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Resistance of a material to uniform pressure
The bulk modulus ( K {\displaystyle K} or B {\displaystyle B} or k {\displaystyle k} ) of a substance is a measure of the resistance of a substance to
Bulk_modulus
Physical property that measures stiffness of material
inverse of compressibility. The bulk modulus is an extension of Young's modulus to three dimensions. Flexural modulus (Eflex) describes the object's tendency
Elastic_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
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 designed to manipulate sound waves
gases, liquids, and solids. By tailoring effective parameters such as bulk modulus (β), density (ρ), and in some cases chirality, they can be engineered
Acoustic_metamaterial
Equation in Fluid Mechanics, relating density & pressure
{(B+P)}{C}}} where K {\displaystyle K} is the isothermal mixed bulk modulus. This above equation is popularly known as the Tait equation. The integrated
Tait_equation
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
Material with Vickers hardness exceeding 40 gigapascals
other properties must be taken into account. In contrast to bulk modulus, shear modulus measures the resistance to shape change at a constant volume
Superhard_material
Parameter used to calculate the volume change of a fluid or solid in response to pressure
reciprocal of compressibility at fixed temperature is called the isothermal bulk modulus. The specification above is incomplete, because for any object or system
Compressibility
Stress-strain relation in a linear elastic material
just 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
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)
chiral, lattice and negative metamaterials (e.g., negative bulk modulus or negative elastic modulus) are ripe followed by origami and cellular metamaterials
Mechanical_metamaterial
Speed of sound wave through elastic medium
}}},} where K is the bulk modulus of the elastic materials; G is the shear modulus of the elastic materials; E is the Young's modulus; ρ is the density;
Speed_of_sound
Force needed to pull a spring grows linearly with distance
direction), 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
Hooke's_law
Pressure surge when a fluid is forced to stop or change direction suddenly
equivalent bulk modulus of elasticity of the system fluid–pipe, ρ = density of the fluid, K = bulk modulus of elasticity of the fluid, E = elastic modulus of
Hydraulic_shock
Topics referred to by the same term
teeth of a rotating gear Bulk modulus, a measure of compression resistance Elastic modulus, a measure of stiffness Shear modulus, a measure of elastic stiffness
Modulus
Measure of material deformation perpendicular to loading
5. 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
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
Experimental method in X-ray diffraction
of such quantities as the thermal expansion tensor and the isothermal bulk modulus, as well determination of the full equation of state of the material
Powder_diffraction
Degree to which a material under stress irreversibly deforms before failure
the relevant elastic modulus is Young's; the equivalent for deforming under bulk compression, i.e. when using the bulk modulus, is malleability. Historically
Ductility
State of matter
of the shear modulus is 0. This is sometimes seen as the defining property of a liquid. However, like the bulk modulus K, the shear modulus G is also frequency-dependent
Liquid
Equation in mechanics
solids at high compression. Generally, at constant temperature, the bulk modulus is defined by: K = − V ( ∂ P ∂ V ) T . {\displaystyle K=-V\left({\frac
Murnaghan_equation_of_state
6.8×51mm rifle cartridge by SIG Sauer
strength is based on Young's modulus, but the relevant modulus for how much pressure a cartridge can withstand is the bulk modulus - the material is being
.277_Fury
Topics referred to by the same term
Look up bulk in Wiktionary, the free dictionary. Bulk can refer to: Bulk cargo Bulk carrier Bulk liquids Bulk mail Bulk material handling Bulk pack, packaged
Bulk
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
Equation in mechanics
deformed volume, B0 is the bulk modulus, and B0' is the derivative of the bulk modulus with respect to pressure. The bulk modulus and its derivative are usually
Birch–Murnaghan equation of state
Birch–Murnaghan_equation_of_state
Chemical element with atomic number 90 (Th)
pressure (around 100 GPa; body-centred tetragonal). Thorium metal has a bulk modulus (a measure of resistance to compression of a material) of 54 GPa, about
Thorium
Physical and chemical properties of pure water
decreases, being 3.9×10−10 Pa−1 at 0 °C and 100 megapascals (1,000 bar). The bulk modulus of water is about 2.2 GPa. The low compressibility of non-gasses, and
Properties_of_water
Material property relevant for characterizing fluid flow
resistance, over and above the reversible resistance caused by isentropic bulk modulus, to a compression or expansion of a fluid. At the molecular level, it
Volume_viscosity
Chemical element with atomic number 76 (Os)
temperatures. It has a very low compressibility. Correspondingly, its bulk modulus is extremely high, reported to be between 395 and 462 GPa, which rivals
