Physics - Classical Mechanics - Volumetric Stress and Strain

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Introduction

    Hey it's a me again @drifter1! Today we continue with Physics and more specifically the branch "Classical Mechanics" to continue with the chapter of Equilibrium and Elasticity. In this article we will get into Volumetric Stress and Strain. So, without further ado, let's dive straight into it!

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Volumetric Stress

    In the previous article we talked about how forces can affect the length of an object. That so called stress causes an deformation or strain of the object. If the forces acting on an object deform it in such a way that their is a change to the volume of that object, then we are talking about volumetric stress.

Volumetric Stress is equal to the following pressure:

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Volumetric Strain

    When their is volumetric stress, volumetric deformation or volume strain changes the volume of the body. Mathematically, we define that change as:



Similar to Tensile Strain, Volumetric Strain also has no units.

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Bulk's Modulus of Elasticity

    Bulk's Modulus is a numerical constant that describes the elastic properties of a solid or fluid when it is under pressure on all surfaces. The applied pressure reduces the volume of the material.

Mathematically, Bulk's Modulus is defined as:

• B = Bulk modulus in N/m² or Pa
• ΔP = Change of the pressure that applied on the material
• ΔV = Change of the volume of the material
• V = Initial volume of the material

When the value is independent of pressure, this equation is basically a specific form of Hooke's law of elasticity.

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Compressibility

    The resiprocal of B (1/ B) is called Compressiblity and its S.I. unit is the m²/N or Pa^-1.

    After the pressure applied is removed the object returns back to its original volume up to a point. The Bulk modulus can be used as a measurement of the ability of a material to withstand changes in volume under compression on all sides. The case where the material can't withstand the pressure or stress is referred to as incompressibility.

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RESOURCES:

References

1. https://byjus.com/physics/bulk-modulus-of-elasticity-definition-formula/
2. https://www.britannica.com/science/bulk-modulus
3. https://thefactfactor.com/facts/pure_science/physics/bulk-modulus/4826/

Images

1. https://commons.wikimedia.org/wiki/File:Isostatic_pressure_deformation.svg

Mathematical equations used in this article, where made using quicklatex.

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Previous articles of the series

Rectlinear motion

• Velocity and acceleration in a rectlinear motion -> velocity, acceleration and averages of those
• Rectlinear motion with constant acceleration and free falling -> const acceleration motion and free fall
• Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity
• Rectlinear motion exercises -> examples and tasks in rectlinear motion

Plane motion

• Position, velocity and acceleration vectors in a plane motion -> position, velocity and acceleration in plane motion
• Projectile motion as a plane motion -> missile/bullet motion as a plane motion
• Smooth Circular motion -> smooth circular motion theory
• Plane motion exercises -> examples and tasks in plane motions

Newton's laws and Applications

• Force and Newton's first law -> force, 1st law
• Mass and Newton's second law -> mass, 2nd law
• Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction
• Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications
• Contact forces and friction -> contact force, friction
• Dynamics of Circular motion -> circular motion dynamics, applications
• Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications
• Contact force and friction examples -> exercises in force and friction
• Circular dynamic and vertical circle motion examples -> exercises in circular dynamics
• Advanced Newton law examples -> advanced (more difficult) exercises

Work and Energy

• Work and Kinetic Energy -> Definition of Work, Work by a constant and variable Force, Work and Kinetic Energy, Power, Exercises
• Conservative and Non-Conservative Forces -> Conservation of Energy, Conservative and Non-Conservative Forces and Fields, Calculations and Exercises
• Potential and Mechanical Energy -> Gravitational and Elastic Potential Energy, Conservation of Mechanical Energy, Problem Solving Strategy & Tips
• Force and Potential Energy -> Force as Energy Derivative (1-dim) and Gradient (3-dim)
• Potential Energy Diagrams -> Energy Diagram Interpretation, Steps and Example
• Internal Energy and Work -> Internal Energy, Internal Work

Momentum and Impulse

• Conservation of Momentum -> Momentum, Conservation of Momentum
• Elastic and Inelastic Collisions -> Collision, Elastic Collision, Inelastic Collision
• Collision Examples -> Various Elastic and Inelastic Collision Examples
• Impulse -> Impulse with Example
• Motion of the Center of Mass -> Center of Mass, Motion analysis with examples
• Explaining the Physics behind Rocket Propulsion -> Required Background, Rocket Propulsion Analysis

Angular Motion

• Angular motion basics -> Angular position, velocity and acceleration
• Rotation with constant angular acceleration -> Constant angular acceleration, Example
• Rotational Kinetic Energy & Moment of Inertia -> Rotational kinetic energy, Moment of Inertia
• Parallel Axis Theorem -> Parallel axis theorem with example
• Torque and Angular Acceleration -> Torque, Relation to Angular Acceleration, Example
• Rotation about a moving axis (Rolling motion) -> Fixed and moving axis rotation
• Work and Power in Angular Motion -> Work, Work-Energy Theorem, Power
• Angular Momentum -> Angular Momentum and its conservation
• Explaining the Physics behind Mechanical Gyroscopes -> What they are, History, How they work (Precession, Mathematical Analysis) Difference to Accelerometers
• Exercises around Angular motion -> Angular motion examples

Equilibrium and Elasticity

• Rigid Body Equilibrium -> Equilibrium Conditions of Rigid Bodies, Center of Gravity, Solving Equilibrium Problems
• Force Couple System -> Force Couple System, Example
• Tensile Stress and Strain -> Tensile Stress, Tensile Strain, Young's Modulus, Poisson's Ratio

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Final words | Next up

And this is actually it for today's post!

Next time we will continue with Isotropic Tension and Strain...

See ya!

Keep on drifting!