The ideal properties of a shoe sole depend on the shoe’s intended use and the wearer’s preferences. Everyday use, recreational sports, and competitive athletics all have different requirements. One demand, however, is almost universal: over a wide load range, the sole should provide a consistent spring effect—especially in the heel area, where the highest loads occur when the foot strikes the ground. This peak load must be effectively absorbed with every step—when walking and especially when running. Foam-based soles, which are predominantly used in shoe soles today, have the disadvantage that they compress significantly under higher loads and therefore feel “harder” and less comfortable.

The aim is to add functional value to existing products, improve the CPM’s methods in an application context, and promote the new material concept of ProgMat. The shoe sole proved to be an ideal example product: almost everyone uses it, and its mechanical properties can be felt directly. This example not only communicates the idea of ProgMat to potential users, it also demonstrates clear improvements of a novel sole compared to conventional models.

As a result of the Serendipity Day, the sole development work at CPM is now accompanied by a Puma employee as product owner. The target sole properties are defined in close coordination with Puma; sole development is carried out at CPM, and results will later be assessed by Puma in terms of performance and applicability. At present, different sole structures are being developed that become active in defined load ranges, pass the load on to each other, and thus cushion optimally. This expands the load range in which CPM’s ProgMat can deliver a spring effect perceived as comfortable—an appreciable advantage over pure foam soles. The CPM structures are currently being produced using additive manufacturing methods such as fused filament fabrication (FFF) or thermoforming and are being tested for their function and mechanical properties.

ProgMat brings algorithms into materials

What underpins the so-called ProgMat—and why the hope of solving the problem described above? The basis is that CPM brings complex functionalities into materials: by programming algorithms into their internal structure, the material’s behavior adapts in a predetermined way to external influences. This can, for example, avoid multi-material solutions altogether, lowering costs and improving product recyclability. The concept of programmable materials expands the design space of materials in unprecedented ways: a component can be made from a single material while exhibiting different properties in different areas—and even changing those properties. Depending on the loads acting on the component, a ProgMat reacts “as programmed.” The key lies in its internal structure. This structure—similar to the natural material wood—consists of a multitude of small, repeating basic units, unit cells, each designed and dimensioned to suit the application.

Metamaterials follow a similar approach in that they also consist of unit cells, giving them properties not found in nature—for example, negative stiffness (the force required to deform the material decreases as deformation increases) or a negative Poisson’s ratio. In contrast to metamaterials, the unit cells in ProgMat are varied within the component volume, which enormously increases the options for achieving a desired component behavior.

Images, left and top center: example of a metamaterial—under tensile strain the stretched structure becomes wider rather than, as with almost all materials, narrower; it exhibits a negative Poisson’s ratio. Image, top right: by varying the unit-cell structure within the material volume, the material responds with an asymmetric change in width to uniaxial compressive loading.

The new material concept requires a new way of thinking and a new approach to component design and manufacturing, since ProgMat cannot be described using conventional material properties. With the “ProgMatCode” software package, the CPM is developing a new tool for design, dimensioning, and optimization, enabling unit cells to be created according to a desired component behavior and arranged within the component volume. In addition, work is being carried out on adapted manufacturing methods for unit cell–based materials and components made from metallic and polymeric materials, since conventional manufacturing methods are generally not suitable for these.

Images: ProgMatCode, the tool for developing and optimizing unit cells and their assemblies.

On the way to series production

At present, the basic working principle of the unit cells to be used in the shoe sole has been defined. Work is underway on their optimal functional design, their arrangement in the midsole, and material selection. Both the choice of material and the design of the unit cells have a decisive influence on the sole’s capabilities. The energy introduced into the sole on ground contact can be released during subsequent unloading to enable locomotion with minimal fatigue.

To establish such a ProgMat shoe sole on the market, it must be producible at scale. Another goal is therefore to use conventional manufacturing processes for thermoplastics, such as injection molding. If successful, the soles developed together with Puma could represent a beneficial innovation in sports footwear and beyond. The potential has been recognized, and the research and development work is proceeding “with powerful momentum and well cushioned.”