Table 7.

Laplace law

Fibers	R (mm)	T (mm)	$V_{\mathrm{wall}}$ (${\text{cm}}^3$)	$V_0$ (ml)	$V_{\mathrm{infl}}$ (ml)	$V_{\mathrm{cont}}$ (ml)	IF (%)	EF (%)	${\overline{\sigma }}_{\mathrm{infl}}^{1\mathrm{st}}$ (kPa)	${\overline{\sigma }}_{\mathrm{cont}}^{1\mathrm{st}}$ (kPa)	${\overline{\sigma }}_{\mathrm{infl}}^{\mathrm{circ}}$ (kPa)	${\overline{\sigma }}_{\mathrm{cont}}^{\mathrm{circ}}$ (kPa)	${\sigma }_{\mathrm{infl}}^{\mathrm{La}}$ (kPa)	${\sigma }_{\mathrm{cont}}^{\mathrm{La}}$ (kPa)
isotropic	20	0.5	2.6	33.5	59.7	58.6	178.0	1.8	53.3	52.8	46. 4	45.9	46. 6	46.6
tr. iso.	20	0.5	2.6	33.5	57.0	43.7	170.2	23.4	52.8	42.8	48. 4	40.8	44. 6	44.7
ortho.	20	0.5	2.6	33.5	56.0	49.9	167.3	11.0	50.5	44.8	44. 0	39.0	43. 8	43.9
incomp.	20	0.5	2.6	33.5	55.9	50.5	166.9	9.6	50.4	47.0	43. 9	41.0	43. 7	43.8
isotropic	20	2.5	14.2	33.5	48.6	47.7	145.0	1.7	8.7	7.9	7. 5	6.7	7. 1	7.2
tr. iso.	20	2.5	14.2	33.5	46.3	22.9	138.2	50.5	8.5	12.8	7. 7	8.6	6. 8	7.1
ortho.	20	2.5	14.2	33.5	45.5	22.0	136.0	51.7	8.1	5.1	7. 0	3.2	6. 7	7.0
isotropic	20	5.0	31.9	33.5	44.5	43.8	133.0	1.6	4.0	3.1	3. 4	2.5	3. 1	3.1
tr. iso.	20	5.0	31.9	33.5	42.5	21.7	126.9	48.9	3.9	13.0	3. 5	4.2	2. 9	3.2
ortho.	20	5.0	31.9	33.5	41.8	20.7	124.8	50.5	3.7	4.3	3. 1	− 1.1	2. 9	3.1
isotropic	25	0.5	4.0	65.4	119.9	117.7	183.2	1.8	68.5	68.0	59. 7	59.2	60. 2	60.2
tr. iso.	25	0.5	4.0	65.4	114.5	98.4	175.0	14.1	67.9	60.7	62. 3	57.5	57. 5	57.5
ortho.	25	0.5	4.0	65.4	112.4	104.2	171.7	7.3	64.9	60.1	56. 5	52.3	56. 4	56.5
incomp.	25	0.5	4.0	65.4	112.0	104.8	171.2	6.4	64.8	61.9	56. 4	54.0	56. 3	56.3
isotropic	25	2.5	21.7	65.4	97.5	95.8	149.0	1.7	11.1	10.3	9. 7	8.8	9. 3	9.3
tr. iso.	25	2.5	21.7	65.4	93.0	45.7	142.2	50.8	10.9	13.3	10. 0	10.3	8. 9	9.2
ortho.	25	2.5	21.7	65.4	91.5	43.9	139.9	52.1	10.5	5.8	9. 0	4.6	8. 8	9.1
isotropic	25	5.0	47.6	65.4	89.5	87.0	136.8	1.7	5.1	4.2	4. 4	3.5	4. 1	4.1
tr. iso.	25	5.0	47.6	65.4	85.3	43.0	130.4	49.5	5.0	12.7	4. 5	5.5	3. 9	4.1
ortho.	25	5.0	47.6	65.4	83.8	41.2	128.2	50.8	4.7	4.5	4. 0	0.3	3. 8	4.1
isotropic	30	0.5	5.8	113.1	212.1	208.3	187.5	1.8	84.0	83.7	73. 2	72.9	74. 1	74.1
tr. iso.	30	0.5	5.8	113.1	202.3	183.3	178.9	9.4	83.4	78.0	76. 6	73.7	70. 7	70.7
ortho.	30	0.5	5.8	113.1	198.3	187.5	175.3	5.4	79.5	75.2	69. 3	65.5	69. 3	69.3
incomp.	30	0.5	5.8	113.1	197.5	188.2	174.7	4.7	79.5	76.9	69. 2	67.0	69. 0	69.1
isotropic	30	2.5	30.7	113.0	172.2	169.2	152.4	1.8	13.7	12.9	11. 9	11.0	11. 5	11.5
tr. iso.	30	2.5	30.7	113.0	164.4	80.9	145.5	50.8	13.4	14.1	12. 2	11.9	11. 0	11.3
ortho.	30	2.5	30.7	113.0	161.9	77.3	143.2	52.3	12.9	6.9	11. 1	5.9	10. 9	11.2
isotropic	30	5.0	66.5	113.0	158.2	155.5	139.9	1.7	6.3	5.4	5. 4	4.5	5. 1	5.1
tr. iso.	30	5.0	66.5	113.0	150.7	75.4	133.3	50.0	6.1	12.6	5. 5	6.6	4. 8	5.1
ortho.	30	5.0	66.5	113.0	148.2	72.3	131.1	51.2	5.8	4.7	5. 0	1.4	4. 8	5.0

Comparison of FE-based mean principal stresses (${\overline{\sigma }}_{\mathrm{infl}}^{1\mathrm{st}}$, ${\overline{\sigma }}_{\mathrm{cont}}^{1\mathrm{st}}$) and mean circumferential fiber stresses (${\overline{\sigma }}_{\mathrm{infl}}^{\mathrm{circ}}$, ${\overline{\sigma }}_{\mathrm{cont}}^{\mathrm{circ}}$) with Laplace estimations (${\sigma }_{\mathrm{infl}}^{\mathrm{La}}$, ${\sigma }_{\mathrm{cont}}^{\mathrm{La}}$) for the inflated (infl.) and the fully contracted (cont.) state. Radius (R), which is the inverse of curvature C, and thickness (T) of the spheres are varied. Three different fiber laws are applied to each of the resulting spheres: isotropic, transversely isotropic (tr. iso.), and orthotropic (ortho.). For the thinnest spheres, ($T=0.5\text{mm}$) a fully incompressible (incomp.) case is included. Additionally, wall volume $V_{\mathrm{wall}}$, initial cavity volume $V_0$, inflated cavity volume $V_{\mathrm{infl}}$ and cavity volume at contracted state $V_{\mathrm{cont}}$ are given as well as inflation fraction (IF) and ejection fraction (EF)

In bold are the circumferential fiber stresses and Laplace estimations for the inflated state; in these cases the Laplace laws are known to be almost exact