Stress and strain, Hooke's law

Elasticity is the property of a material to return to its original shape and size after the removal of an external force.
Stress is defined as the internal restoring force per unit area induced in a material when subjected to an external force.
The formula for stress is: Stress = Force / Area, and its unit is Pascals (Pa).
Strain is the measure of the deformation of a material, defined as the ratio of change in dimension to the original dimension.
There are no units for strain as it is a dimensionless quantity.
The relationship between stress and strain is determined by the material's elastic modulus.
Hooke's Law states that within the elastic limit, the stress applied to a material is directly proportional to the strain produced.
The mathematical expression for Hooke's Law is: Stress = Elastic Modulus × Strain.
The elastic modulus is a constant that depends on the material's properties.
There are three types of elastic moduli: Young's modulus, shear modulus, and bulk modulus.
Young's modulus (Y) describes the elasticity of a material under tensile or compressive stress.
The formula for Young's modulus is: Y = (Longitudinal Stress) / (Longitudinal Strain).
Shear modulus (G) measures the material's response to shear stress, where the shape changes but volume remains constant.
The formula for shear modulus is: G = (Shear Stress) / (Shear Strain).
Bulk modulus (K) defines how incompressible a material is under uniform pressure.
The formula for bulk modulus is: K = (Volume Stress) / (Volume Strain).
For most materials, Young's modulus is significantly larger than the shear or bulk modulus.
Stress can be classified into three types: tensile stress, compressive stress, and shear stress.
Tensile stress is caused when a material is stretched, increasing its length.
Compressive stress occurs when a material is compressed, reducing its length.
Shear stress is caused by forces acting tangentially to the surface of a material.
Elastic limit is the maximum stress a material can withstand without undergoing permanent deformation.
If stress exceeds the elastic limit, the material enters the plastic region, where deformation is irreversible.
The point where a material breaks under stress is called the breaking point.
The region of stress-strain behavior before the elastic limit is the elastic region.
The area under the stress-strain curve in the elastic region represents the elastic energy stored in the material.
Materials with high elastic modulus are considered stiffer and more resistant to deformation.
The Poisson's ratio is the ratio of lateral strain to longitudinal strain and is dimensionless.
For most materials, Poisson's ratio lies between 0 and 0.5.
Rubber has a low Young's modulus, making it highly elastic and deformable under stress.
Steel has a high Young's modulus, making it strong and resistant to deformation.
Elastic hysteresis occurs when the strain lags behind stress during cyclic loading and unloading.
The spring constant (k) is a measure of stiffness and is related to Hooke's law by the formula: F = k × x, where F is force and x is deformation.
In isotropic materials, the mechanical properties are identical in all directions.
Anisotropic materials have varying mechanical properties depending on the direction of stress.
Applications of Hooke's Law include designing springs, beams, and structures subjected to elastic deformation.
The modulus of resilience measures the amount of energy a material can absorb without permanent deformation.
The modulus of toughness represents the total energy a material can absorb before failure.
The concept of elasticity is essential in engineering, material science, and structural analysis.
In engineering, materials are chosen based on their elastic properties to ensure safety and efficiency.
Stress-strain analysis helps predict the failure of materials under different loading conditions.
The SI unit for stress is Pascals (Pa), while strain has no unit.
Understanding elasticity is crucial for designing shock absorbers and suspension systems.
The stress-strain curve provides valuable insights into a material's mechanical behavior.
Materials like glass, ceramics, and some polymers are brittle and have low elastic limits.
Ductile materials, like metals, can sustain significant deformation before breaking.
Hooke's Law is valid only within the elastic limit of a material.