In many ways the subject of micromechanics prompts more questions than it answers in a world where many see everything as black or white with no grey areas. If you have been through the basic engineering courses, you will understand the classic model of materials: they are linear, homogeneous, isotropic and Hookean. If you were to trust the model to completely convey reality, you’d think everything is a straight line, predictable and controllable. No doubt you would also have studied several materials’ curves but you were told that studies are always confined to the linear part, that plasticity and viscoelasticity come very late in education and are far-fetched from alloys. You may have been advised that this is the interval where we used materials anyway and that once we leave it, well, we’d better not leave it.
The science of micromechanics v reality
If you have furthered your education or knowledge, you know that this representation is an idealized version of a rather messy, even chaotic reality and it can get messier once you leave the scope of alloys or ferritic materials. Treating composites, more so the ones that are neither neat plies nor savantly knotted ones, will put you in front of the actual reality of nature. It is heterogeneous, by the versatility of the materials within the materials, the defects, the shapes and the difference in properties depending on heat or direction and many other factors. All of this can change depending on temperature, loading conditions or chemical reactions, and if it is not enough, predicting how this agglomeration will behave will rely fundamentally on defining its properties. How would you define the properties of an agglomeration?
Creating firm foundations
The beginnings of micromechanics were sparked by such questions. To address the random and heterogeneous nature of most materials was as revolutionary as the study of fractals was to mathematics and geography: it was wide-spread, present in everything and the prime model of nature. It broke with the linear understanding of our environment and set the path to harder and more complicated investigations. If a material had several lumps of “phases” – near perfect homogeneous material – along with defects and voids on the microscopic scale, how can we know its toughness or elasticity or endurance? Does averaging cover all the properties? Will averaging rely on the density or the actual properties of the phases? And what about defects and voids, how can one average them? However, most importantly, once we can answer those questions within a microscopic scale, how can we relate them to the macroscopic one?
The importance of John Douglas Eshelby
Micromechanics relies on the early works of Eshelby, who related phases to inclusions stuck within an infinite volume. He relied on strain and energy to come up with the average properties of a miscroscopic volume then related them to the macroscopic one. To this day, his solution is the only closed-form expression we rely on and it offers an elegant description to a rather entangled problem.
Several scientists added to his work afterwards to describe more practical problems and develop the calculations behind averaging. After all, Eshelby assumed an infinite volume, which meant a very diluted heterogeneous material. Though in reality, a heterogeneous material is far from diluted. Versatile chunks of different materials are lumped to one another and Eshelby’s results no longer apply correctly – the estimation will be far from the results of experiments. The works that followed focused on Eshelby’s tensors as a starting point but relied on the availability of computers to come up with numerical solutions. Then, experiments to compare the resulting numbers with the actual outcome from tensile testing helped prove the accuracy of certain methods over others, or the preferred use of some for specific cases such as cells method and the use of Fourier series, to approximate representative volumes of the materials and come up with their properties.
Micromechanics and the macroscopic scale
Micromechanics doesn’t stop there however: The discipline involves describing micromechanical fields of stress and displacements and relating them to the macroscopic scale. The process is known as dehomogenization or localization. It also focuses on the study of interfaces between distinct phases, which wasn’t taken into consideration before and, consequently, has had an unquantified impact on materials. The most common example is the debonding phenomenon between the fiber and the matrix in structural composites.
Failure, cracks and defects
Finally, we can also cite the branch of micromechanics that focuses on failure, and most importantly the mechanisms of microcracks and defects. Being able to describe and improve on the micromechanical scale the state of the material will almost always guarantee the absence of cracks. This not only helps in preventing failure, but will also improve the toughness and overall properties of the materials.
The importance of micromechanics’ is growing with innovative technology as the latter is realizing, in different disciplines, that understanding the microscale and the ability to transport the information throughout different scales, are mathematics and practices that are yet to be created and proved. It might be frightening to dive into the intensive mathematics which micromechanics requires, but the thrill of being part of a science that is still growing and unravelling new territory is worth the effort to understand functionals and sixth degree tensors.