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Rubber Parts by the Numbers

Designing stretched, inflated and gripping rubber parts: hardness and stiffness, large stretch, inflation limits, friction, temperature, ageing and tests

Design rubber parts that stretch, inflate and grip with numbers: hardness and modulus, large stretch, biaxial thinning, inflation limits, friction, temperature and ageing.

9 chapters · About 90 minutes · Free to read · Intermediate mechanical design

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About this book

Rubber behaves like no other engineering material. It stretches to several times its length and springs back. Its volume barely changes however it is deformed. Its stiffness comes mostly from entropy rather than from atomic bonds, so it gets stiffer, not softer, as it warms. And when it is inflated, it can reach a pressure beyond which it no longer resists, and simply keeps growing until it bursts. Designers who carry the habits of steel into rubber, small strains, linear springs and a fixed modulus, get answers that are wrong by large factors.

This book works through rubber’s numbers in the order a stretched or inflated rubber part is designed: stiffness from hardness, stress at large stretch in one and two directions, inflation and its pressure limit, contact and friction, temperature and the thermoelastic effect, relaxation and ageing, and finally testing. Rubber mounts and vibration isolators are covered in Vibrating Machine Elements by the Numbers; this book concentrates on parts that stretch a long way.

It suits mechanical designers, product engineers and maintenance engineers. It assumes school algebra, the idea of stress and strain, and a little familiarity with gases and pressure. No previous study of rubber is needed.

The running case

Every chapter follows one fictional product. This is an illustration. A small manufacturer of plumbing test equipment designs TP-100, an inflatable test plug for pipes with a 100 mm bore. It is a plain rubber sleeve, 88 mm outside diameter with a 4 mm wall, clamped between two metal end plates 120 mm apart. Air at 150 kPa gauge inflates the sleeve against the pipe wall, sealing the pipe so that a section of drainage can be filled with water and pressure tested. The sleeve is a natural rubber compound of 50 Shore A.

Real test plugs are often reinforced with fabric or cord and carry their makers’ own ratings. TP-100 is deliberately unreinforced so that the rubber’s own behaviour can be followed through the book. The manufacturer, the compound’s properties, the test pressures and every mistake are invented and do not describe KEVOS® work or a real product.

Source limits and professional responsibility

The geometry, gas laws and rubber models in this book are standard, and every calculation was checked by running it. The models describe idealised rubber; real compounds differ with their recipe, filler, cure and age, and a compound’s own test data takes precedence over any estimate here. The neo-Hookean and Gent models are used because they show the shape of rubber’s behaviour clearly, not because they fit every compound.

Inflatable equipment stores energy and can fail violently. Pressure testing of plumbing and drainage is governed by Australian standards, plumbing regulators and the equipment maker’s instructions, and nothing in this book replaces them. The book is educational; the design and rating of real pressurised rubber products are matters for competent engineers working from tested data. The thermodynamics text listed in the references was used only as a map of ideas; nothing from it is reproduced.

Who this book is for

Mechanical designers, product engineers and maintenance engineers who specify or design rubber parts that stretch a long way, such as bladders, sleeves, diaphragms, seals and grippers, and need numbers rather than rules of thumb.

What you will learn

Estimate a rubber compound's stiffness from its hardness and know where that estimate stops being reliable.
Calculate stress, stretch and thickness for rubber stretched in one and two directions, well beyond small strain.
Find the pressure at which an inflated rubber part stops resisting further inflation, and design so that it never reaches it unrestrained.
Estimate contact pressure, friction grip and holding force for an inflated rubber part, with honest margins for friction and temperature.
Plan for temperature, relaxation, ageing and ozone, and test a rubber part before it is trusted.

Inside this book

Chapters

Figure 1Steel and rubber compared as engineering materials

	Structural steel	Natural rubber compound
Young's modulus	about 200,000 MPa	about 1 to 6 MPa, from hardness
Strain in normal service	well under 0.2%	10% to over 100%
Strain at break	20% to 30%, after yielding	400% to 700%
Poisson's ratio	about 0.3	about 0.5, volume nearly constant
Stiffness as temperature rises	falls slowly	rises in proportion to absolute temperature, until the compound degrades
Stress–strain curve	linear to yield	curved from the start, stiffening at large stretch

This is an illustration using round, typical values. A specific compound's data sheet and tests take precedence. The contrast, not the exact numbers, is the point.

What rubber does that metal does notSee why rubber stretches so far, keeps its volume and gets stiffer as it warms, set out the test plug's requirements, and catch a linear calculation that called a dangerous inflation safe.

Figure 2TP-100's compound at a stretch of 1.5 in three membrane states

	Other in-plane stretch	Thickness, fraction of original	True stress in the stretched direction
Uniaxial, free to narrow	0.82	0.82	1.30 MPa
Plane strain, held in the other direction	1.00	0.67	1.48 MPa
Equibiaxial, stretched both ways	1.50	0.44	1.68 MPa

This is an illustration with G = 0.82 MPa. The thinning, and with it the force a membrane can carry per unit length, depends strongly on what the other direction is doing.

Stretching in two directionsCalculate stress and thinning in rubber membranes stretched in two directions, follow the test plug's sleeve into a pipe, and catch a thickness rule borrowed from balloons that rejected a good use.

