Universal breakdown of elasticity at the onset of material failure

A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and reloaded.

The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...

Brittle materials, including glass, cast iron, and stone, exhibit unique characteristics. They fracture without considerable change in their elongation rate, indicating that their breaking and ultimate strength are equivalent. Such materials also show lower strain levels at the point of rupture. The failure in brittle materials predominantly results from normal stresses, as evidenced by the rupture created along a surface perpendicular to the applied load. These materials do not display...

Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear portion of...

Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.

Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...