Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark difference that makes applied mechanics an essential understanding for practical everyday life. It has numerous applications in a wide variety of fields and disciplines, including but not limited to

structural engineering Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and ca ...

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

, oceanography,

meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...

hydraulics Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid coun ...

mechanical engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, ...

aerospace engineering Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is s ...

nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal o ...

structural design Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and cal ...

, earthquake engineering,

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...

, planetary sciences, and other life sciences. Connecting research between numerous disciplines, applied mechanics plays an important role in both

science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...

and

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

. Pure mechanics describes the response of bodies (solids and fluids) or systems of bodies to external behavior of a body, in either a beginning state of rest or of motion, subjected to the action of forces. Applied mechanics bridges the gap between physical theory and its application to

technology Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, scie ...

. Composed of two main categories, Applied Mechanics can be split into

classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...

; the study of the mechanics of macroscopic solids, and

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...

; the study of the mechanics of macroscopic fluids. Each branch of applied mechanics contains subcategories formed through their own subsections as well.

Classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...

, divided into statics and dynamics, are even further subdivided, with statics' studies split into rigid bodies and rigid structures, and dynamics' studies split into kinematics and

kinetics Kinetics ( grc, κίνησις, , kinesis, ''movement'' or ''to move'') may refer to: Science and medicine * Kinetics (physics), the study of motion and its causes ** Rigid body kinetics, the study of the motion of rigid bodies * Chemical k ...

. Like

is also divided into two sections: statics and dynamics. Within the practical sciences, applied mechanics is useful in formulating new ideas and theories, discovering and interpreting phenomena, and developing experimental and computational tools. In the application of the natural sciences, mechanics was said to be complemented by

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...

, the study of heat and more generally

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...

, and electromechanics, the study of

electricity Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as describ ...

and

magnetism Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particle ...

Overview

Engineering problems are generally tackled with applied mechanics through the application of theories of

and

. Because applied mechanics can be applied in engineering disciplines like

civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...

, materials engineering, and biomedical engineering, it is sometimes referred to as engineering mechanics. Science and engineering are interconnected with respect to applied mechanics, as researches in science are linked to research processes in civil, mechanical, aerospace, materials and biomedical engineering disciplines. In

, applied mechanics’ concepts can be applied to structural design and a variety of engineering sub-topics like structural, coastal, geotechnical, construction, and earthquake engineering. In

, it can be applied in mechatronics and

robotics Robotics is an interdisciplinarity, interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist human ...

, design and drafting,

, machine elements, structural analysis, friction stir welding, and

acoustical engineering Acoustical engineering (also known as acoustic engineering) is the branch of engineering dealing with sound and vibration. It includes the application of acoustics, the science of sound and vibration, in technology. Acoustical engineers are typic ...

. In

, applied mechanics is used in aerodynamics, aerospace structural mechanics and propulsion, aircraft design and flight mechanics. In materials engineering, applied mechanics’ concepts are used in thermoelasticity,

elasticity theory In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are ...

, fracture and failure mechanisms, structural design optimisation, fracture and fatigue, active materials and composites, and computational mechanics. Research in applied mechanics can be directly linked to biomedical engineering areas of interest like orthopaedics; biomechanics; human body motion analysis; soft tissue modelling of muscles, tendons, ligaments, and cartilage; biofluid mechanics; and dynamic systems, performance enhancement, and optimal control.

Brief history

The first science with a theoretical foundation based in mathematics was

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 ...

; the underlying principles of mechanics were first delineated by

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the g ...

in his 1687 book '' Philosophiæ Naturalis Principia Mathematica''''.'' One of the earliest works to define applied mechanics as its own discipline was the three volume ''Handbuch der Mechanik'' written by German physicist and engineer

Franz Josef Gerstner Franz Josef Gerstner (from 1810 Franz Josef Ritter von Gerstner, cs, František Josef Gerstner; 23 February 1756 – 25 July 1832) was a German-Bohemian physicist, astronomer and engineer. Life Gerstner was born in Komotau in Bohemia then part ...

. The first seminal work on applied mechanics to be published in English was A ''Manual of Applied Mechanics'' in 1858 by English mechanical engineer William Rankine. August Föppl, a German mechanical engineer and professor, published ''Vorlesungen über techische Mechanik'' in 1898 in which he introduced

