Name: volume change under hydrostatic pressure
Uploaded: 2025-05-22T09:06:18.000Z
Duration: 1 min 21 s
Channel: JoVE

El módulo de volumen mide la resistencia de un material a la compresión uniforme. Se define como la constante de proporcionalidad entre un cambio en la presión y el cambio de volumen relativo resultante.
Considere un cubo isótropo de unidad de volumen. Cuando se somete a tensiones normales, se deforma en un paralelepípedo rectangular con un nuevo volumen.
La diferencia entre este nuevo volumen y el original se denomina dilatación del material. La dilatación se puede expresar como la suma de las deformaciones en las tres direcciones.
En el caso de un cuerpo sometido a una presión hidrostática uniforme, cada componente de la tensión es igual al negativo de la presión hidrostática.
Sustituyendo estos valores en la ecuación de dilatación se obtiene una expresión que introduce la constante conocida como módulo de volumen, expresada en las mismas unidades que el módulo de elasticidad.
Los materiales estables bajo presión hidrostática disminuyen de volumen, lo que hace que la dilatación sea negativa y el módulo aparente positivo.
Un material ideal con una relación de Poisson cero puede estirarse sin contracción lateral. Por el contrario, la relación de Poisson de 0,5 significa una incompresibilidad perfecta.

módulo masivo

El módulo de volumen es un término científico utilizado para describir la resistencia de un material a la compresión uniforme. Es la constante de proporcionalidad la que vincula un cambio de presión con el cambio de volumen relativo resultante.

<img alt="Equation 1" src="/files/ftp_upload/15601/15601_Equation_1.svg" style="text-align: center; height: 44px;">
Este concepto se vuelve más claro cuando un elemento material isotrópico se visualiza como un cubo de unidad de volumen. Este cubo, cuando se somete a tensiones normales, sufre una deformación, cambiando su forma hasta convertirse en un paralelepípedo rectangular con diferente volumen. La discrepancia entre este nuevo volumen y el original se denomina dilatación del material. La dilatación se puede calcular como la suma acumulativa de las deformaciones en las tres direcciones espaciales. Cuando el cuerpo está bajo una presión hidrostática uniforme, cada componente de tensión es igual al negativo de esta presión. Al insertar estos valores en la fórmula de dilatación se obtiene una expresión que introduce el módulo de volumen.

<img alt="Equation 2" src="/files/ftp_upload/15601/15601_Equation_2.svg" style="text-align: center; height: 48px;">
Este módulo tiene las mismas unidades que el módulo de elasticidad. Bajo presión hidrostática, los materiales estables reducen su volumen, lo que hace que la dilatación sea negativa y el módulo de volumen positivo. Un material ideal con una relación de Poisson de cero podría estirarse en una dirección sin contracción lateral. Por otro lado, un material con un índice de Poisson de 0,5 sería perfectamente incompresible.

Módulo masivo

El módulo de volumen mide la resistencia de un material a la compresión uniforme. Se define como la constante de proporcionalidad entre un cambio en la presión ...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Stress and Strain - Axial Loading

Esfuerzo y deformación - Carga axial

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Bulk Modulus

volume change under hydrostatic pressure

Bulk modulus describes how much a material resists a uniform squeeze. It links a change in pressure to the relative change in volume. For high school students, it is easiest to think of it as a measure of how hard it is to compress a material evenly from all sides.

The idea becomes clearer when an isotropic material element is treated as a cube with unit volume. When normal stresses act on the cube, it deforms into a rectangular parallelepiped and its volume changes. The difference between the new volume and the original volume is called dilatation. Dilatation is found by adding the strains in the three spatial directions.

Under uniform hydrostatic pressure, each stress component is equal to the negative of that pressure. Substituting those stress values into the dilatation formula leads to the expression for bulk modulus. The bulk modulus has the same units as the modulus of elasticity. Stable materials usually lose volume under hydrostatic pressure, so dilatation is negative and the bulk modulus is positive.

The transcript also connects bulk behavior to Poisson's ratio. An ideal material with a Poisson's ratio of zero could stretch in one direction without a lateral contraction. A material with a Poisson's ratio of 0.5 would be perfectly incompressible.

Volume Change Under Hydrostatic Pressure

normal strain under axial loading

Axial Stress and Strain in a Rod

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stress-strain diagram - brittle materials

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hooke's law

Stress-Strain Limits in Materials

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plastic behavior

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fatigue

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deformation of member under multiple loadings

deformation-of-member-under-multiple-loadings

Calculating Rod Stretch from Mixed Loads

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statically indeterminate problem solving

Axial Rod Reactions with Redundant Support

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thermal strain

Thermal Expansion of a Free Rod

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poisson's ratio

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generalized hooke's law

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bulk modulus

Bulk modulus describes how much a material resists a uniform squeeze. It links a change in pressure to the relative change in volume. For high school students, it is easiest to think of it as a measure of how hard it is to compress a material evenly from all sides. The idea becomes clearer when an isotropic material element is treated as a cube with unit volume. When normal stresses act on the cube, it deforms into a rectangular parallelepiped and its volume changes. The difference between the...

shearing strain

Shear Modulus and Angular Change

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relation between poisson's ratio, modulus of elasticity and modulus of rigidity

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saint-venant's principle

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stress concentrations

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residual stresses

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Residual stresses are stresses that remain in a structure after the original load or heat source is removed. They often form when different parts of a material undergo uneven plastic deformation, which means permanent shape change. A rod stretched past its yield point is one example. It will not return to its original length, and some stress stays inside even after the load is gone. These stresses can also develop during welding. Heat changes the material during the weld and can cause plastic...

key terms and concepts

Learn how hydrostatic pressure changes a material’s volume, how dilatation is calculated, and why bulk modulus stays positive for stable materials.

Volume Change Under Hydrostatic Pressure | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Volume Change Under Hydrostatic Pressure

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