Compression fatigue of elastomeric foams used in midsoles of running shoes

Figures & data

Figure 1. (a) Reaction foot-ground force f_z during a stride of a runner (75 kg, 12 km h⁻¹), adapted from previous studies (Clarke et al., 1983; Nigg, 1986). (b) Vertical slice obtained by X-ray tomography of the first studied running shoe with a zoom on the sole structure and on the 3D microstructure of its midsole foam F₁ obtained by X-ray microtomography. (A) Stiffer plate and (B) air volume inserted in the midsole. (c) Vertical slices obtained by X-ray tomography of the other studied soles and their respective midsoles F₂, F₂*, F₃ and F₄ (for (b) and (c), see materials and methods for acquisition parameters and shoes information).

Figure 2. Typical stress–strain behaviour (case of foam F1) during the first compression cycle. The three densification phases during loading are noted (i), (ii) and (iii). (A) Illustration of a typical undeformed sample (case of foam F1) mounted between the compression platens, corresponding to ${\epsilon }^0$, (M) same sample at maximum strain ${\epsilon }^{\mathrm{\text{max}}}$ and (R) at residual strain ${\epsilon }^{\mathit{\text{res}}}$.

Table 1. Foams under study and their properties.

Foam	Polymer	Lightness	Cushioning	Rebound	Durability
F1	EVA		X	X	X
F2, F2*	EVA	X	X		X
F3	TPU		X		X
F4	PEBA	X		X

Table 2. Structural descriptors and mechanical properties during N = 1.

		F1	F2	F2*	F3	F4
Structural	$\rho$ (g cm^−3)	0.17 ± 0.02	0.13 ± 0.02	0.23 ± 0.02	0.24 ± 0.02	0.09 ± 0.02
	$\varphi$ (-)	0.79 ± 0.02	0.79 ± 0.02	0.71 ± 0.02	0.72 ± 0.02	0.90 ± 0.02
	$C$ (µm)	80 ± 47 %	35 ± 29 %	111 ± 46 %	–	87 ± 36 %
	$t$ (µm)	19 ± 44 %	5 ± 23 %	33 ± 61 %	–	10 ± 19 %
Mechanical	${\sigma }_c$ (MPa)	0.1 ± 0.1	0.1 ± 0.1	0.1 ± 0.1	0.1 ± 0.1	–
	${\sigma }_{\mathrm{\text{max}}}/\rho$ (MPa cm^3 g^−1)	7.2 ± 0.2	8.8 ± 0.2	3.9 ± 0.2	3.3 ± 0.3	6.4 ± 0.1
	$W_{\mathit{\text{abs}}}^{\mathrm{\text{max}}}$ /ρ (mJ g^−1)	3.9 ± 0.1	4.9 ± 0.1	2.7 ± 0.1	2.1 ± 0.1	3.6 ± 0.1
	$\eta$ (-)	0.13 ± 0.01	0.14 ± 0.01	0.12 ± 0.01	0.05 ± 0.01	0.06 ± 0.01
	${\epsilon }^{\mathit{\text{res}}}$ (-)	0.16 ± 0.02	0.15 ± 0.01	0.14 ± 0.01	0.05 ± 0.02	0.09 ± 0.01

Figure 3. 2D grey levels slices obtained with μCT showing the inner microstructure the studied foams along the compression plane (x, z).

Figure 4. Stress–strain behaviour of all foams at (a) N = 1 and (b) N = 200,000. Volumetric absorbed energy diagram at (c) N = 1 and (d) N = 200,000. Volumetric absorbed energy diagram normalized by the Young modulus of the foam parent polymer at (e) N = 1 and (f) N = 200,000.

Figure 5. Evolution of (a) the maximum specific stress, (b) the maximum specific volumetric absorbed energy, (c) the damping loss factor and (d) the residual strain, as a function of the number of compression cycles for all foams. The errors bars represent the standard deviation of the data of the three tested sample. The legend is the same as Figure 4.

Clarke, T. E., Frederick, E. C., & Cooper, L. B. (1983). Effects of shoe cushioning upon ground reaction forces in running. International Journal of Sports Medicine, 4(4), 247–251. https://doi.org/10.1055/s-2008-1026043

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Nigg, B. M. (Ed.). (1986). Biomechanics of running shoes. Human Kinetics.

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