GENERAL CONCEPTS AND DEFINITIONS
Most Important types of mechanical properties
The mechanical response properties of materials, including therefore those of polymers, encompass a wide variety of very important physical behaviours exhibited under the effect of external stress loads (for example how much the material under consideration can be stretched or bent). The regime of linear elasticity is arguably the most significant of these mechanical properties, since it describes the initial response of the sample to relatively small stresses and resulting strains, whereby the sample is then able to fully recover its original (before deformation) size and shape upon the release of the external loading force.
In general, the mechanical properties of polymers can be characterized in very much the same way as in the case of metals or other standard crystalline materials, in particular through the moduli of elasticity and various other classes of strength measurements, such as the yield and tensile strengths. We provide below a general summary of the most important mechanical and elastic properties of polymeric materials:
- Strength: represents the stress force necessary to fracture the material sample under consideration, whenever the applied force is stronger than a simple linear elastic deformation. Some of the most relevant types of strength quantities involved in typical materials characterization measurements comprise the tensile strength (stretching of the
polymer), compressional strength (compressing the polymer), flexural strength (bending of the polymer), torsional strength (twisting of the polymer), and impact strength (e.g. under the effects of direct hammering).
- Percent Elongation to Break (Ultimate Elongation): this quantity indicates the maximum strain that the polymer sample can attain before it ultimately fractures (at the above-mentioned strength point), as measured in terms of percentage change in the length of the material.
- Young’s Modulus: the ratio of stress to the strain in the linearly elastic response region of the material, thus effectively providing a measure of its overall stiffness.
Some physical factors which affect the strength and overall mechanical properties of semicrystalline polymers include the following considerations:
- The tensile strength of the polymer rises with increase in molecular weight. This correlation can be understood through the following reasoning: at low values of the molecular weight, the polymer chains are loosely tied together by weak intermolecular van der Waals interactions (thus resulting in low strength), whereas for the case of polymers with large molecular weights, the chains become bulky and consequently entangled together, producing high strength values for the polymer.
- The presence of a cross-linked morphology within the polymer structure inhibits the relative motion of the chains, and this results in a strengthening of the polymer.
- The strength of the polymer also increases with its degree of crystallinity, since crystalline phases are typically characterized by stronger intermolecular interactions.
An overview of the mechanical properties of a selection of important polymer materials is offered in the table below (reproduced from Ref. ):
Room-Temperature Mechanical Characteristics of Some of the More Common Polymers 
The Stress-Strain Curve
The overall mechanical characteristics of most polymer materials are embodied in the standard stress-strain curve, the simplest way to visualize the response of a general material under the effects of stress-induced mechanical deformation and loading. Such mechanical response properties are in general sensitive towards numerous external factors, such as the rate of deformation (the so-called strain-rate), the temperature of the sample, and even on the presence of additional chemical products affecting the environment, such as water or organic solvents.
The mechanical behaviour of different classes of polymers is demonstrated in the below image (reproduced from Ref. ), in the form of distinct stress-strain curves. It can be seen that there are essentially three different such classes of stress-strain behaviour within the world of polymers.
Stress–strain behavior of different types of materials. 
From the above image, we deduce that rigid materials such as brittle polymers have high Young’s modulus, but at the same time will undergo fracture when subject to stress and associated elastic compression much earlier (in terms of total elongation strain) than the other classes of polymer materials, as denoted by the end of their corresponding stress-strain curves. At the other extreme, we find the mechanical behaviour of a highly elastic and rubbery class of polymers known as elastomers, that have both low values of the Young’s modulus and are capable of enduring large amounts of recoverable stretching, before ultimately breaking.
For the intermediate case of ductile (plastic) polymers shown above, the distinction between elastic deformation (the initial linear part of the curve) and plastic flow (everything that follows) mechanical behaviours of the material is particularly striking. The stress point separating these two behavioural regimes is known as the yield strength or elastic limit σy of the material. As mentioned previously, as the external stress load and associated sample strain are progressively increased even further, any material will ultimately reach also its tensile strength (TS), at which point the total fracturing and breaking of the material occurs, and thus it no longer makes sense to continue plotting its stress-strain curve. The position of these two limiting behaviours are depicted in the image below (reproduced from Ref. ).
Schematic stress–strain curve for a plastic polymer showing how yield and tensile strengths are determined. 
Moreover, it is worth mentioning that all the mechanical response properties presented so far can be significantly impacted by changes in the temperature of the polymer sample. Some examples of such thermal effects on a certain fixed polymer composition are portrayed in the image below (reproduced from Ref. ), demonstrating how higher temperatures imply reduced rigidity and increased rubber-like ductile behaviour:
Effect of temperature on the mechanical properties of polymer. 
In the specific context of the mechanical properties of polymers, it is important to also discuss the issue of viscoelasticity, which represents a distinct type of deformation as compared with purely elastic response. Under the regime of elasticity in fact, the deformational strain appears immediately within the material upon application of an external stress load, and this strain only vanishes when the stress is completely released, at which point the sample will fully recover its original shape.
Whenever viscous deformation occurs on the other hand, the material does not get strained instantaneously, but rather in a time-dependent fashion. Furthermore, some of this strain deformation will be permanent and irreversible, in the sense that the material will never fully recover its initial dimensions, in very much the same way as in plastic deformation.
