Thermal-Mechanical Simulation: When Materials Disagree About Temperature

A device left on a car dashboard in summer, then carried into a cold winter evening, never drops and never gets hit -- yet it can still crack, bow or come apart. The cause is quiet and invisible: every material in it wants to change size by a different amount when the temperature changes.

Thermal-mechanical simulation predicts what happens when those materials are bonded, screwed or clamped together and are not allowed to go their own way. This article explains the physics, the typical failure modes and the design levers.

CTE Mismatch: The Core Idea

Almost every material expands when heated and shrinks when cooled. The amount is described by the coefficient of thermal expansion (CTE): the change in length per unit length per degree.

The problem is that common product materials have very different CTEs. As general textbook orders of magnitude:

many plastics expand several times more than metals,
aluminium expands noticeably more than steel,
glass and ceramics expand much less than most metals,
a printed circuit board has its own, direction-dependent expansion, set by glass fibre and copper,
adhesives and foams can expand a great deal, but are also very soft.

On its own, each part would simply grow or shrink. Bonded together, they cannot. One part pulls, the other pushes, and the result is internal stress, bending or both -- without any external load at all.

A familiar illustration is the bimetal strip in an old thermostat: two metals bonded together curl when heated because one side wants to get longer than the other. Every bonded stack in a product -- glass on a frame, a display on a housing, a chip on a board -- is a bimetal strip in disguise.

Temperature Scenarios

Products see several kinds of thermal loading:

Hot and cold storage (soak) -- the whole product sits at a high or low temperature long enough to become uniform. Typical of transport, warehouses and cars.
Operating temperature -- heat from processors, batteries and displays creates local hot spots and gradients inside the device.
Temperature cycling and thermal shock -- the product is moved repeatedly between cold and hot, slowly or quickly. Each cycle repeats the stress, which is what drives fatigue.

Public environmental test standards describe such conditions, for example IEC 60068-2-1 (cold), IEC 60068-2-2 (dry heat) and IEC 60068-2-14 (change of temperature). We mention them as public reference only; each product programme defines its own levels and durations.

What Can Go Wrong

Warpage. Asymmetric stacks bend. A housing with a metal plate on one side, a display module bonded to a plastic frame, or a board with components mostly on one side can bow visibly. Warpage causes gaps, misalignment, rattles and uneven contact pressure.

Stress at bonded joints. The adhesive layer between two mismatched parts carries the shear that tries to slide them apart. Stress is usually highest at the ends and corners of a bond line, which is where failures start.

Stress in glass. Glass is strong in compression but sensitive to tension at its surface and edges. A cover glass or lens bonded to a frame that shrinks more in the cold can be put into bending or edge tension -- sometimes enough to add risk on top of daily use loads.

Delamination. When the joint stress exceeds what the interface can hold, layers separate: adhesives peel, coatings lift, laminated stacks open. Delamination often grows slowly over many cycles.

Solder joint fatigue. On a circuit board, components and board expand differently. Each temperature cycle shears the small solder joints in between. At a high level, this is the classic mechanism behind many electronics reliability failures after long service.

Why Soft Materials Need Real Properties Here

In impact simulations, very soft layers such as adhesives, foams and gap fillers are sometimes treated in a simplified way because they carry little load during a fast event. In thermal-mechanical analysis this shortcut can be badly wrong.

Here, the soft layer is often the key player:

Its stiffness decides how much of the mismatch is passed from one part to the other. A soft adhesive lets parts move relative to each other and lowers stress; a stiff one locks them together.
Its own large expansion can push on neighbouring parts.
Many adhesives and polymers change stiffness strongly with temperature -- soft and rubbery when hot, much stiffer when cold.

So the simulation needs realistic, ideally temperature-dependent, properties for these materials. Getting the adhesive wrong can change the predicted stress in the glass or the warpage of a module by a large factor.

A Quasi-Static Problem

Temperature changes in storage and cycling are slow compared with the structural response of a product. There are no impacts and no meaningful vibrations. The physics is quasi-static: at each moment the structure is in equilibrium with the current temperature field.

This has practical consequences for simulation:

Implicit static analysis is a natural choice: temperature is applied in steps and the solver finds equilibrium at each step.
Explicit dynamic solvers can also be used if the temperature is ramped slowly enough; then the analyst must check that kinetic energy stays small compared with internal energy, so that inertia does not pollute the result.
Uniform soak cases only need the temperature value; operating cases first need a thermal analysis to find the temperature distribution, which is then passed to the structural model.
The model must be supported in a way that allows free thermal expansion -- otherwise the supports themselves create fake stress.

Results and How to Read Them

Typical outputs of a thermal-mechanical study include:

Warpage maps: out-of-plane displacement of housings, boards and displays at hot and cold extremes.
Stress and strain in brittle parts: surface tension in glass and lenses, especially near edges and bond lines.
Joint loading: shear and peel in adhesive layers, highest usually at bond ends and corners.
Gap changes: whether clearances close (parts touch and load each other) or open (seals leak, parts rattle).
Cycle ranges: for fatigue questions, the change between hot and cold states matters more than either state alone.

Design Levers

Once the stress paths are visible, the remedies are often straightforward:

Material pairing. Choose neighbouring materials with closer CTEs where possible -- for example a filled plastic instead of an unfilled one next to metal or glass.
Adhesive choice. A more compliant adhesive, or a thicker bond line, absorbs mismatch instead of passing it on. The trade-off with bond strength and impact performance has to be checked.
Compliant mounting. Slots instead of tight holes, floating mounts, gaskets and flexible features let parts expand without fighting each other.
Symmetric layups. Balancing materials on both sides of a stack -- or at least balancing stiffness times expansion -- greatly reduces warpage.
Bond geometry. Shorter bond segments, rounded bond ends and avoiding bonds right at glass edges lower peak stress.

Designing for the Whole Temperature Range

Thermal-mechanical problems are easy to overlook because nothing dramatic happens: no drop, no impact, just time and temperature. Yet warpage, cracked glass and failed joints after storage or cycling are among the more frustrating findings late in a programme. Simulation brings them forward, when material choices and mounting concepts are still open.

AutoCAE.AI helps product teams predict warpage, joint stress and glass risk under hot, cold and cycling conditions, and turn the results into practical design changes. Learn more at www.autocae.ai.