# Mechanics Of Solids : Continuum physics

Introduction

According to Wikipedia Mechanics of solids is a part of Continuuom Mechanics that studies behaviour of solid materials,especially their motion and deformation under effects of various forces , temperature changes etc.Solid Mechanics is the important branches of physics

What is Solid?

According to Chemistry it is one of the states of matter.It’s definition is a body which is not perfectly rigid but have definite shape and volume.

Properties of solids

A) Elasticity:-The property of body to regain by the virtue of which it tends to regain its original configuration after applying force

B) Plasticity:- The inability of body to regain its original configuration after applying force

C) High density

D) Definite shape and volume,mass

E) Definite interaction force

F) Incompressible

The elastic properties of solid body are described in terms of Stress and Strain

Stress

The internal restorating force per unit area of a body is called Stress

Stress=deforming force/area=|F| /A

SI unit : N m^-2 or Pascal

Types of Stress

1. Longitudinal stress:-

Stress produced by a deforming force acting along the length of the body is called longitudinal Stress

Volume Stress:-

Stress produced by a deforming force acting along the volume of the body is called volume stress.

Shearing Stress:-

The restoring force developed per unit area due to the applied tangential force is called Shearing Stress

Strain:-

Strain is defined as the ratio of change in dimensions of the body to its original dimensions.

Types of Strain

1.Longitudinal strain

The strain produced by a tensile deforming force is called longitudinal strain

2. Volume strain.

A deforming force acting perpendicular to the entire surface of a body produces a volume strain.

3.Shearing strain

The relative displacement of the bottom face and the top face of the cube is called shearing strain.

Hooke’s Law

Statement: Within an elastic limit, stress is directly proportional to strain

Mathematically written as

Stress α Strain

Elastic limit

The maximum value of stress upto which stress is directly proportional to strain is called the elastic limit.

Modulus of elasticity

The modulus of elasticity of a material is the ratio of stress to the corresponding strain.

Types of modulus of elasticity

Young’s modulus (Y): It is the modulus of clasticity related to change in length of an object like a metal wire, rod, beam, etc., due to the applied deforming force.

Bulk modulus (K): It is the modulus of elasticity related to change in volume of an object due to applied deforming force.

Shear modulus or Modulus of rigidity(η): The modulus of elasticity related to change in shape of an object is called modulus of rigidity.

Poisson ‘s ratio (σ)

Within elastic limit, the ratio of lateral strain to the linear strain is called the Poisson’s ratio.

Strain Energy

The elastic potential energy gained by a wire during elongation by a stretching force is called as strain energy.

Hardness

Hardness is the property of a material which enables it to resist plastic deformation.

Toughness

Toughness is the ability of a material to resist fracturing when a force is applied to it.