Name: strain energy in stressed materials
Uploaded: 2024-05-23T13:00:12.000Z
Duration: 1 min 22 s
Channel: JoVE

Cuando un material se somete a una carga axial, experimenta una tensión normal, lo que conduce a la generación de energía de deformación. Esta ecuación es válida para tensiones distribuidas uniformemente, y la densidad de energía de deformación es constante en todo el material.
Para un material que tiene una distribución de tensiones no uniforme, la densidad de energía de deformación se define para el pequeño volumen del material.
Aquí, la densidad de energía de deformación se expresa como el producto de la tensión aplicada y la deformación producida.
La integración de la densidad de energía de deformación en todo el volumen del material proporciona la energía de deformación total almacenada en el material.
La ecuación obtenida para la energía de deformación solo se aplica a la deformación elástica y también se denomina energía de deformación elástica.
Cuando el material se somete a una carga axial céntrica, se supone que las tensiones normales son uniformes en cualquier sección transversal. Aquí, la tensión normal se escribe como la relación entre las fuerzas internas y el área de la sección transversal bajo consideración.
La energía de deformación almacenada en tales casos se escribe en términos de fuerza interna y módulo de elasticidad.

energía de deformación elástica para tensiones normales

Elastic Strain Energy for Normal Stresses

<div>
 La energía de deformación cuantifica la energía almacenada dentro de un material debido a la deformación bajo condiciones de carga, un concepto fundamental en la ciencia e ingeniería de materiales. La energía de deformación se puede modelar cuando un material se somete a una carga axial con tensión uniformemente distribuida. En este escenario, la tensión experimentada por el material es la fuerza interna dividida por el área de la sección transversal, y la deformación inducida es directamente proporcional a esta tensión a través del módulo de elasticidad.
 
 Si la distribución de tensiones es uniforme, la densidad de energía de deformación, definida como el producto de la tensión y la deformación, se puede integrar en todo el volumen del material para producir la energía de deformación total almacenada.
 
 <img alt="Equation 1" src="/files/ftp_upload/15684/15684_Equation_1v2.svg" style="text-align: center; height: 50px;">
 Sin embargo, calcular la energía de deformación se vuelve más complejo para materiales con distribuciones de tensiones no uniformes. En tales casos, la densidad de energía de deformación debe definirse para los volúmenes pequeños para tener en cuenta las variaciones locales de tensión y deformación. La energía de deformación total es la suma de estas densidades en todo el volumen del material.
 
 <img alt="Equation 2" src="/files/ftp_upload/15684/15684_Equation_2v2.svg" style="text-align: center; height: 40px;">
 Esta consideración supone un comportamiento elástico, donde la deformación es reversible y el material vuelve a su forma original cuando se retira la carga. Comprender y calcular la energía de deformación es vital para diseñar materiales y componentes que puedan soportar tensiones operativas sin fallar.
 
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Energía de deformación elástica para tensiones normales

Cuando un material se somete a una carga axial, experimenta una tensión normal, lo que conduce a la generación de energía de deformación. Esta ecuación es válida para ...

elastic-strain-energy-for-normal-stresses

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strain energy in stressed materials

Strain energy in stressed materials describes the energy stored when a material deforms under load. It is an important idea in materials science and engineering. For axial loading with a uniform stress distribution, the stress is the internal force divided by the cross-sectional area, and the strain follows from the stress through the modulus of elasticity.

When the stress is uniform, the strain energy density can be found from the product of stress and strain. That density is then integrated over the full volume of the material to calculate the total strain energy stored. This approach works for elastic behavior, where the deformation is reversible and the material returns to its original shape after the load is removed.

The calculation becomes more complex when stress is not distributed evenly. In those cases, strain energy density must be defined for small volumes so local changes in stress and strain are included. The total strain energy is then the sum of these small energy contributions across the material. This idea is useful for understanding how materials and components can handle operating stresses without failure.

Strain Energy in Stressed Materials

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elastic strain energy for normal stresses

Strain energy in stressed materials describes the energy stored when a material deforms under load. It is an important idea in materials science and engineering. For axial loading with a uniform stress distribution, the stress is the internal force divided by the cross-sectional area, and the strain follows from the stress through the modulus of elasticity. When the stress is uniform, the strain energy density can be found from the product of stress and strain. That density is then integrated...

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Beam deflection from a central load can be found with Castigliano's theorem. The method applies to a simply supported beam with a point load at the center. It links the deflection at the load point to the strain energy stored in the beam. For this beam, the supports share the load equally. Each support carries half of the force. The bending moment at any point along the beam comes from these reactions and is written using the distance from the nearest support. Castigliano's theorem says the...

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Learn how strain energy is stored in materials under load, how uniform stress is used in calculations, and why local stress changes matter.

Strain Energy in Stressed Materials | 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

Strain Energy in Stressed Materials

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