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Sheet metal forming defects > Shape defects evaluation - Differential geometry
   
  > Mechanical defects evaluation and compensation - Continuum mechanics


Continuum mechanics

Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i.e., liquids and gases).
The fact that matter is made of atoms and that it commonly has some sort of heterogeneous microstructure is ignored in the simplifying approximation that physical quantities, such as energy and momentum, can be handled in the infinitesimal limit. Differential equations can thus be employed in solving problems in continuum mechanics.
Some of these differential equations are specific to the materials being investigated and are called constitutive equations, while others capture fundamental physical laws, such as conservation of mass or conservation of momentum. In fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.

The physical laws of solids and fluids do not depend on the coordinate system in which they are observed. Continuum mechanics thus uses tensors, which are mathematical objects that are independent of coordinate system. These tensors can be expressed in coordinate systems for computational convenience.

Continuum mechanics Solid mechanics is the study of the physics of continuous solids with a defined rest shape. Elasticity (physics) describes materials that return to their rest shape after removal of an applied force.
Plasticity describes materials that permanently deform (change their rest shape) after a large enough applied force. Rheology: Given that some materials are viscoelastic (exhibiting a combination of elastic and viscous properties), the boundary between solid mechanics and fluid mechanics is blurry.
Fluid mechanics (including Fluid statics and Fluid dynamics) deals with the physics of fluids. An important property of fluids is viscosity, which is the force generated by a fluid in response to a velocity gradient. Non-Newtonian fluids
Newtonian fluids

Differential geometry and topology

 In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It arises naturally from the study of the theory of differential equations. Differential geometry is the study of geometry using differential calculus (cf. integral geometry). These fields are adjacent, and have many applications in physics, notably in the theory of relativity. Together they make up the geometric theory of differentiable manifolds - which can also be studied directly from the point of view of dynamical systems.


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