular_arithmetic
Ratio of stiffness to mass for a material
Specific modulus is a materials property consisting of the elastic modulus per mass density of a material. It is also known as the stiffness to weight
Specific_modulus
Measure of material deformation perpendicular to loading
For soft materials, such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer
Poisson's_ratio
Catalytic activity is related to the size of particle
represents the square of the Thiele Modulus, which we now see rises naturally out of the material balance. Then the Thiele modulus for a first order reaction is:
Thiele_modulus
Mathematical theorem in complex analysis
mathematics, the maximum modulus principle in complex analysis states that if f {\displaystyle f} is a holomorphic function, then the modulus | f | {\displaystyle
Maximum_modulus_principle
Function in mathematical analysis
it admits a modulus of continuity. Moreover, relevance to the notion is given by the fact that sets of functions sharing the same modulus of continuity
Modulus_of_continuity
American musical instrument manufacturer
Modulus Graphite (formerly, Modulus Guitars) is an American manufacturer of musical instruments best known for building bass guitars with carbon fiber
Modulus_Guitars
Mathematical term
In real analysis, a branch of mathematics, a modulus of convergence is a function that tells how quickly a convergent sequence converges. These moduli
Modulus_of_convergence
Physical property when materials or objects return to original shape after deformation
of a material is quantified by the elastic modulus such as the Young's modulus, bulk modulus or shear modulus which measure the amount of stress needed
Elasticity_(physics)
Dimensionless parameter of the Weibull distribution
by two different modes. In this equation m1 is the modulus for the first mode, and m2 is the modulus for the second mode. Φ is the fraction of the sample
Weibull_modulus
a confined compression configuration. The aggregate modulus can be calculated from Young's modulus (E) and the Poisson ratio (v). H a = E ( 1 − v ) ( 1
Aggregate_modulus
Distance from zero to a number
In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the (non-negative) magnitude of x measured without regard to its sign
Absolute_value
Technique used to study & characterize materials
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
Dynamic_mechanical_analysis
Algorithm for generating pseudo-randomized numbers
is equivalent to a generator with modulus m/4 and c ≠ 0. A more serious issue with the use of a power-of-two modulus is that the low bits have a shorter
Linear_congruential_generator
Electronic circuit
through the feedback loop of the system. The modulus of a prescaler is its frequency divisor. A dual-modulus prescaler has two separate frequency divisors
Dual-modulus_prescaler
Logarithmic distance scale
Large Magellanic Cloud (LMC) is at a distance modulus of 18.5, the Andromeda Galaxy's distance modulus is 24.4, and the galaxy NGC 4548 in the Virgo Cluster
Distance_modulus
Species of gastropod
Modulus modulus, commonly known as the buttonsnail, is a species of small sea snail, a marine gastropod mollusc in the family Modulidae. This species
Modulus_modulus
Identifier for a security
3 + 8 + 3 + 0) = 45 Take the 10s modulus of the sum: 45 mod 10 = 5 Subtract from 10: 10 − 5 = 5 Take the 10s modulus of the result (this final step is
International Securities Identification Number
International_Securities_Identification_Number
Household robot
Design - The "Base" Modulus Jehudah Design - The "Service & Security" Modulus Jehudah Design - The "Service & Security" Modulus with arm expansion Jehudah
Modulus_robot
Mexican banking standard
digits. The control digit is calculated as the modulus 10 of 10 minus the modulus 10 of the sum of the modulus 10 of the product of the first 17 digits by
CLABE
Resistance to deformation in response to force
of twist The elastic modulus of a material is not the same as the stiffness of a component made from that material. Elastic modulus is a property of the
Stiffness
Material ability to absorb energy when deformed elastically
_{y}}{2}}} where Ur is the modulus of resilience, σy is the yield strength, εy is the yield strain, and E is the Young's modulus. This analysis is not valid
