## What is meant by solid mechanics?

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

This area is of extreme importance in the mechanical and civil engineering domain. In a practical scenario, the material is exposed to various loads, these loads cause internal structure changes and deformations. Solid mechanics provides tools and principles for such deformation analysis. The area also aids in determining the external forces in the structures, and the induced stresses and strains.

## Uses of solid mechanics

Solid mechanics is used in a wide range of applications. Some of them are outlined below:

### Civil engineering

The concept of solid mechanics is widely used in civil engineering to design and analyze foundations and structures. Civil engineering applies the concepts of physics and mathematics and studies the behavior of solid materials and advanced materials under the influence of external forces. Advanced materials are specially engineered materials that are intentionally created to achieve specific properties. Researchers from various research groups implement the study of solid mechanics such as non-linear elasticity of solid materials, computational modeling of solid under the influence of large strains and stresses, numerical analysis and simulation of wave propagation problems, fluid mechanics, and viscoelasticity of viscoelastic fluids, and non-linear creep behavior. Civil engineering primarily applies the concepts of solid mechanics to analyze structures such as frames and trusses that undergo deformations under the influence of externally applied forces and moments. Besides, solid mechanics provide relations and structural properties that are implemented in the finite element method that further aids in numerical analysis and calculations. In the building design and analysis, solid mechanics aids in determining the foundations' strength, deformations values, and critical stresses that a beam and columns can withstand. Knowing the material behavior and properties makes an engineer capable of selecting the right concrete mixture and reinforcement options available.

### Mechanical engineering

Mechanical engineers implement the principles of solid mechanics to design and analyze machine components. Functional machine components can be modeled with assumptions to behave as structures, where the concepts of solid mechanics can be applied to determine critical stresses and deformation values. For instance, the crankshaft of an internal combustion engine, which is supported by two bearings at the two ends, can be modeled as a simply supported beam under uniformly distributed loads. Here, all of the concepts of solid mechanics can be applied to determine the stresses, strains, and deformations under known forces. Fluid mechanics applies the concepts of solid mechanics to study the effects caused by hydrostatic forces on large surfaces. Solid mechanics provides the required relations and material properties to determine internally induced forces and deformations. In mechanical engineering, solid mechanics finds its major application in the area of fracture mechanics, since machine components are always functional and are prone to fracture due to continuous cyclic loadings, as in bearings. Fracture mechanics provides a way and methodology to estimate and diagnose a machine part due to crack initiation and probable failure due to fracture. When a cracked machine component develops stress concentrations at the cracked zone, which initiates crack propagation, the estimation of the magnitude of stress concentration is done through solid mechanics concepts.

### Geo-mechanics

Geo-mechanics deals with the study of the earth's surface and associated tectonics under changes in stresses. Tectonics is also affected by the change of earth temperature and pressure. Under such circumstances, the earth's surface and rocks move past one another, the effect of these situations can be predicted by solid mechanics which falls under geomechanics and engineering. The area can be further subdivided into soil mechanics and rock mechanics. The area studies the mechanical behavior of the rocks and soil under extreme shear stresses.

### Nano-mechanics and micromechanics

Nano-mechanics is the application of concepts of mechanics at a nano scale, whereas micromechanics is the application of mechanics concepts at a micro scale. The area of Nano-mechanics deals with the elastic, thermal, and kinematic behaviors. Nano-mechanics primarily is a combination of solid mechanics with quantum mechanics, nanotechnology, and biophysics. Micromechanics deals with application of solid mechanics concepts for composite behavior estimations, it provides tools to analyze materials at molecular level.

## Computational methods in solid mechanics

Civil structures and mechanical components having simple geometry can be easily analyzed with traditional mathematical approaches by using the principles of solid mechanics. Complexity arises when the components and structural geometries become complex. Under those situations, traditional mathematical approaches become very tedious and time-consuming. Hence, over time, researchers from different research groups develop a numerical analysis technique that aids fast and robust approximate solutions to the problems. Such approximation techniques are also known as computational approaches. The finite element method is one such tool. In the finite element method, the structure-property is implemented along with the solid mechanics relations to establish computational methodologies. The structure-property is implemented to develop governing stiffness matrices of finite elements. Using the finite element method, multi-scale and multi-dimensional problems such as two-dimensional and three-dimensional problems can be estimated with ease. The civil engineering structures and machine components are practically three-dimensional.

For instance, a building under experimental analysis provides real-time data based on a time scale, this time scale data is first converted into the frequency domain by using the fast Fourier transforms, and then implemented in the finite element method to derive the stresses such as shear stresses and deformations.

Many engineering software implement finite element methods such as ANSYS, COMSOL Multiphysics, STAAD Pro, and so on.

## Context and Applications

The topic is primarily taught in second-year engineering degree courses of civil engineering and mechanical engineering. The topic is also included in curriculums of science degree courses such as bachelor of science and master of science.

• Bachelors in Technology (Mechanical Engineering)
• Bachelors in Technology (Civil Engineering)
• Masters in Technology (Mechanical Engineering)
• Bachelors in Science (Physics)

## Practice Problems

1. Which of the following is true for the finite element method?

1. It can be used for multi-scale domain
2. It can be used for multi-dimensional problems
3. It is a computational approach
4. All of these

Correct option- d

Explanation: A finite element method is a computational approach that can be applied to multi-scale and multi-dimensional problems.

2. Which of the following is finite element software?

3. Autodesk MAYA
4. All of these

Correct option- a

Explanation: STAAD Pro is a structural analysis and design software primarily used by civil engineers.

3. Nano mechanics is a combination of which of the following areas?

1. Quantum mechanics
2. Nuclear physics
3. Biomechanics
4. Inorganic chemistry

Correct option- a

Explanation: Nano mechanics is an area having a combination of biophysics, quantum physics, nanotechnology, and mechanics.

4. Which of the following are the areas where solid mechanics finds its applications?

1. Mechanical engineering
2. Geo-mechanical engineering
3. Civil engineering
4. All of these

Correct option- d

Explanation: Solid mechanics finds its application in the area of geomechanics, mechanical engineering, and civil engineering.

5. Which of the following area in mechanical engineering extensively uses solid mechanics?

1. Fracture mechanics
2. Engineering mechanics
3. Fluid mechanics
4. Hamiltonian mechanics

Correct option- a

Explanation: Fracture mechanics extensively uses solid mechanics concepts for mechanical engineering applications.

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