# The shape of softness

## What a foam name can tell us

A midsole is a manufactured structure. Its polymer supplies the solid material; processing gives that material cells, surfaces and interfaces; the designer gives the resulting foam a shape. During running, that shaped structure interacts with the foot and the rest of the shoe. Understanding any one level helps, but it does not eliminate the others.

This is why familiar labels can mislead. EVA, TPU, PEBA and TPEE identify chemical families. Aliphatic TPU identifies a branch within TPU. Supercritical describes a processing condition, and expanded beads describe a structure that can be joined into a part. BASF’s current portfolio, for example, includes aliphatic TPU for bead molding, autoclave foaming and SCF injection. These are intersecting choices, rather than successive generations on one performance ladder. [BASF’s manufacturing portfolio](https://plastics-rubber.basf.com/emea/en/performance_polymers/products/infinergy).

The useful question is how each choice changes the next level: which molecular arrangements are possible, which cellular structures can be manufactured, and what the complete shoe actually does under a specified load.

## The solid inside the bubbles

EVA is a statistical copolymer of ethylene and vinyl acetate. Its architecture differs from the deliberately segmented hard-and-soft arrangement of many thermoplastic elastomers. Vinyl-acetate content and crosslinking both influence the material’s thermal and rheological behavior. The shorthand “EVA” therefore leaves important formulation choices unspecified. [Primary study of EVA crystallinity and crosslinking](https://www.sciencedirect.com/science/article/pii/S0032386105014308).

In PEBA, polyamide blocks and polyether blocks play distinct roles. Arkema identifies PA12-based standard Pebax grades and PA11-based Pebax Rnew grades. TPU instead uses polyurethane chemistry, while common TPEE architectures combine polyester hard blocks and polyether soft blocks. These descriptions explain the families; they do not identify a particular shoe’s blend or processing history. [Arkema’s architecture description](https://hpp.arkema.com/en/product-families/pebax-elastomer-family/), [primary PBT/PTMG foaming study](https://hgxb.cip.com.cn/EN/10.11949/0438-1157.20191196).

The distinction between a chain and a network is essential. Covalent bonds connect the units along a polymer chain. Separate chains can also be joined by covalent bridges, or restrained through physical associations and crystalline regions. A diagram should make those connections legible. Drawing every connection as an identical spring hides precisely the chemistry that distinguishes the materials.

## Aliphatic is a choice, not a performance guarantee

Changing a TPU’s isocyanate changes molecular geometry and possible interactions. Yet aromaticity alone does not decide the outcome. A study comparing linear aliphatic and cycloaliphatic hard segments found that symmetry, steric effects and hard-segment content had to be considered together. Saturated rings remain rings; removing aromaticity does not turn every building block into a freely jointed strand. [Seidler et al., structural comparison](https://onlinelibrary.wiley.com/doi/10.1002/pola.29190).

There is a well-supported optical distinction: aromatic TPU can form colored structures under ultraviolet exposure, and aliphatic alternatives address that yellowing pathway. That helps explain their use where color stability matters. It does not establish a universal foam-density or fatigue advantage. Those require evidence from the actual formulations and specimens being compared. [Covestro’s optical-properties explanation](https://solutions.covestro.com/en/highlights/articles/theme/product-technology/optical-properties).

For footwear, the promising question is which combinations of chemistry and processing deliver the intended response. “A-TPU” begins that explanation. It cannot finish a comparison with a PEBA shoe whose geometry, density and loading history are different.

## Making gas space is a separate engineering problem

A blowing agent supplies gas. A crosslinker changes the network. Chemical blowing produces gas through a reaction or decomposition; physical blowing introduces a fluid such as nitrogen or carbon dioxide. These distinctions concern different operations, so a physically blown foam can still contain covalent crosslinks.

Zotefoams’ public process illustrates the sequence particularly clearly. Its general platform first creates polymer slabs, with a crosslinking stage, then saturates them with nitrogen in an autoclave. Gas-charged slabs subsequently expand in a lower-pressure vessel. This is a documented manufacturing pathway, not a disclosure of every commercial PEBA product’s formulation. [Zotefoams’ three-stage process](https://www.zotefoams.com/who-we-are/3-stage-process/).