Osmium
Oxide mineral
the bulk modulus is 240 GPa. Single crystal corundum fibers have potential applications in high temperature composites, and the Young's modulus is highly
Corundum
Audible vibration that travels via pressure waves in matter
known as the Newton–Laplace equation. In this equation, K is the elastic bulk modulus, c is the velocity of sound, and ρ {\displaystyle \rho } is the density
Sound
Application of balanced forces which push inwards on an object
can bear. It affects the volume of the material, as quantified by the bulk modulus and the volumetric strain. The inverse process of compression is called
Compression_(physics)
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
Chemical element with atomic number 5 (B)
et al. (1993). "Neutron- and x-ray-diffraction measurements of the bulk modulus of boron". Phys. Rev. B. 47 (13): 7668–7673. Bibcode:1993PhRvB..47.7668N
Boron
Thermodynamic concept imporant in astrophysics
polytrope) has been shown to be equivalent to the pressure derivative of the bulk modulus where its relation to the Murnaghan equation of state has also been demonstrated
Polytrope
Phenomenon of wave mechanics
on the fluid's mass density ( ρ {\displaystyle \rho } ) and adiabatic bulk modulus ( K {\displaystyle K} ), according to the Newton-Laplace formula: v =
Hot_chocolate_effect
Chemical element with atomic number 13 (Al)
magnetic susceptibility +16.5×10−6 cm3/mol Young's modulus 70 GPa Shear modulus 26 GPa Bulk modulus 76 GPa Speed of sound thin rod (rolled) 5000 m/s (at r
Aluminium
930 °C). The bulk modulus of c-BC2N is 282 GPa which is one of the highest bulk moduli known for any solid, and is exceeded only by the bulk moduli of diamond
Heterodiamond
Chemical element with atomic number 82 (Pb)
with a fingernail. It is very malleable and moderately ductile. Its bulk modulus—a measure of resistance to compression—is 45.8 GPa, compared with 75
Lead
Type of wave
{\displaystyle \ G\ ~~} is the shear modulus and K b {\displaystyle \ K_{b}\ } is the bulk modulus; ρ {\displaystyle \ \rho ~~~} is the
Longitudinal_wave
Materials engineered to have properties that have not yet been found in nature
sound waves is mostly accomplished through the bulk modulus β, mass density ρ and chirality. The bulk modulus and density are analogs of permittivity and
Metamaterial
Weight per unit volume of a material
as 9.80665 m/s2. Pressure may also affect values, depending upon the bulk modulus of the material, but generally, at moderate pressures, has a less significant
Specific_weight
Chemical element with atomic number 98 (Cf)
frees them to bond. The bulk modulus of a material is a measure of its resistance to uniform pressure. Californium's bulk modulus is 50±5 GPa, which is
Californium
linear elasticity, the P-wave modulus M {\displaystyle M} , also known as the longitudinal modulus, or the constrained modulus, is one of the elastic moduli
P-wave_modulus
Medium to transfer power in hydraulic machinery
environments, for temperature ranges of 10 to 1,400 °F (−12 to 760 °C). Its bulk modulus at 1,000 °F (538 °C) is 310,000 psi (2.14 GPa), higher than of a hydraulic
Hydraulic_fluid
page Elastic properties of the elements: Young's modulus, Poisson's ratio, bulk modulus, shear modulus data page Electrical resistivity data page Electron
Table of specific heat capacities
Table_of_specific_heat_capacities
Gassmann's relation, of the following form, to transform the saturated bulk modulus: K s a t ( 2 ) K m i n e r a l − K s a t ( 2 ) − K f l u i d ( 2 ) ϕ
Gassmann's_equation
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
Glossary_of_engineering:_A–L
Interface between crystallites in a polycrystalline material
that there is an inverse relationship with the bulk modulus meaning that the larger the bulk modulus (the ability to compress a material) the smaller
Grain_boundary
Repulsive force in quantum mechanics
this pressure is an important contributor to the compressibility or bulk modulus of metals. Electron degeneracy pressure will halt the gravitational collapse
Electron_degeneracy_pressure
Hyperelastic material model
}{2}}} where κ {\displaystyle \kappa } is the bulk modulus and μ {\displaystyle \mu } is the shear modulus or the second Lamé parameter. Alternative definitions
Neo-Hookean_solid
Chemical element with atomic number 93 (Np)
below the lanthanide promethium. Neptunium is a hard metal, having a bulk modulus of 118 GPa, comparable to that of manganese. Neptunium metal is similar
Neptunium
Chemical element with atomic number 78 (Pt)
tarnish is well suited to use in fine jewelry. Platinum does not corrode, and bulk platinum does not oxidize in air at any temperature, but heated metal wires
Platinum
Chemical element with atomic number 74 (W)
such material, the mechanical properties differ fundamentally from those of bulk tungsten. Such tungsten nanowires have potential applications in nanoelectronics
Tungsten
Chemical element with atomic number 51 (Sb)
magnetic susceptibility −99.0×10−6 cm3/mol Young's modulus 55 GPa Shear modulus 20 GPa Bulk modulus 42 GPa Speed of sound thin rod 3420 m/s (at 20 °C)
Antimony
Quantum mechanics principle
stars are the most "rigid" objects known; their Young modulus (or more accurately, bulk modulus) is 20 orders of magnitude larger than that of diamond
