Solid mechanics

Definition: Solid mechanics is the study and testing of a solid material and structure as it reacts to outside influences such as force and temperature. Its practical applications include testing the load and stress limits of structures such as roofs and airplanes and structural materials such as pine and carbon composites. Solid mechanics uses applications that require an understanding of mathematics, computer algorithms, and the laws of physics. Successfully predicting the reaction of a material to a variety of physical stresses addresses safety, economic, and practical concerns. The principles of solid mechanics are used across many branches of engineering.

Basic Principles

The theories and applications of solid mechanics have been practiced for centuries, with basic principles of engineering and mechanics first explained by the ancient Greeks. Greek mathematician Archimedes (ca. 287–ca. 212 BCE), for instance, developed the law of the lever, which explains mechanical force and stress. Fifteenth-century Italian artist and architect Leonardo da Vinci designed mechanisms made of beams and then identified stress distribution across a beam’s section (deformation). Sixteenth-century Italian mathematician Galileo Galilei tested beams to their breaking point (failure). These discoveries and elucidations allowed early builders to know, among other things, the amount of stress materials could withstand before bending or breaking and subsequently compromising the structure being built. Today, advances in the study of solid mechanics have made calculating either the mass of a planet or the properties of a nanoparticle solvable tasks.

The field of solid mechanics still tests solids for stress, deformation, and failure by using a combination of physical testing and mathematics to predict the interactions of matter and force. An additional distinction is now made, however, between statics (the study of objects that are motionless) and dynamics (those that are in motion). Additionally, if the shape of a solid is changed through stress or deformation and the solid returns to its original shape, it is considered elastic. If it remains changed, it is considered plastic.

Additionally, some materials show characteristics that are both solid and fluid, and these are studied in the related field of rheology. Rheology studies material that is primarily in a liquid state, but material that is plastic in nature is also studied. Solid mechanics and its sibling fluid mechanics are known together as “continuum mechanics,” which studies the physical properties of both solids and fluids using mathematical objects and values. However, as solid matter studies delve deeper into micro- and nanotechnology, new mathematical models are constantly needed and being developed.

Core Concepts

The field of solid mechanics began as a branch of mathematics and did not become a branch of engineering until the mid-twentieth century. However, its principles and subspecialties have existed for centuries.

Early Discoveries and Applications of Solid Mechanics. Seventeenth-century English physicist and mathematician Isaac Newton developed three laws of motion that shaped the field of classical mechanics by explaining the relationship between forces applied to a material and the resulting motion caused by those forces. However, his laws did not take into consideration the motion of rigid bodies (solid material that does not change shape or size when force is applied) or of deformable bodies (solid material that undergoes a temporary or a permanent change in shape when force is applied). German mathematician Leonard Euler extended Newton’s laws in 1750 by applying calculus equations in order to include rigid and deformable material in the laws of motion.

Robert Hooke, a late-seventeenth-century mechanician, studied the behavior of metal springs and made important progress in the subfield of elasticity. He discovered Hooke’s law, which explains that force and deformation are related in a linear way: The amount of deformation of an object is in direct proportion to the deforming force, and when the force is removed, the object returns to its original shape and size.

In the nineteenth century, French mathematician Augustin Louis Cauchy developed the present-day mathematical theory of elasticity by studying the effect of pressure on a flat surface. Through this work he introduced the concepts of stress and strain into the theory of elasticity.

Force and Stress. Solid mechanics is concerned with the study of material as it is affected by external force that may or may not cause it to undergo a change in its position or shape. Stress is the measure of the effect (such as twisting, bending, compressing, or stretching) that the external force has on an object or material.

Force can bear on a solid in a “normal” (or perpendicular) direction, or it can bear “in shear.” Shear stress occurs when force is applied at an angle, and materials that don’t support shear stress are generally considered fluids. When shear stress causes an object to twist, the resulting condition is called torsion.

Deformation (Strain), Elasticity, and Plasticity. Deformation, often referred to as strain, is the change in shape, size, or temperature of an object as a result of force being applied to it. Strain measures any internal or external change in the material and informs the mechanician how and where the solid object is changing as it accumulates stress. Applied force or temperature can lead to temporary or permanent deformation of an object or can cause structural failure, which is the complete loss of the material’s ability to support a load.

