# Mechanics of Materials/Introduction to Mechanics of Materials

Author(s): Aaron D. Mazzeo

# 1. Introduction to Mechanics of Materials

Welcome to our undergraduate course on the mechanics of materials. The goal is to crowd-source all the information you would need to learn and understand the concepts taught in a standard university/college level course for mechanical or engineering undergraduates.

## 1.1 Background

This Wikibook is to provide living content for an undergraduate course in mechanics of materials or strength of materials. The material here will eventually be of sufficient quality and interest for self-learning or prescribed study by instructors/faculty members. One objective is that the material here would facilitate in-class discussions, group projects, or problem-solving that would leverage the instructors' expertise to enhance learning outcomes. Another objective is to facilitate students, instructors, professionals, and interested users adding/curating content to accommodate learning styles that might benefit from a spectrum of insights coming from learners and teachers with diverse backgrounds. The course will draw on material openly available with inspiration from key relevant texts. There is also a crowd-sourced mind map available (needs updating) on GitHub for this Wikibook on undergraduate mechanics of materials.

## 1.2 Why Mechanics of Materials?
### We are "Living in the Material World"

George Harrison acknowledged we are "living in the material world." And while he was referring to his journey toward enlightenment through his music, materials and structures surround us. Even the earth on which we stand supports us, and its reaction force against the pull of gravity on us is a form of equilibrium.

### Raw Materials

Materials surround us and even in the natural environment, they are often structurally stacked before going from raw material to feedstock to mechanical structures.

### Scalability

What if there were a set of characteristics associated with solids that could help us determine whether a material will break? Well, these material properties exist and have standardized units and defined metrics for their characterization. These parameters also apply across multiples scales of length. In fact, the material properties go beyond only determining the likelihood of failure, yielding, or breaking, but they also help us determine how much deflection/displacement we should expect at a range of scales.
The study of structural mechanics and materials allows us to predict with reasonable accuracy how much a structure will deflect and its safety against catastrophic failure. Indeed, it is a revolutionary concept to test a small sample of material to characterize its elasticity and strength that we can then relate to anticipated levels of stress and strain within an engineered structure. As our ability to characterize materials and predict invisible distributions of stress within structures has improved, our confidence in the predictions and accepted factors have decreased by an order of magnitude.

#### Small Structures

These materials properties are applicable to small structures at the micron scale (1/1000th of a millimeter). Engineering examples include a small micro chain created by engineers at Sandia National Labs. Material properties such as elastic modulus and strength would be relevant to potential yielding and deflection of these micro components. Nonetheless, characteristic material properties, such as those associated with silicone and silicon, can change from their bulk properties at larger sizes in significant fashion as the size of features approaches the micron scale.

#### Medium Structures

Examples of medium-sized structures might have the length, width, or thickness of a surfboard. In addition to needing support static loads that might be distributed or concentrated along its surfaces, a surfboard must also be able to withstand repetitive or cyclic loads that could lead to fatigue-based failure.

#### Large Structures

We might think about the loading -- forces and stresses -- acting on the columns of buildings in the Roman Forum. We might envision corrosion and its effects on decreasing the effective cross-sectional areas of structures and how the stresses could build up to lead to mechanical failure.
We can also think about the distribution of stress within the crust of the earth. While we have not introduced a formal definition of stress, you can begin to image that as pieces (e.g., plates) exert forces on each other, there is a buildup of internal loading on the material within these structures, which constitutes stress.

### Safety

Content forthcoming

### New Technologies

Content forthcoming

### Sustainability

Content forthcoming

## 1.3 Available Formats
### Wikibook

This Wikibook on Mechanics of Materials is the primary source for content and updates.

### Mind Map

We have started to create MechMatMindMap on GitHub, which has a mind map created in Freeplane. This mind map should mirror the content on this Wikibook. This mind map lags the content here, and we welcome updates from the community.

### PDFs

In the same GitHub project (MechMatMindMap), we will provide a PDF of this Mechanics of Materials Wikibook. The most current printable version/PDF of this Wikibook is available by clicking on the appropriate link on the Mechanics of Materials page.