Typically, polymers exhibit a combination of both elastic and plastic behaviours, in relation to their temperatures and strain rate, with elastic response dominating at low temperatures and high strain rates (and vice versa for viscous behaviour). The intermediate combined situation of viscoelasticity in polymer science is thus observed in between these two extremes.
INDUSTRIAL APPLICATIONS AND BENEFITS
Polymeric materials are employed in a very broad array of industrial applications, ranging from construction materials to microelectronic devices. In fact, the end-use applications of polymers can be used by itself as a classification method, consisting for example in plastics, elastomers (rubbers), fibres, coatings, adhesives, foams, films, etc. Some examples of fields of industrial application for some common categories of plastic polymers are listed in the table below, for illustrative purposes (figure reproduced from Ref. ):
Trade Names, Characteristics, and Typical Applications for a Number of Plastic Materials 
A good example of a polymer material with remarkable mechanical properties is ultrahigh molecular weight polyethylene (UHMWPE). This polymer consists in linear polyethylene, synthesized in a form that has a particularly large molecular weight. This specific property yields a very tough and resistant material, with the highest impact strength of any thermoplastic being currently manufactured. On the downside, this polymeric material suffers from having an unusually low melting temperature. As a result, its mechanical performance and overall strength are severely weakened at high temperatures. This exceptional set of mechanical properties implies that UHMWPE has progressively found a broad range of industrial and commercial applications, including in biomedical prostheses and implants, bullet-proof vests and other forms of ballistic protection, and for the support of marine structures.
The field of discovery and design of new polymer compositions with enhanced elastic and physical properties continues to this day to be an active area of research and development, particularly as a result of the sheer number of materials compositional and structural possibilities left to discover within the realm of organic chemistry. The use of first principles simulation and machine learning techniques has often played a crucial role in facilitating such novel discoveries. The reader is referred to Refs. [7-9] for examples of exciting recent discoveries and innovations in the world of polymer materials research.
PREDICTION OF MECHANICAL PROPERTIES OF POLYMERS THROUGH CLASSICAL FORCE FIELDS AND MOLECULAR DYNAMICS SIMULATIONS
Classical Molecular Dynamics (MD) simulations lend themselves very well for computing the equilibrium molecular structure of organic materials, as well as the mechanical behaviour of such molecular systems under the effects of applied stress loadings. MD is a computational technique by which the atomic trajectories of a system of numerous particles are generated by numerical time integration of Newton's classical equations of motion (within a given statistical ensemble). Both polymers and polymer-based nanocomposites have been subjected to extensive investigations through such MD techniques [3, 6]. Ref.  in particular offers a thorough introduction on the best practices and computational method choices available for getting started with polymer computational research.
In the context of this short introduction, it suffices to know that classical MD codes such as LAMMPS and GROMACS have in the past proven to be effective in determining both the molecular structures and physical/chemical properties of polymer-based materials, depending of course on an appropriate and careful choice for the interatomic potential (force field) governing the conduct of atomic motion and interactions during MD simulations and structural relaxation calculations. Several such potentials dedicated to organic materials are available for use today, both for modelling direct covalent bonding between atoms as well as the inter-molecular interactions (e.g. Van der Waals forces).
: “Materials Science and Engineering” (10 th edition). William D. Callister, David G. Rethwisch. Wiley, 2020 (https://fac.ksu.edu.sa/sites/default/files/ch15.pdf)
: Biosurfaces: A Materials Science and Engineering Perspective, First Edition. Edited by Kantesh Balani, Vivek Verma, Arvind Agarwal, Roger Narayan. The American Ceramic Society. Published 2015 by John Wiley & Sons, Inc. (https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118950623.app1)
: “Modeling and Simulations of Polymers: A Roadmap”. Thomas E. Gartner and Arthi Jayaraman. Macromolecules 52, 755−786, 2019. (https://pubs.acs.org/doi/pdf/10.1021/acs.macromol.8b01836)
: “Mechanical Properties of Polymers”. Anil K. Bhowmick. MATERIALS SCIENCE AND ENGINEERING – Vol. I – Mechanical Properties of Polymers (https://www.eolss.net/sample-chapters/c05/E6-36-01-03.pdf)
: “Plastics: Materials and Processing” (3 rd edition). A. Brent Young. Pearson, 2006.
: “Prediction of Mechanical Properties of Polymers with Various Force Fields”. Gregory M. Odegard, Thomas C. Clancy and Thomas S. Gates. American Institute of Aeronautics and Astronautics, 2005. (https://ntrs.nasa.gov/api/citations/20050198872/downloads/20050198872.pdf)
: University of Delaware. "Bundlemers (new polymer units) could transform industries: New building blocks could usher in exciting era of materials discovery." ScienceDaily. ScienceDaily, 30 October 2019. (www.sciencedaily.com/releases/2019/10/191030155834.htm).
: “The Next 100 Years of Polymer Science”. Alaa S. Abd-El-Aziz et al. Macromol. Chem. Phys. 221, 2000216 (2020). (https://onlinelibrary.wiley.com/doi/epdf/10.1002/macp.202000216)
: Wu, S., Kondo, Y., Kakimoto, Ma. et al. Machine-learning-assisted discovery of polymers with high thermal conductivity using a molecular design algorithm. npj Comput Mater 5, 66 (2019). (https://doi.org/10.1038/s41524-019-0203-2)
Virtual Lab. Inc.