Pauli_exclusion_principle
Lubricant used for internal combustion engines
derived from crude oil, with additives to improve certain properties. The bulk of a typical motor oil consists of hydrocarbons with between 18 and 34 carbon
Motor_oil
Chemical element with atomic number 24 (Cr)
susceptibility +180.0×10−6 cm3/mol (273 K) Young's modulus 279 GPa Shear modulus 115 GPa Bulk modulus 160 GPa Speed of sound thin rod 5940 m/s (at 20 °C)
Chromium
Chemical element with atomic number 22 (Ti)
favored due to their low rate of corrosion, long life, and low Young's modulus. A titanium alloy that contains 6% aluminium and 4% vanadium commonly used
Titanium
Chemical element with atomic number 73 (Ta)
is metastable and converts to the alpha phase upon heating to 750–775 °C. Bulk tantalum is almost entirely alpha phase, and the beta phase usually exists
Tantalum
Type of energy propagation
{C}{\rho }}}} where C is a coefficient of stiffness, the bulk modulus (or the modulus of bulk elasticity for gas mediums), ρ {\displaystyle \rho } is the
Acoustic_wave
Chemical element with atomic number 19 (K)
oxygen. Finely powdered potassium ignites in air at room temperature. The bulk metal ignites in air if heated. Because its density is 0.89 g/cm3, burning
Potassium
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
Sound of a drop of water falling into water
behavior by accounting for the gas compressibility factor, or the gas bulk modulus K = ρ g c g 2 {\displaystyle K=\rho _{g}c_{g}^{2}} f = 1 2 π a ( 3 K
Minnaert_resonance
Chemical element with atomic number 10 (Ne)
lighter than the molecules of diatomic nitrogen and oxygen which form the bulk of Earth's atmosphere; a balloon filled with neon will rise in air, albeit
Neon
Model of electrons within a metallic solid
the same energy level. This pressure defines the compressibility or bulk modulus of the metal B = − V ( ∂ P ∂ V ) T , μ = 5 3 P = 2 3 n E F . {\displaystyle
Free_electron_model
Glass consisting of pure silica
strength: 48.3 MPa Compressive strength: > 1.1 GPa Bulk modulus: ~37 GPa Rigidity modulus: 31 GPa Young's modulus: 71.7 GPa Poisson's ratio: 0.17 Lamé elastic
Fused_quartz
Chemical element with atomic number 4 (Be)
structure. It has exceptional stiffness (Young's modulus 287 GPa) and a melting point of 1287 °C. The modulus of elasticity of beryllium is approximately 35%
Beryllium
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
Solid form of the 7th element
160%–300% the energy density of HMX. cg-N is also very stiff with a bulk modulus around 298 GPa, similar to diamond. Another network solid nitrogen called
Solid_nitrogen
Chemical element with atomic number 14 (Si)
Matthew A.; Nix, William D.; Kenny, Thomas W. (2010). "What is the Young's Modulus of Silicon?". Journal of Microelectromechanical Systems. 19 (2): 229. doi:10
Silicon
Alloy steel
Elastic Properties Elastic modulus E {\displaystyle E} (GPa) 207 Poisson's Ratio ν {\displaystyle \nu } .30 Shear modulus G = E / 2 ( 1 + ν ) {\displaystyle
HY-80
Dimensionless number in fluid mechanics
bulk modulus of elasticity, (SI units: Pa) For isentropic processes, the Cauchy number may be expressed in terms of Mach number. The isentropic bulk modulus
Cauchy_number
Type of metallic alloy
elastic, shear, and bulk modulus than in quaternary-, full-, and inverse-Hausler alloys. DFT also predicts a decrease in elastic modulus with temperature
Heusler_compound
Measure of a material's resistance to localized plastic deformation
small-scale shear modulus in any direction, not to any rigidity or stiffness properties such as its bulk modulus or Young's modulus. Stiffness is often
Hardness
Chemical compound
δ-P3N5 is the most incompressible triphosphorus pentanitride, having a bulk modulus of 313 GPa. Triphosphorus pentanitride has no commercial applications
Triphosphorus_pentanitride
Class of chemical substance
computationally that a more mesoporous structure has a lower bulk modulus. However, an increased bulk modulus was observed in systems with a few large mesopores
Metal–organic_framework
Chemical element with atomic number 6 (C)
This carbyne is of considerable interest to nanotechnology as its Young's modulus is 40 times that of the hardest known material – diamond. In 2015, a team
Carbon
page Elastic properties of the elements: Young's modulus, Poisson's ratio, bulk modulus, shear modulus data page Electrical resistivity data page Electron
Atomic radii of the elements (data page)
Atomic_radii_of_the_elements_(data_page)
Chemical compound
the hardest known oxide with the Vickers hardness of 38 GPa and the bulk modulus of 431 GPa (i.e. close to diamond's value of 446 GPa) at atmospheric
Titanium_dioxide
Deepest known point of Earth's seabed
vertical plane. The speed is determined by the water's bulk modulus, mass, and density. The bulk modulus is affected by temperature, pressure, and dissolved
Challenger_Deep
Properties Material Vickers hardness (GPa) Bulk Modulus (GPa) Melting point (°C) W2B 2670 WB ~20 2655 WB2 ~20 2365 WB4 ~30
Tungsten_borides
Capacity of a material or structure to withstand loads tending to reduce size
ideal test condition. For all practical purposes the volume of a high bulk modulus material (e.g. solid metals) is not changed by uniaxial compression.