### PowerPoint Slides

Content forthcoming

### YouTube

Content forthcoming

## 1.4 How to Use and Contribute Living Content

We aim to become a living source of content for undergraduate courses in mechanics of materials for independent study and meaningful learning sessions with peers and expert instructors. We invite instructors and students to work together with crowd-sourced content freely available on GitHub and Wikimedia sites using open-source platforms. We hope to create, assemble, and curate high-quality content, examples, problems, and videos to allow university-level mastery in an engaging format.
Students and instructors may use the material curated and created for the teaching and studying of Mechanics of Materials. This material is to provide living content for an undergraduate course in mechanics of materials or strength of materials. The material here will eventually be of sufficient quality and interest for self-learning or prescribed study by instructors/faculty members. One objective is that the material here would facilitate in-class discussions, group projects, or problem-solving that would leverage the instructors' expertise to enhance learning outcomes. Another objective is to facilitate students, instructors, professionals, and interested users adding/curating content to accommodate learning styles that might benefit from a spectrum of insights coming from learners and teachers with diverse backgrounds.
We also hope that students and instructors will contribute original problems or examples in whatever their form to this Wikibook or the GitHub project (MechMatMindMap) to be formatted and incorporated into this body of work.

## 1.5 Invitation to Contribute

We welcome contributions, as there is not a set cap on the number of illustrative examples/problems we include, nor do we care if the examples come from learners or instructors. We just ask that the problems be thoughtful and relevant. Contributors should also be open to a shuffling order or categorization of shown examples/problems.

## 1.6 Learning Objectives and Philosophy

The hope is that these problems will become part of in-class discussions, small-group learning, projects, or personal study. For classes in which instructors give graded exams, we encourage instructors to create original problems for the students to solve independently. After an exam, the instructors could make the problems available for others to study and add to open-source sites like this Wikibook. This pattern of teaching, learning, and assessment limits ethical concerns/temptations, strengthens the validity of course outcomes, and decreases the anxiety of honest learners who feel they go into exams at a disadvantage to others planning to refer to available databases of solved problems or real-time tutoring services. For engineering students, it also discourages rote memorization and an "arms race" to create an increasing number of "solutions manuals" that inevitably become public. No person or system is flawless or perfect, especially given the stresses and constraints on instructors and learners. Nonetheless, this open-source Wikibook aims to enhance open and transparent learning.

## 1.7 Illustrative Examples/Problems

Content Forthcoming

## References

* ↑ Crandall, Stephen H.; Dahl, Norman C.; Lardner, Thomas J. (1999). An Introduction to the Mechanics of Solids (2nd ed.). McGraw-Hill.
* ↑ Eshbach, Ovid W., ed. (1936). Handbook of Engineering Fundamentals. John Wiley & Sons, Inc.
* ↑ Hibbeler, R. C. (2014). Mechanics of Materials. Prentice Hall.
* ↑ Norton, Robert L. (2014). Machine Design: An Integrated Approach (5th ed.). Prentice Hall.
* ↑ Ashby, Michael F.; Jones, David R. H. (1980). Engineering Materials 1: An Introduction to their Properties and Applications. International Series on Materials Science and Technology. Pergamon Press, Inc.
* ↑ Juvinall, Robert C.; Marshek, Kurt M. (2012). Fundamentals of Machine Component Design (5th ed.). John Wiley & Sons, Inc.
* ↑ Fogiel, Max, ed. (1999). The Handbook of Mechanical Engineering. Research & Education Association.
* ↑ Ucker, Jr., John J.; Pennock, Gordon R.; Shigley, Joseph E. (2017). Theory of Machines and Mechanisms (5th ed.). Oxford University Press.
* ↑ Shigley, Joseph Edward; Mitchell, Larry D. (1983). Mechanical Engineering Design (4th ed.). McGraw-Hill Book Company.
* ↑ Juvinall, Robert C.; Marshek, Kurt M. (2012). Fundamentals of Machine Component Design (5th ed.). John Wiley & Sons, Inc. pp. 273–274.
* ↑ Xu, Wenwei; Chahine, Nadeen; Sulchek, Todd (2011). "Extreme Hardening of PDMS Thin Films Due to High Compressive Strain and Confined Thickness". Langmuir. 27 (13): 8470–8477.
* ↑ Chen, Ming; Pethö, Laszlo; Sologubenko, Alla S.; Ma, Huan; Michler, Johann; Spolenak, Ralph; Wheeler, Jeffrey M. (5/2020). "Achieving micron-scale plasticity and theoretical strength in Silicon". Nature Communications. {{cite journal}}: Check date values in: |date= (help); Cite has empty unknown parameter: |1= (help)
* ↑ Zang, Arno; Stephansson, Ove (2010). Stress Field of the Earth’s Crust. Springer, Dordrecht.