Resilience (materials science)
Resilience_(materials_science)
Product of a number by itself
absolute value of a complex number is called its absolute square, squared modulus, or squared magnitude.[better source needed] It is the product of the complex
Square_(algebra)
Material property in strain-stress relationship
called the shear modulus, and is sometimes denoted by G instead of μ. Typically the notation G is seen paired with the use of Young's modulus E, and the notation
Lamé_parameters
waves. In linear elasticity, the P-wave modulus M, also known as the longitudinal modulus, or the constrained modulus, is one of the elastic moduli available
P-wave_modulus
Force needed to pull a spring grows linearly with distance
c can be reduced to only two independent numbers, the bulk modulus K and the shear modulus G, that quantify the material's resistance to changes in volume
Hooke's_law
Degree to which part of a structural element is displaced under a given load
beam) is interpreted as its curvature, E {\displaystyle E} is the Young's modulus, I {\displaystyle I} is the area moment of inertia of the cross-section
Deflection_(engineering)
Chemical data page
properties can be well-characterized by the Young's modulus, Poisson's ratio, Bulk modulus, and Shear modulus or they may be described by the Lamé parameters
Elastic properties of the elements (data page)
Elastic_properties_of_the_elements_(data_page)
Material property
Flexural strength, also known as modulus of rupture, bend strength, or transverse rupture strength, is a material property defined as the maximum stress
Flexural_strength
modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of
Modulus and characteristic of convexity
Modulus_and_characteristic_of_convexity
Relation between properties and composition of a compound
composite material. For the Young's modulus E {\displaystyle E} , the rule of mixtures states that the overall modulus equals E ¯ V = f E 1 + ( 1 − f ) E
Rule_of_mixtures
Lévy's modulus of continuity theorem is a theorem that gives a result about an almost sure behaviour of an estimate of the modulus of continuity for Wiener
Lévy's modulus of continuity theorem
Lévy's_modulus_of_continuity_theorem
Exponentation in modular arithmetic
modular_pow(base, exponent, modulus) is if modulus = 1 then return 0 c := 1 for e_prime = 0 to exponent-1 do c := (c * base) mod modulus return c A third method
Modular_exponentiation
Hardness-testing device
indentation hardness, a relation between the ASTM D2240 hardness and the Young's modulus for elastomers has been derived by Gent. Gent's relation has the form:
Shore_durometer
Size of a set in mathematics
In mathematics, cardinality is an inherent property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The
Cardinality
Speed of sound wave through elastic medium
compressibility, shear modulus, and density. The speed of shear waves is determined only by the solid material's shear modulus and density. In fluid dynamics
Speed_of_sound
Standard procedure for measuring modulus of elasticity in bending
ϵf=6DdL2 Calculation of flexural modulus Ef Ef=L3m4bd3 in these formulas the following parameters are used: σf = Modulus of Rupture, the stress required
Three-point_flexural_test
Material made from a combination of two or more unlike substances
be described with the following material properties: Young's Modulus, the shear modulus, and the Poisson's ratio, in relatively simple mathematical relationships
Composite_material
Unique numeric book identifier since 1970
modular arithmetic is convenient for calculating the check digit using modulus 11. The remainder of this sum when it is divided by 11 (i.e. its value
ISBN
Model of viscoelastic material
}{\eta }}+{\frac {1}{E}}{\frac {d\sigma }{dt}}} where E is the elastic modulus and η is the material coefficient of viscosity. This model describes the
Maxwell_model
Material underneath a road or track
traffic loading is commonly quantified using the resilient modulus (Mr). The resilient modulus represents the ratio of applied cyclic stress to recoverable
Subgrade
Stress-strain relation in a linear elastic material
two independent components, which can be chosen to be the bulk modulus and shear modulus. The most general linear relation between two second-rank tensors