Direct injection offers another sequence. Trexel describes metering supercritical fluid into molten polymer, mixing it into a polymer–gas solution and developing cells during molding. Its published packaging example establishes the process principle, without establishing a universal shoe-molding cycle or performance result. [Trexel’s technical sheet](https://trexel.com/wp-content/uploads/2019/06/Trexel_P-300_datasheet_2019_FINAL.pdf).

The manufacturing distinction is practical: the gas may enter an existing solid preform or a melt; expansion may precede final shaping or occur inside the shaping process. “Supercritical” alone leaves these choices open.

## Cells form, grow and sometimes shrink again

Gas expansion needs a material that can deform, but also enough structural support to retain useful cells. Researchers can adjust polymer rheology, crystallization, temperature and gas conditions to pursue that balance. A PEBA chain-extension study, for example, investigated increasing melt strength and changing crystallization behavior to improve foam expansion. This is a formulation intervention, not evidence that all PEBA naturally foams the same way. [Primary chain-extension study](https://pubs.acs.org/doi/full/10.1021/acs.iecr.4c04375).

Expansion is also not the final instant of manufacture. Gas can diffuse through cell walls. In a study of PEBA foamed with CO₂ and N₂ mixtures, nitrogen addition reduced the large shrinkage and recovery excursions seen with pure CO₂ under the tested conditions. Final dimensions depended on what happened after the initial pressure release. [Yang et al.’s gas-mixture experiments](https://onlinelibrary.wiley.com/doi/10.1002/mame.202300437).

This gives a more useful picture than perfectly sealed microscopic balloons. The cellular material has a solid skeleton, gas-filled space and evolving internal structure. A low density measured immediately after foaming need not equal the stable density available to a shoe designer.

## Beads introduce another scale

An expanded bead contains many cells. Joining thousands of beads adds interfaces between them, creating a second structural scale. BASF’s Infinergy explanation separates expansion of granules from the subsequent steam treatment that softens their outer surfaces for bonding. Steam should not be casually relabeled as the blowing agent in that account. [BASF’s manufacturing explanation](https://www.basf.com/gb/en/media/science-around-us/small-beads-for-long-distances).

A recent ETPU study makes the importance of joining visible. Under weaker welding conditions, failure occurred between beads. Stronger joining shifted failure into the beads; excessive welding could collapse and densify the cellular structure. Surface treatment and welding conditions affected that result. [Himsel et al., welding experiments](https://onlinelibrary.wiley.com/doi/10.1002/pola.70317).

This evidence argues against two appealing shortcuts. Bead skins cannot simply be dismissed as mechanically inactive mass, and their presence cannot guarantee durability. The quality of the connections matters. A continuous foam part avoids interbead interfaces, but that fact alone does not establish higher energy return: the rest of its structure still needs measurement.

## From a cellular structure to a mechanical measurement

Compression changes cell shape and loads the polymer skeleton. At sufficiently large deformation, cell walls approach one another and the material can become much harder to compress further. The useful response is the whole force–displacement relationship over the relevant interval, rather than a single adjective such as soft.

Loading work is the area under the loading curve. Recovered work is the magnitude of the area under unloading. Their ratio gives a return fraction for that cycle. The difference is loop loss. If “hysteresis” means the fractional loss with the same denominator, return is one minus hysteresis. If hysteresis means an area in joules, that subtraction is meaningless.

Definitions can vary even in careful papers. Aimar and colleagues used a loss factor normalized by π times loading work. It cannot be read directly as the fraction of energy lost. Their extracted foam specimens also differ fundamentally from an assembled shoe. [Aimar et al., compression-fatigue methods](https://doi.org/10.1080/19424280.2024.2317881).

Stiffness, modulus and hardness need similar care. Force per displacement describes a structure’s stiffness; stress per strain introduces geometric normalization. Durometer indentation is another protocol. A larger number on one scale cannot automatically be substituted into another.

