Fiber simulation is a branch of

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...

that deals with modeling the dynamics and

rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid ( liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an appl ...

fibers Fiber or fibre (from la, fibra, links=no) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often incorporate ...

, i.e. particles of large aspect ratio length to diameter. Fiber simulations are used to gain a better understanding of production processes including fibers (textile and paper industry), biological systems or computer graphics.

Modeling fibers

Many of the models used to simulate fibers were developed by researchers in the field of

. Rheologically speaking fiber suspensions are

non-Newtonian fluid A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for exa ...

s, and can display

normal stress In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...

differences.

Simulation techniques

Early fiber simulations employed particles which were rigid rods or prolate

spheroids A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with ...

, whose

equations of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...

have analytical solutions. More recent models are able to represent flexible fibers. The models rely heavily on

continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such m ...

concepts and the numerical methods employed have some similarities to those employed in

molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the ...

, or in dynamics of multi body systems. The use of computers facilitates greatly the solution of fiber simulation problems. The complexity of the simulations arise from the system having a large number of

degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

, and from the numerous possible interparticle interactions having place, such as

friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...

, hydrodynamic interactions, and other kinds of interparticle forces such as

colloidal A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...

forces that exert attractive or repulsive forces.

References

{{DEFAULTSORT:Fiber Simulation Materials science