Elasticity_tensor
Variable length, discrete barcode symbology
Code 39 (also known as Alpha39, Code 3 of 9, Code 3/9, Type 39, USS Code 39, or USD-3) is a variable length, discrete barcode symbology defined in ISO/IEC
Code_39
Integer that is a perfect square modulo some integer
modulo any power of p if and only if it is a residue modulo p. If the modulus is pn, then pka is a residue modulo pn if k ≥ n is a nonresidue modulo
Quadratic_residue
Material designed to manipulate sound waves
force constant is identical to the modulus of the material. With phononic crystals of materials with differing modulus the calculations are more complicated
Acoustic_metamaterial
Type of linear congruential generator with no additive constant
composite modulus is possible, but the generator must be seeded with a value coprime to m, or the period will be greatly reduced. For example, a modulus of F5
Lehmer random number generator
Lehmer_random_number_generator
Device storing number of times an event or process occurred
Gray code, and one-hot. The modulus of a counter is the number of states in its count sequence. A counter that has modulus value m is commonly referred
Counter_(digital)
Mathematical inequality
an inequality relating the maximum modulus of a complex polynomial function on the unit disk with the maximum modulus of its derivative on the unit disk
Bernstein's theorem (polynomials)
Bernstein's_theorem_(polynomials)
Model of viscoelastic material
Thus, the real and imaginary components of the dynamic modulus are referred to as storage modulus E ′ {\displaystyle E^{\prime }} and E ′ ′ {\displaystyle
Kelvin–Voigt_material
Material testing procedure that makes a very small mark in a surface
corner (90°) tip is 2.598. The reduced modulus E r {\displaystyle E_{\text{r}}} is related to Young's modulus E s {\displaystyle E_{\text{s}}} of the
Nanoindentation
Chemical element with atomic number 47 (Ag)
susceptibility −19.5×10−6 cm3/mol (296 K) Young's modulus 83 GPa Shear modulus 30 GPa Bulk modulus 100 GPa Speed of sound thin rod 2680 m/s (at r.t.)
Silver
Concept in polymer physics
increase in the macroscopic modulus. Moreover, at constant frequency, an increase in temperature results in a reduction of the modulus due to an increase in
Time–temperature superposition
Time–temperature_superposition
Pseudorandom number generator
The reason for choosing these particular values for the multiplier and modulus had been that with a 32-bit-integer word size, the arithmetic of mod 231
RANDU
In the function field case, a modulus is the same thing as an effective divisor, and in the number field case, a modulus can be considered as special form
Modulus (algebraic number theory)
Modulus_(algebraic_number_theory)
Step in the process of designing physical objects
lightness, for a rod that will be pulled in tension the specific modulus, or modulus divided by density E / ρ {\displaystyle E/\rho } should be considered
Material_selection
Collection of residue classes
modulus greater than 1) whose moduli are odd, does not exist. It is known that if such a system exists with square-free moduli, the overall modulus must
Covering_system
Ratio of the thermal resistances of a body's interior to its surface
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot
Biot_number
Method to characterize materials
measures the resonant frequencies in order to calculate the Young's modulus, shear modulus, Poisson's ratio and internal friction of predefined shapes like
Impulse_excitation_technique
Geometric space whose points represent algebro-geometric objects of some fixed kind
introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood
Moduli_space
Titanium alloy
Titanium alloys are used in implanted medical devices due to their lower modulus[which?], higher biocompatibility, and better corrosion resistance than
Ti-6Al-4V
Oxide mineral
Young's modulus is temperature dependent, and has been reported in the [0001] direction as 435 GPa at 323 K and 386 GPa at 1,273 K. The shear modulus of corundum
Corundum
Most common stainless steel
to 153,000 psi). The density is 7,900 kg/m3 (0.286 lb/cu in), and its modulus of elasticity ranges from 183 to 200 GPa (26.6×10^6 to 29.0×10^6 psi).
