Understanding material properties is vital in helping us select the right material for a job and understanding how to use the material in its design to work the way we want. A material's structure is also an important consideration since that influences how it behaves. Homogenization helps to address this and is an important aspect of manufacturing.
Every material has properties. The ABS plastic that is used to make a Lego brick is cheap, stiff and light-weight. The superalloy metal in the blades of our aircraft jet engines can withstand very high temperatures. Aluminum is easy to roll into very thin foil for use in our kitchens. Our ability to understand a material’s properties is crucial to our ability to firstly select a particular material for a particular application, and secondly, to design the part with the correct size and shape so that material and design both work together to give us a performance we expect. This is why ABS plastic, despite its cost advantages, has not found its way into jet engine blades, nor are we likely to see Titanium foil lining our oven pans.
There exists a class of materials however, that are in a gray area between this separation of material and design. We call these materials by many names such as cellular, architected, or meta-materials. A great natural example of this is the bone in our bodies. Each bone has a different shape and size, adapted for its function and position in the body. But that’s not all – peer inside of bone and you notice that it is not a solid chunk of material, shaped to a particular form, like a marble sculpture. Instead, bone consists of tiny, curved structures fused to each other, with empty space surrounding them. It is this empty cell-like structure that makes us say that the structure of bone is cellular in nature. Engineers have been inspired by natural structures like bone, wasp and honeybee nests, and deer antlers to develop similar cellular materials like honeycomb panels that we use in aircraft, or packaging foam used in shipping goods around the world. In all these cases, it’s not just the material itself, but also its structure that influences its behavior.
And this is where it gets interesting. Search for the properties of ABS plastic online, and you will find datasheets that will tell you ABS’s modulus, density and a host of other properties. But what is the property of an aluminum honeycomb panel? Of bone? Of a 3D printed lattice made of ABS? This is harder to determine since it depends on the geometry of the cells that constitute the structure. And this is where homogenization comes to the rescue. Homogenization asks you to imagine that both the material and the empty space around it are in reality just one material – but with different properties. We call these properties effective properties, since they are strictly speaking not true material properties which are valid at every single point. With a cellular material, depending on where you interrogate, you get a different property.
The idea of homogenization is not limited to cellular materials. A class of materials called composites, where two or more constituents are combined into one, also benefits from this approach. In carbon fiber reinforced composites for example, the carbon fiber is an aspect of the material that is separate from the matrix it is embedded in. The properties of the composite depend on the relative amounts of the different materials, and how they are positioned relative to each other.
Effective properties are more challenging to determine experimentally since they are fundamentally dependent on the geometry being tested. Additionally, they are also highly dependent on the direction you test them in. Once determined however, they are critical for designers and engineers who build structures out of them.