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

to the study of applied mechanics. Applied mechanics was established as a discipline separate from

in the early 1920s with the publication of '' Journal of Applied Mathematics and Mechanics'', the creation of the Society of Applied Mathematics and Mechanics, and the first meeting of the '' International Congress of Applied Mechanics''. In 1921 Austrian scientist Richard von Mises started the '' Journal of Applied Mathematics and Mechanics'' (''Zeitschrift für Angewante Mathematik und Mechanik'') and in 1922 with German scientist Ludwig Prandtl founded the Society of Applied Mathematics and Mechanics ( Gesellschaft für Angewandte Mathematik und Mechanik). During a 1922 conference on hydrodynamics and aerodynamics in Innsbruck, Austria, Theodore von Kármán, a Hungarian engineer, and Tullio Levi-Civita, an Italian mathematician, met and decided to organize a conference on applied mechanics. In 1924 the first meeting of the '' International Congress of Applied Mechanics'' was held in Delft, the Netherlands attended by more than 200 scientist from around the world. Since this first meeting the congress has been held every four years, except during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

; the name of the meeting was changed to ''International Congress of Theoretical and Applied Mechanics'' in 1960. Due to the unpredictable political landscape in Europe after the

First World War World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fig ...

and upheaval of World War II many European scientist and engineers emigrated to the United States. Ukrainian engineer Stephan Timoshenko fled the

Bolsheviks The Bolsheviks (russian: Большевики́, from большинство́ ''bol'shinstvó'', 'majority'),; derived from ''bol'shinstvó'' (большинство́), "majority", literally meaning "one of the majority". also known in English ...

Red Army in 1918 and eventually emigrated to the U.S. in 1922; over the next twenty-two years he taught applied mechanics at the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

and Stanford University. Timoshenko authored thirteen textbooks in applied mechanics, many considered the gold standard in their fields; he also founded the Applied Mechanics Division of the American Society of Mechanical Engineers in 1927 and is considered “America’s Father of Engineering Mechanics.” In 1930 Theodore von Kármán left Germany and became the first director of the Aeronautical Laboratory at the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

; von Kármán would later co-found the

Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a federally funded research and development center and NASA field center in the City of La Cañada Flintridge, California, United States. Founded in the 1930s by Caltech researchers, JPL is owned by NASA ...

in 1944. With the leadership of Timoshenko and von Kármán, the influx of talent from Europe, and the rapid growth of the aeronautical and defense industries, applied mechanics became a mature discipline in the U.S. by 1950.

Branches

Dynamics

Dynamics, the study of the motion and movement of various objects, can be further divided into two branches, kinematics and

. For

, kinematics would be the analysis of moving bodies using time, velocities, displacement, and

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...

. Kinetics would be the study of moving bodies through the lens of the effects of forces and masses. In the context of fluid mechanics, fluid dynamics pertains to the flow and describing of the motion of various fluids.

Statics

The study of statics is the study and describing of bodies at rest. Static analysis in classical mechanics can be broken down into two categories, deformable bodies and non-deformable bodies. When studying deformable bodies, considerations relating to the forces acting on the rigid structures are analyzed. When studying non-deformable bodies, the examination of the structure and material strength is observed. In the context of fluid mechanics, the resting state of the pressure unaffected fluid is taken into account.

Relationship to classical mechanics

Applied Mechanics is a result of the practical applications of various engineering/mechanical disciplines; as illustrated in the table below.

Examples

Newtonian Foundation

Being one of the first sciences for which a systematic theoretical framework was developed, mechanics was spearheaded by Sir Isaac Newton's "Principia" (published in 1687). It is the "divide and rule" strategy developed by Newton that helped to govern motion and split it into dynamics or statics. Depending on the type of ''force'', type of ''matter'', and the ''external forces,'' acting on said matter, will dictate the "Divide and Rule" strategy within dynamic and static studies.

Archimedes' Principle

Archimedes' principle is a major one that contains many defining propositions pertaining to fluid mechanics. As stated by proposition 7 of archimedes' principle, a solid that is heavier than the fluid its placed in, will descend to the bottom of the fluid. If the solid is to be weighed within the fluid, the fluid will be measured as lighter than the weight of the amount of fluid that was displaced by said solid. Further developed upon by proposition 5, if the solid is lighter than the fluid it is placed in, the solid will have to be forcibly immersed to be fully covered by the liquid. The weight of the amount of displaced fluids will then be equal to the weight of the solid.

Major topics

This section based on the "AMR Subject Classification Scheme" from the journal ''Applied Mechanics Reviews''''.''

Foundations and basic methods

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 ...

Finite element method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

* Finite difference method * Other computational methods * Experimental system analysis

Dynamics and vibration

* Dynamics (mechanics) * Kinematics * Vibrations of solids (basic) * Vibrations (structural elements) * Vibrations (structures) * Wave motion in solids * Impact on solids * Waves in incompressible fluids * Waves in compressible fluids * Solid fluid interactions *

Astronautics Astronautics (or cosmonautics) is the theory and practice of travel beyond Earth's atmosphere into outer space. Spaceflight is one of its main applications and space science its overarching field. The term ''astronautics'' (originally ''astrona ...

( celestial and orbital mechanics) * Explosions and

ballistics Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially ranged weapon munitions such as bullets, unguided bombs, rockets or the like; the science or art of designing ...