Elasticity is the ability of some materials to return to their original shape and size after external force or temperature is removed. Hooke’s law explains the linear elasticity of most springs: Until a certain level of force is exhibited, the extension of the spring (its deformation) is in direct proportion to the load (or the force) applied to it. The muscles around the heart obey Hooke’s law, as do spring-operated weighing machines. Structural analysts and engineers use mathematical equations to determine the linear elasticity of material in order to determine load capacity.

On the other hand, plasticity is a material’s inability to return to its original size or shape once an applied force is removed. Plasticity is also referred to as nonlinear elasticity and is seen, for example, when metal is bent using force or high temperature.

Fracture, Creep, and Failure. Fractures are cracks in material when force or temperature is applied. Analytical solid mechanics uses mathematics and knowledge of stress and strain of a material to determine the level of force the material can withstand before fracturing. Fracturing occurs suddenly and often results in the failure of a material or object to perform as it was designed. Creep, on the other hand, is the gradual and permanent deformation of a material as a result of stress. It is time dependent, and the speed with which creep occurs is determined by the weight of the force or the temperature that is applied. Creep may or may not result in failure.

Mechanical Engineering.Mechanical engineering and applied mathematics are two subfields of solid mechanics involved in the construction and efficiency of engines, turbines, and motorized vehicles. With modern levels of engine performance, extreme stress and strain are variables for consideration, and engineers must understand and predict potential areas of stress, fracture, creep, strain, and deformation for each piece of the equipment.

Materials Science. Primary areas of research in materials science include energy storage and composite materials design. A relatively new solar energy technology is the development of thin-film photovoltaic cells, whereby any building surface that faces the sun can use strips of thin-film cells to convert solar energy into electricity. Material scientists and engineers also study the change in properties of materials whose dimensions approach nanometers (billionths of a meter).

Applications Past and Present

Geomechanics. Geomechanics is the study of the behavior of the earth’s soil and rock and how they react to fractures, strains, and stresses. Expertise in solid mechanics and knowledge of its related equipment and testing procedures is crucial to being better able to predict earthquakes, developing cleaner and safer methods of extracting oil from the ground, and to devising new technologies in building increasingly tall structures.

Cultural Infrastructure. In the most basic sense, builders throughout history who attached a roof to a structure depended on solid mechanics. Materials science has its roots in the stonemasonry and ceiling management technology that advanced during the age of medieval cathedrals, especially with the addition of flying buttresses, which allowed ceilings of unprecedented height to be constructed. When steel was added to buildings in the nineteenth century, engineers and designers incorporated knowledge of statics, dynamics, and applied mathematics. Rectangular-shaped skyscrapers have often been replace by curving steel shapes with specially engineered glass in shell-type planes. Engineers employ solid mechanics and related technology to predict the thermal and wind stresses glass and other materials can withstand as well as the potential effects of a building’s strain as it expands and contracts with extreme temperatures or shifts in the wind.

Biomedical Engineering or Biomechanics. Biological organisms combine fluid dynamics and solid matter, as body fluids flow within a solid muscular, skeletal structure. Cells have cytoskeletons, and a cell shape, its “geometry,” affects its life and death. Using nanotechnology, a cell’s cytoskeleton can be stress-tested and mathematically analyzed. Biomedical engineering is profoundly affected by advances in solid mechanics. Prosthetic science, for example, has created metal “bones” that are made of carbon-fiber composites, which are lighter and more maneuverable than ever before.

Manufacturing Engineering. Hermann Staudinger, a German chemist, proved the existence of macromolecules and subsequently won the 1953 Nobel Prize in Chemistry. Polymers are a kind of macromolecule composed of many similar units of molecules strung together. If one were to knit a scarf, for example, then knit another scarf onto the end of the first and a third onto the end of the second and so on, one would have an analogous design—a very long scarf made of scarves. Solid mechanicians engineer new polymers and design the machines and other processes used to make them. Polymers have certain qualities that make them useful, such an ability to “stick” together. Naturally occurring cellulose polymers form wood by bonding together to make trees strong. Manufactured polymers have been used in plastics for many years in beverage bottles, garbage bags, and clothing such as raincoats. But new uses continually arise. Polyurethane, Teflon, and Dacron are well known for their uses in wood preservation, frying pan coatings, and cloth, but all three materials are also used in the manufacture of advanced technology such as artificial heart valves.

Manufacturing engineering is also concerned with formulating new metals and testing them for fracture and deformation as well as for thermal stress and strain. Engineers also predict a material’s potential as a structural component and then determine the effective applications of the material. Polycrystalline substances that are used in solar cells and composites that are used in aerospace and military applications are solids that undergo the constant need for upgraded technology in order to allow them to perform efficiently and economically.

