Introduction and Elastic Behavior of Solids

Introduction

Solids, liquids, and gases are the three common states of matter. We have previously studied the mechanical properties of solids as rigid bodies, an idealisation where the shape and size of the object do not change under applied forces. However, in reality, all materials deform when subjected to external forces. The study of how materials behave under the influence of forces and the resulting deformations is the subject of mechanics of materials or properties of matter.

In this topic, we will focus on the mechanical properties of solids, particularly their response to applied forces that tend to deform them. We will explore concepts like stress, strain, and elasticity, which describe how materials resist deformation and how they recover their original shape and size after the deforming forces are removed.

The ability of a material to resist deformation and regain its original state is crucial in engineering and everyday life. Think about the materials used in buildings, bridges, vehicles, or even simple objects like rubber bands and springs. Their functionality relies heavily on their mechanical properties.

We classify materials based on their response to deformation. Some materials, like rubber, are easily deformable. Others, like steel, are much harder to deform but can withstand large forces before breaking. Understanding these behaviours allows us to select appropriate materials for specific applications.

This study is fundamental to various branches of engineering (civil, mechanical, materials engineering) and contributes to the design and safety of structures and machines.

Elastic Behaviour Of Solids

When external forces are applied to a solid body, they can cause the body to deform, meaning its shape or size changes. When these deforming forces are removed, the body may or may not return to its original shape and size. The ability of a material to recover its original shape and size after the deforming forces are removed is called elasticity.

Elasticity and Plasticity

Materials can exhibit different types of behaviour under stress:

• Elastic Behaviour: If a material returns to its original shape and size completely upon removal of the deforming forces, it is said to exhibit elastic behaviour. The deformation is temporary and reversible.
• Plastic Behaviour: If a material does not return to its original shape and size after the deforming forces are removed, it is said to exhibit plastic behaviour. The deformation is permanent and irreversible.

Most materials exhibit both elastic and plastic behaviour, depending on the magnitude of the applied force. Initially, the deformation is elastic. If the force exceeds a certain limit (the elastic limit or yield point), the material starts to deform plastically. Applying even larger forces can lead to fracture.

A perfectly elastic body is an idealisation that completely recovers its original shape and size immediately after the removal of deforming forces. Examples of materials that are close to perfectly elastic under small deformations include steel, glass, and quartz fibres.

A perfectly plastic body is an idealisation that undergoes permanent deformation even under the smallest applied force and does not recover its original shape at all. Modelling clay or putty can approximate this behaviour under certain conditions.

Origin of Elastic Behaviour (Intermolecular Forces)

The elastic behaviour of solids originates from the intermolecular (or interatomic) forces between the constituent particles. In a solid, atoms or molecules are held together by strong attractive forces, and there are also repulsive forces that prevent them from coming too close.

These forces can be visualised as if the particles are connected by tiny springs. In the equilibrium state of a solid, the particles are at equilibrium distances where the net force between them is zero. When a deforming force is applied (e.g., stretching a wire), the distances between the particles change, moving them away from their equilibrium positions. This creates restoring forces (like the spring forces) that try to bring the particles back to their original equilibrium positions. When the deforming force is removed, these restoring forces cause the material to regain its original shape.

If the deformation is too large, the particles might be displaced so far from their equilibrium positions that these restoring forces are no longer effective in bringing them back completely, leading to plastic deformation.

(Image Placeholder: A simple 2D lattice of atoms or molecules, represented as spheres, connected by springs. Show equilibrium state, and then show a stretched state with forces pulling particles apart, and restoring forces trying to pull them back.)

Deforming Force and Restoring Force

When an external force is applied to deform a body, it is called a deforming force. As the body deforms, internal forces arise within the material that oppose the deformation and try to restore the body to its original state. These internal forces are called restoring forces.

In equilibrium (when the deformation is stable under the applied load), the restoring forces within the material balance the external deforming forces.

The study of elastic behaviour involves quantifying the applied forces (in terms of stress) and the resulting deformations (in terms of strain) and understanding the relationship between them.