Name: load-deformation and stored strain energy
Uploaded: 2025-05-22T09:06:18.000Z
Duration: 1 min 13 s
Channel: JoVE

Considérons une tige fixée à une extrémité et soumise à une force axiale à l’extrémité libre, ce qui induit une contrainte et conduit à un allongement de la tige. 
Lorsque la force axiale augmente, l’allongement augmente. Le tracé de la force axiale en fonction de l’allongement donne un tracé charge-déformation caractéristique.
Le travail effectué par la force axiale, lorsque la tige s’allonge légèrement, est le produit de la force axiale et de l’allongement correspondant.
Ce travail est égal à l’aire sous le graphique de déformation, dont la largeur est égale à la petite déformation.
Le travail total effectué peut être calculé en intégrant l’équation dans les limites d’allongement et est égal à l’aire sous la courbe charge-déformation à l’intérieur des mêmes limites d’allongement.
Le travail total effectué sur la barre représente l’apport d’énergie dans le système, connu sous le nom d’énergie de déformation.
À l’intérieur de la limite élastique, la force axiale est proportionnelle à la quantité d’allongement. Ainsi, l’énergie de déformation est proportionnelle au carré de l’allongement.

Énergie de déformation

Strain Energy

L'énergie de déformation est un concept fondamental dans le domaine de la science des matériaux et de l'ingénierie des structures, décrivant l'énergie absorbée par un matériau ou une structure lorsqu'il est déformé sous charge.

Considérons une tige fixée à une extrémité et soumise à une force axiale à l'extrémité libre. Cette force axiale induit une contrainte au sein de la tige, conduisant à son allongement. À mesure que la force axiale augmente, l’allongement de la tige augmente également, illustrant une relation directe entre la force appliquée et la déformation résultante. Ce comportement peut être représenté graphiquement par un tracé charge-déformation.

Le travail effectué par la force axiale pour allonger légèrement la tige est égal au produit de la force et de l’allongement correspondant. Graphiquement, ce travail correspond à l'aire sous la courbe charge-déformation pour un allongement donné. Pour calculer le travail total effectué sur la tige pour un allongement donné, il faut intégrer l'équation force-allongement sur les limites d'allongement. Ce travail total représente l’apport d’énergie au système, qui est stocké sous forme d’énergie de déformation. Dans la limite élastique du matériau, l'énergie de déformation U stockée dans le matériau en raison de la déformation élastique est proportionnelle au carré de l'allongement.

<img alt="Equation 1" src="/files/ftp_upload/15682/15682_Equation_1.svg" style="text-align: center; height: 52px;">

Le concept d'énergie de déformation permet aux ingénieurs de quantifier la capacité d'absorption d'énergie d'un matériau ou d'un composant, ce qui est essentiel pour évaluer sa capacité à résister aux charges sans subir de déformation ou de rupture permanente. L'énergie de déformation joue également un rôle central dans diverses applications d'ingénierie, telles que la conception d'amortisseurs, de dispositifs de stockage d'énergie et dans l'analyse des forces d'impact.

Considérons une tige fixée à une extrémité et soumise à une force axiale à l’extrémité libre, ce qui induit une contrainte et conduit à un allongement de la tige.
Comme le ...

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load-deformation and stored strain energy

Strain energy is the energy stored in a material when it deforms under load. It is a key idea in materials science and structural engineering. A loaded rod fixed at one end shows this clearly. When an axial force pulls on the free end, the rod stretches and stress builds inside it.

As the axial force increases, the rod elongates more. This creates a direct link between the applied force and the amount of deformation. Engineers can show this relationship with a load-deformation plot. The plot makes it easier to see how much the rod stretches at each load.

The work done by the axial force over a small elongation is the force multiplied by that elongation. On the graph, this work appears as the area under the load-deformation curve for a given elongation. To find the total work for any elongation, the force-elongation equation is integrated over the elongation limits. That total work is the energy put into the system, and it is stored as strain energy.

Within the elastic limit of the material, the strain energy stored in the rod is proportional to the square of the elongation. This means the stored energy rises as the deformation increases, as long as the material still behaves elastically. Knowing strain energy helps engineers judge how much energy a material or component can absorb before permanent deformation or failure. It is also useful in shock absorbers, energy storage devices, and impact force analysis.

Load-Deformation and Stored Strain Energy

load-deformation-and-stored-strain-energy

strain energy

Strain energy is the energy stored in a material when it deforms under load. It is a key idea in materials science and structural engineering. A loaded rod fixed at one end shows this clearly. When an axial force pulls on the free end, the rod stretches and stress builds inside it. As the axial force increases, the rod elongates more. This creates a direct link between the applied force and the amount of deformation. Engineers can show this relationship with a load-deformation plot. The plot...

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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...

key terms and concepts

Explore how load creates deformation in a rod, how work becomes stored strain energy, and why this matters in shock absorbers and impact analysis.

Load-Deformation and Stored Strain Energy | 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

Load-Deformation and Stored Strain Energy

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