Compressive_strength
Nanocrystalline form of diamond
known material, with an isothermal bulk modulus of 491 gigapascals (GPa), while a conventional diamond has a modulus of 442–446 GPa; these results were
Aggregated_diamond_nanorod
Wire with a diameter in the nanometres
applied to study the modulus of silver nanowires, and again the modulus was found to be 88 GPa, very similar to the modulus of bulk Silver (85 GPa) These
Nanowire
page Elastic properties of the elements: Young's modulus, Poisson's ratio, bulk modulus, shear modulus data page Electrical resistivity data page Electron
Hardnesses of the elements (data page)
Hardnesses_of_the_elements_(data_page)
Chemical element with atomic number 46 (Pd)
indicated that the element harms humans. Like other platinum-group metals, bulk Pd is quite inert. Although contact dermatitis has been reported, data on
Palladium
Chemical compound
(m2/s) Conductivity (W/m·K) Thermal diffusivity (m2/s) Prandtl number Bulk modulus (K−1) 00 1276.03 2.261 8.31×10−3 0.282 9.83×10−8 84700 4.7×10−4 10 1270
Glycerol
Chemical element with atomic number 77 (Ir)
Iridium's modulus of elasticity is the second-highest among the metals, surpassed only by osmium. This, together with a high shear modulus and a very
Iridium
Chemical element with atomic number 11 (Na)
silvery metal that combines with oxygen in the air, forming sodium oxides. Bulk sodium is usually stored in oil or an inert gas. Sodium metal can be easily
Sodium
Chemical element with atomic number 45 (Rh)
susceptibility +111.0×10−6 cm3/mol (298 K) Young's modulus 380 GPa Shear modulus 150 GPa Bulk modulus 275 GPa Speed of sound thin rod 4700 m/s (at 20 °C)
Rhodium
Chemical element with atomic number 20 (Ca)
When finely divided, it spontaneously burns in air to produce the nitride. Bulk calcium is less reactive: it quickly forms a hydration coating in moist air
Calcium
Chemical compound
environments, for temperature ranges of −12 to 760 °C (10 to 1,400 °F). Its bulk modulus at 538 °C (1,000 °F) is 2.14 GPa, higher than of a hydraulic oil at room
Sodium–potassium_alloy
Hard, dense and stiff chemical compound
around 2600. It has a Young's modulus of approximately 530–700 GPa, a bulk modulus of 379–381 GPa, and a shear modulus of 274 GPa. It has an ultimate
Tungsten_carbide
Chemical element with atomic number 23 (V)
anhydride: 2 C4H10 + 7 O2 → 2 C4H2O3 + 8 H2O Phthalic anhydride and several other bulk organic compounds are produced similarly. These green chemistry processes
Vanadium
Type of seismic wave
+2\mu \;}{\rho }}}} where K is the bulk modulus (the modulus of incompressibility), μ is the shear modulus (modulus of rigidity, sometimes denoted as G
P_wave
Chemical element with atomic number 28 (Ni)
cobalt and gadolinium. Its Curie temperature is 355 °C (671 °F), meaning that bulk nickel is non-magnetic above this temperature. The unit cell of nickel is
Nickel
Chemical element with atomic number 27 (Co)
frequently mentioned by Agricola, namely the kobel/köbel (Latinized as modulus). Another theory given by the Etymologisches Wörterbuch derives the term
Cobalt
is calculated from bulk modulus (K, or B) and volume at room temperature, or from Eq (1) at high P-T. A pressure gauge's bulk modulus is known, and its
Thermal equation of state of solids
Thermal_equation_of_state_of_solids
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BULK MODULUS
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