## Returning more work is not a metabolic percentage

Hoogkamer and colleagues tested complete shoes under a running-like vertical load. Figure 3 reports 11.9 mm peak compression and 7.46 J returned work for the PEBA-and-plate Nike prototype, 6.1 mm and 3.28 J for the Nike Zoom Streak 6, and 5.9 mm and 3.56 J for the adidas Adios Boost 2. This article follows the figure’s Streak value; the discussion prints 3.38 J, a discrepancy the source does not resolve. The prototype’s higher return fraction accompanied substantially greater deformation. Eighteen high-caliber male runners also used the shoes in metabolic testing, with masses matched; the prototype reduced average metabolic cost by about 4%. [Hoogkamer et al., 2018](https://doi.org/10.1007/s40279-017-0811-2).

That is evidence about complete designs. Foam, stack, plate and geometry changed together. It does not assign the whole benefit to PEBA chemistry, and the mechanical return percentage is not the percentage of metabolic energy saved. Nike funded the study, with company employment and consultancy relationships disclosed.

A more closely matched EVA/TPU prototype study found smaller average oxygen-consumption improvements with the softer, more resilient shoe. Even there, compliance and resilience changed together. The experiment supports the combined design change rather than independently estimating each contribution. [Worobets et al., 2014](https://doi.org/10.1080/19424280.2014.918184).

## Wear asks a different question

Initial response and response after use are separate properties. A runner may care about thickness loss, changing stiffness, tearing, comfort or retained running economy. Those outcomes should not be merged into an undefined lifespan score.

Rodrigo-Carranza and colleagues tested 22 men in fresh and 450-km-worn EVA and PEBA prototypes. Metabolic cost increased significantly in the worn PEBA condition, while the corresponding EVA change was not significant. The tested shoes differed in dimensions, and one researcher accumulated their road mileage. The result should remain attached to those prototypes and that exposure. [Primary fresh-versus-worn study](https://onlinelibrary.wiley.com/doi/full/10.1111/sms.14526).

Its mechanical measurements require an especially important label: they came from three-point bending of the complete shoe, not foam compression. The study provides two wear endpoints. A curve drawn through intermediate distances would imply observations that were never made. Likewise, no significant change in one condition does not prove that every EVA midsole remains unchanged over that distance.

## Temperature belongs in the test report

Low-temperature flexibility is useful, but a low glass-transition temperature does not make a foam temperature-invariant. One study of a particular expanded TPU grade reported compression moduli of 1.19 MPa at −20°C, 0.87 MPa at 23°C and 0.82 MPa at 40°C for an approximately 250 kg/m³ material. Those are quasi-static specimen results under a stated method, not a prediction of running feel for every TPU shoe. [Meuchelböck et al., temperature study](https://link.springer.com/article/10.1186/s40712-024-00149-9).

The same principle applies to rate, preconditioning, humidity and recovery time. A comparison becomes useful when those conditions are visible. One shoe’s impact rebound at room temperature and another resin’s small-amplitude dynamic loss factor are not interchangeable observations merely because both concern elasticity.

## Carrying the evidence back to the runner

There are four distinct objects in this story: resin, foam specimen, complete shoe and person running. Chemistry studies explain possible structures. Manufacturing studies show how to obtain and stabilize them. Mechanical tests describe an identified object under a controlled load. Human experiments establish whether a complete design changes a measured outcome for the participants and conditions studied.

The links between these levels are where shoe engineering becomes interesting. Less dense foam can change the mass budget available for a given volume; its response must still support the intended deformation. Greater returned mechanical work can change the shoe–runner interaction; its usefulness cannot be assumed from an isolated percentage. None of these steps, by itself, establishes fewer injuries or less loading at a particular joint.

The evidence supports asking sharper questions rather than memorizing a ranking. Identify the actual product, the tested object, the input load and the reported outcome. Keep unmatched recipes and different tests visibly separate. That approach leaves room for innovation within every family while making extraordinary claims easier to evaluate.

*Research checked September 2026. This synthesis combines primary mechanical studies with primary materials experiments and supplier process documentation. Full-text methods/results were consulted where available; the PEBA chain-extension and structural-comparison passages rely on publisher abstracts/previews. Manufacturer pages establish their own materials and routes, not independent category rankings. No matched five-family study establishes universal rebound, cold-response or service-life rankings here.*