SAE_304_stainless_steel
Material with Vickers hardness exceeding 40 gigapascals
shear modulus, the greater the ability for a material to resist shearing forces. Therefore, the shear modulus is a measure of rigidity. Shear modulus is
Superhard_material
Liquid, gas, or other continuously deforming and flowing material
under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force
Fluid
Curve representing a material's response to applied forces
the elastic region, and the slope of this region is the modulus of elasticity or Young's modulus. Plastic flow initiates at the upper yield point and continues
Stress–strain_curve
Alloys with high proportions of several metals
properties. Both values of hardness and related moduli like reduced modulus (Er) or elastic modulus (E) will significantly increase through the magnetron sputtering
High-entropy_alloy
Species of gastropod
Modulus cerodes A. Adams, 1851. 16 September 2025. Retrieved through: World Register of Marine Species. Adams, A. (1851). "A monograph of Modulus, a
Modulus_cerodes
Strong fabric of the type used to make ships' sails
latter having a 50% higher initial modulus than Type 29 but a lower flex loss. DuPont has developed higher modulus Types 129, 149 and 159, but these have
Sailcloth
Material ability to absorb energy and plastically deform without fracturing
divided by two times the Young's modulus of elasticity. That is, Modulus of resilience = Yield stress2/2 (Young's modulus) The toughness of a material
Toughness
Geometric representation of the complex numbers
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
Complex_plane
Natural number
condition for wavefunctions requires the integral of a wavefunction's squared modulus to be equal to 1. In chemistry, hydrogen, the first element of the periodic
1
Non-local formulation of continuum mechanics
where k {\displaystyle k} is the material bulk modulus. Following the same approach the micro-modulus constant c {\displaystyle c} can be extended to
Peridynamics
Sequence of points that get progressively closer to each other
|x_{m}-x_{n}|<1/k.} Any sequence with a modulus of Cauchy convergence is a Cauchy sequence. The existence of a modulus for a Cauchy sequence follows from the
Cauchy_sequence
Construction element
requiring the least material) needed to achieve a given section modulus. Since the section modulus depends on the value of the moment of inertia, an efficient
I-beam
Resistance offered by a structure while bending
exhibits Isotropic behavior then the Flexural Modulus is equal to the Modulus of Elasticity (Young's Modulus). Flexural rigidity has SI units of Pa·m4 (which
Flexural_rigidity
Material fibers about 5–10 μm in diameter composed of carbon
strength and higher elastic modulus, such as T400 from Toray with a tensile strength of 4,000 MPa and M40 with a modulus of 400 GPa. Intermediate carbon
Carbon_fibers
Left-invariant (or right-invariant) measure on locally compact topological group
{\displaystyle \Delta } from the group to the positive reals, called the Haar modulus, modular function or modular character, such that for every Borel set S
Haar_measure
Stress–strain behaviour of rubber
(roughly 20%), the storage modulus approaches a lower bound. In that region where the storage modulus decreases the loss modulus shows a maximum. The Payne
Payne_effect
Insect protein
amount of force. Hydrated resilin has a tensile modulus of 640–2000 kPa, an unconfined compressive modulus of 600–700 kPa, and a strain to break of 300%
Resilin
Algorithm
checksum has Fletcher-16 with a 256 modulus, as do the checksums of UBX-* messages from a U-blox GPS. Which modulus is used is dependent on the implementation
Fletcher's_checksum
Algorithm for public-key cryptography
private exponent d, one can efficiently factor the modulus n = pq. And given factorization of the modulus n = pq, one can obtain any private key (d', n) generated
RSA_cryptosystem
is a modulus of elasticity, one of several kinds that depend on the specific strain being examined: bulk modulus, shear modulus, Young's modulus, or P-wave
Strength_of_materials
dislocation motion within the material. Common in Crystals. Specific modulus: Modulus per unit volume (MPa/m^3) Specific strength: Strength per unit density
List_of_materials_properties
Continuum mechanics
against bending deflection/deformation. It is a function of the Young's modulus E {\displaystyle E} , the second moment of area I {\displaystyle I} of
Bending_stiffness
Chemical process by which polymeric materials are hardened
elastic modulus. To measure the elastic modulus of a system during curing, a rheometer can be used. With dynamic mechanical analysis, the storage modulus (G′)
Curing_(chemistry)
travel, tourism, insurance
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