Figure 2Pressure to hold TP-100's sleeve at a given hoop stretch, free of the pipe

	Neo-Hookean	Gent, Jm = 97	Sleeve mean diameter	Wall thickness
λ = 1.149, in the pipe	33.2 kPa	33.3 kPa	97 mm	3.48 mm
λ = 1.5	62.6 kPa	63.0 kPa	126 mm	2.67 mm
λ = 2	73.1 kPa	74.8 kPa	168 mm	2.00 mm
λ = 4	77.7 kPa	90.8 kPa	336 mm	1.00 mm
λ = 6	77.9 kPa	120.0 kPa	504 mm	0.67 mm

This is an illustration with G = 0.82 MPa, a 4 mm wall at 42 mm mean radius and ends held. The Gent model's late stiffening is what would finally stop free inflation at 150 kPa, at a stretch near 7, close to the compound's breaking stretch.

Inflation and the pressure that stops risingFind the pressure beyond which an inflated rubber sleeve or balloon cannot resist, see why a fixed charge of air is safer than a regulated supply, and catch a plug inflated half out of its pipe.

06
Figure 3TP-100's slip test
Prepare the pipea 400 mm length of the pipe material, cleaned, wetted or greased as the condition requires
Insert and inflateplug fully inserted past its mark, inflated to 150 kPa, held five minutes to settle
Load slowlypull axially through a load cell at a slow, steady rate
Record the peakthe force at which the plug first slides
Hold testat half the peak force, hold for thirty minutes and record any creep movement
Calculatefriction coefficient from peak force over normal force; report mean and lowest
This is an illustration of the manufacturer's test, run for each pipe material and condition the plug is rated for. Results are averaged over five plugs and three pulls each.
Contact, friction and holding forceTurn inflation pressure into contact pressure, sealing and friction grip, set a safety factor that survives wet and greasy pipes, and catch a handbook friction value that let a plug slide out.↗

Figure 2Temperature rise in a fast stretch of TP-100's compound

	Stored energy, neo-Hookean	Temperature rise if no heat escapes
Sleeve in the pipe, plane strain, λ = 1.149	0.032 MJ/m³	about 0.02 K
Strip stretched to λ = 4	5.5 MJ/m³	about 2.6 K
Strip stretched to λ = 6	13.6 MJ/m³	about 6.5 K

This is an illustration. Ideal rubber, all stretching work turned to heat; G = 0.82 MPa; heat capacity about 2.1 MJ/m³·K, an assumed typical value. At very small strains, around 10% or less, real rubber's thermal expansion reverses the effect and it cools slightly on stretching.

Temperature and the thermoelastic effectSee why rubber stiffens as it warms and warms as it stretches, follow the test plug's trapped air from a hot ute to a cold pipe, and catch a falling gauge blamed on a valve that was not leaking.

Apply This in Practice

Use these KEVOS® tools to try the method from this reading with your own numbers.

Explained in this book
Rubber Swelling Test: Crosslink Density, Chain Molar Mass and Network Modulus (Flory–Rehner)
Works G = NkT backwards from a swelling test: it finds the network chain density by the Flory–Rehner equation and reports the shear modulus that density implies.
Used in Temperature and the thermoelastic effect, Relaxation, set, ageing and ozone
Open the calculator

References and source notes

The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 27 October 2026.

J. L. Ericksen (Springer-Verlag, New York; first edition Chapman & Hall, 1991). Introduction to the Thermodynamics of Solids, revised edition (1998). Supplied copyright text, read as a subject map only: the thermodynamic view of rubber elasticity, the inflation stability of balloons under controlled pressure and controlled gas mass, and biaxial stretch of rubber sheets. No passages, equations as set out, figures or exercises are reproduced; the treatment, case and calculations here are this book's own.
L. R. G. Treloar (Clarendon Press, Oxford). The Physics of Rubber Elasticity, 3rd edition (1975). Standard text for the neo-Hookean and Mooney–Rivlin descriptions of rubber, the entropic origin of rubber's stiffness, the thermoelastic effect and the inflation of rubber membranes, used in Chapters 1, 3, 4, 5 and 7.
A. N. Gent, Rubber Chemistry and Technology, vol. 31, no. 4, pp. 896–906. On the relation between indentation hardness and Young's modulus (1958). Source of the relation between Shore A hardness and Young's modulus used in Chapter 2, which departs from measurements below about 40 Shore A.
A. N. Gent, Rubber Chemistry and Technology, vol. 69, pp. 59–61. A new constitutive relation for rubber (1996). Source of the limited-extensibility strain energy used in Chapters 3 and 5 to show how real rubber stiffens at large stretch. The parameter value used here is an illustration.
A. N. Gent (editor) (Hanser). Engineering with Rubber: How to Design Rubber Components, 3rd edition (2012). General reference for compounds, stress relaxation, set, ageing, ozone attack and testing, discussed in Chapters 7 to 9. No values are quoted from it.
International Organization for Standardization. ISO 48-4, ISO 37, ISO 815-1 and ISO 1431-1 (rubber hardness, tensile, compression set and ozone resistance tests) (editions as called up). Named by number and scope as the test methods a rubber specification usually calls up. No values or clauses are quoted from them.
Standards Australia and Standards New Zealand. AS/NZS 3500.2 Plumbing and drainage: Sanitary plumbing and drainage (edition as called up). Named as the standard under which drainage pipework in the running case is tested. The test pressures in this book are illustrations; the standard and the authority set the real ones.

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