Understanding Continuum Mechanics: Exploring the Concept of Continuum in Physics

In summary, continuum mechanics is a branch of mechanics that considers materials to have a continuous distribution of properties without taking into account intrinsic length scales. The term "discrete" refers to the reality of materials, and continuum mechanics works over a wide range of size scales. A continuum is the smallest possible chunk of stuff that can be analyzed without considering atomic and molecular interactions. The size of the continuum varies for different materials based on their molecular composition.
  • #1
chandran
139
1
What is continuum mechanics. What does the word "continuum mean"?

What is discrete?
 
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  • #2
Continuum mechanics is a branch where the material is considered to have continuous distribution of constitutive properties (material properties) and the whole modeling scheme is typically performed without intrinsic length scales (with some exceptions of course, but I'm thinking you're interested about the elementary end). Discrete is the reality material wise.
 
  • #3
Yea - what PII said. You treat the material as if you didn't know it was composed of discrete (i.e separate) atoms.

The remarkable thing about continuum mechanics is the range of size scales over which it works - you can use the same mechanics to describe the behaviour of a few drops of water or a whole ocean.
 
  • #4
Just adding or supplementing to whatever has been said... A continuum is basically the smallest possible chunk of stuff you can analyze without having to take atoms and molecules into account. Because the stuff in the universe cannot be cut in half an infinite number of times. We eventually get to a point when we're at the atomic level. So continuum mechanics works as long as you make the continuum large enough to neglect the quatumn physics involved in atomic level interactions. That being said, you can imagine the size of the contiuum for different materials will be different since they are made of different stuff in the molecular level.
 

1. What is continuum mechanics?

Continuum mechanics is a branch of mechanics that deals with the behavior of materials that are continuously distributed, such as fluids and solids. It studies the physical laws that govern the motion and deformation of these materials under different conditions.

2. What are the fundamental principles of continuum mechanics?

The fundamental principles of continuum mechanics are conservation of mass, conservation of momentum, and conservation of energy. These principles are applied to study the behavior of materials under various loading and deformation conditions.

3. How is continuum mechanics different from classical mechanics?

Classical mechanics deals with the behavior of individual particles and their interactions, while continuum mechanics takes into account the behavior of a large number of particles and their collective properties. It also considers the effects of time and length scales, which are usually neglected in classical mechanics.

4. What are some applications of continuum mechanics?

Continuum mechanics has many practical applications, including the design and analysis of structures and machines, the study of fluid flow and heat transfer, and the understanding of geological processes such as earthquakes and landslides. It is also used in fields such as biomechanics, materials science, and aerospace engineering.

5. What are the challenges in studying continuum mechanics?

One of the main challenges in studying continuum mechanics is the complexity of the physical laws that govern the behavior of materials. These laws can be highly nonlinear and difficult to solve mathematically. Additionally, the behavior of materials can vary greatly under different conditions, making it challenging to develop accurate and comprehensive models.

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