* Acoustics

Automatic control

* System theory and design * Optimal control system * System and control applications *

Robotics Robotics is an interdisciplinarity, interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist human ...

Manufacturing Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to a ...

Mechanics of solids

* Elasticity * Viscoelasticity * Plasticity and

viscoplasticity Viscoplasticity is a theory in continuum mechanics that describes the rate-dependent inelastic behavior of solids. Rate-dependence in this context means that the deformation of the material depends on the rate at which loads are applied. The in ...

* Composite material mechanics * Cables, rope, beams, etc * Plates, shells, membranes, etc * Structural stability ( buckling, postbuckling) * Electromagneto solid mechanics * Soil mechanics (basic) * Soil mechanics (applied) * Rock mechanics * Material processing * Fracture and damage processes * Fracture and damage mechanics * Experimental stress analysis * Material Testing * Structures (basic) * Structures (ground) * Structures (

ocean The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wo ...

and coastal) * Structures (

mobile Mobile may refer to: Places * Mobile, Alabama, a U.S. port city * Mobile County, Alabama * Mobile, Arizona, a small town near Phoenix, U.S. * Mobile, Newfoundland and Labrador Arts, entertainment, and media Music Groups and labels * Mobile ...

) * Structures (containment) *

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

and wear * Machine elements * Machine design * Fastening and joining

Mechanics of fluids

* Rheology *

Hydraulics Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid coun ...

* Incompressible flow * Compressible flow * Rarefied flow * Multiphase flow * Wall Layers (incl boundary layers) * Internal flow ( pipe, channel, and couette) * Internal flow (inlets, nozzles, diffusers, and cascades) * Free shear layers (mixing layers, jets, wakes, cavities, and plumes)\ * Flow stability *

Turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...

* Electromagneto fluid and plasma dynamics * Navel hydromechanics * Aerodynamics * Machinery fluid dynamics * Lubrication * Flow measurements and visualization

Thermal sciences

Thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...

Heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction ...

(one phase

convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...

) *

(two phase convection) * Heat transfer ( conduction) * Heat transfer (

radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, vi ...

and combined modes) * Heat transfer ( devices and systems) * Thermodynamics of solids *

Mass transfer Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtra ...

(with and without heat transfer) *

Combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combust ...

* Prime movers and propulsion systems

Earth sciences

* Micromeritics * Porous media * Geomechanics * Earthquake mechanics *

Hydrology Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is calle ...

, oceanology, and

Energy systems In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
and
environment Environment most often refers to: NOTOC * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...

* Fossil fuel systems *

Nuclear Nuclear may refer to: Physics Relating to the nucleus of the atom: *Nuclear engineering *Nuclear physics *Nuclear power *Nuclear reactor *Nuclear weapon *Nuclear medicine *Radiation therapy *Nuclear warfare Mathematics *Nuclear space * Nuclear ...

systems * Geothermal systems *

Solar energy Solar energy is radiant light and heat from the Sun that is harnessed using a range of technologies such as solar power to generate electricity, solar thermal energy (including solar water heating), and solar architecture. It is an ...

systems * Wind energy systems * Ocean energy system *

Energy distribution Electric power distribution is the final stage in the delivery of electric power; it carries electricity from the transmission system to individual consumers. Distribution substations connect to the transmission system and lower the transmissio ...

and

storage Storage may refer to: Goods Containers * Dry cask storage, for storing high-level radioactive waste * Food storage * Intermodal container, cargo shipping * Storage tank Facilities * Garage (residential), a storage space normally used to store car ...

* Environmental fluid mechanics * Hazardous waste containment and disposal

Biosciences

Biomechanics Biomechanics is the study of the structure, function and motion of the mechanical aspects of biological systems, at any level from whole organisms to organs, cells and cell organelles, using the methods of mechanics. Biomechanics is a branch ...

* Human factor engineering * Rehabilitation engineering * Sports mechanics

Applications

* Electrical Engineering *

Civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...

Mechanical Engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, ...

* Nuclear engineering * Architectural engineering *

Chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials in ...

* Petroleum engineering

Publications

''Journal of Applied Mathematics and Mechanics''
*
Journal of Applied Mechanics
' *
Applied Mechanics Reviews
' *
Applied Mechanics
' *
Quarterly Journal of Mechanics and Applied Mathematics
' *
Journal of Applied Mathematics and Mechanics (PMM)
' *
Gesellschaft für Angewandte Mathematik und Mechanik
' *
Acta Mechanica Sinica
'

References

External links

;Video and web lectures
Engineering Mechanics Video Lectures and Web NotesApplied Mechanics Video Lectures By Prof.SK. Gupta, Department of Applied Mechanics, IIT Delhi
{{Authority control Mechanics . Structural engineering