Microelectronics and Nanotechnology. The use of solid mechanics in microelectronics and nanotechnology involves creating custom-designed miniature electronic equipment for industry, manufacturing, academics, and the military, among other areas. “Packaging” microchips, microcircuits, and other devices, along with connecting them for better performance, involves consideration of material stress, strain, creep, and failure rates in order to keep up with the current demand for product and technological developments.

Nanotechnology, which merges sciences such as physics, chemistry, biology, and solid materials, involves the study and use of new nanoscale materials that are far lighter and stronger than old ones. These materials must be analyzed from a solid mechanics point of view for their use in, for example, medical devices and drugs, which has generated excitement about new applications but also at times public concern. US government agencies such as the Occupational Safety and Health Administration (OSHA), the Food and Drug Administration (FDA), and the Environmental Protection Agency (EPA) have also voiced concern about the invasiveness and potential for unintended consequences of nanotechnology in medicine.

Social Context and Future Prospects

Research into solid mechanics has changed a great many aspects of modern society. For example, the revolution in information and communication epitomized by cell phones, computers, and the internet was made possible in large part by advances in microelectronics. Specifically, the silicon-based microchip was enabled by solid mechanics research.

Advances in tectonophysics and seismology are bringing us closer to realistic and reliable earthquake prediction, raising hopes of saving countless lives and dollars. The manufacture of composite materials has made vehicles lighter and stronger. Similar benefits are seen in military technologies such as armor and medical applications such as prosthetics. In the pharmaceutical field, new products include nanoparticles that deliver products more effectively to the body, thereby increasing survival rates in cancer patients. Nanomaterials hold much promise in many other areas as well, from cosmetics to waste treatment. However, such futuristic advances can also be controversial, so development will continue to be backed by extensive research and testing as well as ethical considerations.

Bibliography

Adhami, Reza, Peter M. Meenen III, and Dennis Hite. Fundamental Concepts in Electrical and Computer Engineering with Practical Design Problems. 2nd ed. Boca Raton: Universal, 2005. Print. A well-illustrated guide to the kind of math required to analyze electrical circuits, followed by sections on circuits, digital logic, and DSP.

Arteaga, Robert R. The Building of the Arch. 10th ed. St. Louis: Jefferson National Parks Association, 2002. Print. Describes, with illustrations, how the Gateway Arch in St. Louis, Missouri, was built up from both sides and came together at the top.

Davidson, Frank Paul, and Kathleen Lusk-Brooke, comps. Building the World: An Encyclopedia of the Great Engineering Projects in History. Westport, CT: Greenwood, 2006. Print. Examines more than forty major engineering projects, from the Roman aqueducts to the tunnel under the English Channel.

Finn, John Michael. Classical Mechanics. Sudbury: Jones, 2009. Print. Comprehensive introduction to the study of classical and applied mechanics, suitable for advanced students of physics and mathematics. Contains sections on statistical dynamics and fluid mechanics.

Goldfarb, Daniel. Biophysics Demystified. Maidenhead, England: McGraw-Hill, 2010. Print. Examines anatomical, cellular, and subcellular biophysics as well as tools and techniques used in the field. Designed as a self-teaching tool, this work contains ample examples, illustrations, and quizzes.

Hejazi, Farzad, and Kar Chun Tan. Advanced Solid Mechanics: Simplified Theory. CRC, 2021.

Lubarda, Vlado A., and Marko V. Lubarda. Intermediate Solid Mechanics. Cambridge UP, 2020.

National Geographic Society. The Builders: Marvels of Engineering. Washington, DC: National Geographic Society, 1992. Print. Documents some of the most ambitious civil engineering projects, including roads, canals, bridges, railroads, skyscrapers, sports arenas, and exposition halls. Discussion and excellent illustrations are included for each project.

Shurkin, Joel N. Broken Genius: The Rise and Fall of William Shockley, Creator of the Electronic Age. New York: Macmillan, 2006.

"What Is Solid Mechanics?" University of Auckland, pkel015.connect.amazon.auckland.ac.nz/SolidMechanicsBooks/Part‗I/BookSM‗Part‗I/01‗Introduction/01‗Introduction‗01‗Solid‗Mechanics.pdf. Accessed 27 Sept. 2023.

About the Author

Amanda R. Jones has a master of arts degree from Virginia Tech and a doctorate in English from the University of Virginia. She has written several articles for EBSCO and has published in the Children’s Literature Association Quarterly.