Viscoelasticity Fundamentals for Structural Glass Engineers
What Is Viscoelasticity?
Materials in engineering fall on a spectrum. On one end are ideal elastic solids like glass and steel — they deform instantly under load, store all the energy, and spring back completely when the load is removed. On the other end are ideal viscous fluids like water and oil — they flow under load, dissipate all energy as heat, and never recover their shape.
Viscoelastic materials sit in between. They combine both behaviours: part of the deformation is elastic (recoverable), part is viscous (permanent). Their response depends on how fast the load is applied and at what temperature. Glass interlayers — PVB, SentryGlas, EVA, TPU — are all viscoelastic polymers.
Why It Matters for Laminated Glass
Laminated glass is a composite: two or more glass plies bonded by a polymeric interlayer. The interlayer is the viscoelastic component, and its shear modulus G determines whether the glass plies work together (monolithic behaviour) or act independently (layered behaviour).
The interlayer shear modulus spans an enormous range: from 0.01 MPa (soft as a gel) to 300 MPa (stiff as a structural adhesive), depending on temperature and load duration.
The same laminated glass panel can behave almost monolithically in winter and almost as two independent panes in summer. A standard PVB interlayer has G ≈ 250 MPa at −20°C but approaches 0 MPa at 50°C — a shift of over four orders of magnitude.
Historically, structural engineers designed laminated glass ignoring shear coupling entirely — assuming the layered limit (ω = 0). This is safe but extremely conservative, leading to unnecessarily thick, heavy, and expensive glass. Modern standards (EN 16612 and EN 16613) now require engineers to account for the actual interlayer stiffness.
Elastic vs Viscous Behaviour
Hooke’s Law: the elastic component
An ideally elastic material deforms instantaneously under load and returns completely to its original shape when the load is removed. The stress is proportional to the strain:
σ = E · ε (Hooke’s Law)
Where σ is stress [MPa], E is Young’s modulus [MPa], and ε is strain [dimensionless].
Glass itself is essentially perfectly elastic: Eglass = 70,000 MPa (70 GPa), with negligible time-dependence under normal service conditions.
Newton’s Law: the viscous component
An ideally viscous material flows under load. The stress is proportional not to the strain, but to the strain rate:
σ = η · dε/dt (Newton’s Law)
Where η is viscosity [Pa·s] and dε/dt is the strain rate [1/s].
All energy is dissipated as heat — there is no recovery. Water, oil, and polymer melts above their flow temperature approximate this behaviour.
The viscoelastic combination
A viscoelastic material combines both responses. Part of the applied energy is stored elastically (recoverable), and part is dissipated viscously (lost as heat). The balance between these two contributions depends on three factors:
- Load duration (time): short loads → stiffer (more elastic); long loads → softer (more viscous)
- Temperature: low T → stiffer; high T → softer
- Loading rate (frequency): high frequency → stiffer; low frequency → softer
This three-way dependence is what makes viscoelastic materials fundamentally more complex than elastic ones — and why tools like FRACTAN’s Prony Calculator exist.
The Complex Modulus
When a viscoelastic material is tested dynamically (sinusoidal loading), the stress response is also sinusoidal but shifted in phase by an angle δ (delta). This phase shift encodes the balance between elastic and viscous behaviour.
The response is captured by the complex modulus:
G*(ω) = G′(ω) + i·G″(ω)
| Quantity | Symbol | Unit | Physical meaning |
|---|---|---|---|
| Complex modulus | |G*| | MPa | Overall stiffness (stress amplitude / strain amplitude) |
| Storage modulus | G′ | MPa | Energy stored elastically per cycle |
| Loss modulus | G″ | MPa | Energy dissipated as heat per cycle |
| Loss factor | tan(δ) | — | Damping: ratio G″/G′ |
When G′ > G″ (tan δ < 1), the material is predominantly solid-like. When G″ > G′ (tan δ > 1), it is predominantly liquid-like. The crossover G′ = G″ often occurs near the glass transition temperature.
E vs G: DMA instruments often report the Young’s complex modulus E*. For interlayers (nearly incompressible, ν ≈ 0.48), the conversion is simple: G ≈ E / 3. This relationship, E(t) ≈ 3G(t), holds because 2(1 + ν) ≈ 3 when the Poisson ratio is close to 0.5.
Stress Relaxation and Creep
There are two fundamental ways to probe viscoelastic behaviour with static (non-oscillatory) tests:
Stress relaxation
Apply a sudden, constant strain ε0 and measure how the stress σ(t) decreases over time. The ratio σ(t)/ε0 is the relaxation modulus E(t) — the key function described by the Prony series.
At t = 0, the material responds with its maximum modulus. Over time, molecular chains rearrange and the stress decreases. For PVB interlayers, the initial modulus can be 1000× larger than the long-term equilibrium value.
Creep
Apply a sudden, constant stress σ0 and measure how the strain ε(t) increases over time. The ratio ε(t)/σ0 is the creep compliance J(t).
Both tests contain the same information about the material. However, stress relaxation is preferred for interlayer characterisation because the relaxation modulus E(t) is directly represented by the Prony series used in FEM software and design standards.
Important subtlety: the creep compliance J(t) is not the simple reciprocal 1/E(t). The two functions are related by a convolution integral: ∫ G(τ) · J(t − τ) dτ = t. This distinction matters when converting between creep and relaxation data.
The Glass Transition Temperature
The glass transition temperature Tg is the single most important material parameter for an interlayer. It marks the boundary between glassy (stiff) and rubbery (soft) behaviour.
The physical basis is free volume: the empty space between polymer chains. Above Tg, there is enough free volume for molecular rearrangement. Below Tg, the free volume has collapsed and chains are frozen. The fractional free volume at Tg is approximately constant across polymers: fg ≈ 0.025 (about 2.5%).
| Interlayer | Tg (°C) | Structural consequence |
|---|---|---|
| EVA / TPU | < −10 | Always rubbery at service temperatures; low but stable G |
| Standard PVB (BG-R20) | ≈ +8 | Stiff in winter, soft in summer; limited sustained-load capacity |
| Stiff PVB (ES, DG-41) | > +8 | Better sustained-load performance than standard PVB |
| SentryGlas (ionomer) | ≈ +55 | Retains 80 MPa long-term; usable up to ∼50°C |
Why PVB products differ: the plasticiser effect
Different PVB products (standard, acoustic, structural) differ primarily in plasticiser content. Adding plasticiser increases the free volume between polymer chains, which lowers Tg and reduces stiffness. Removing plasticiser does the opposite — hence “Extra Stiff” PVB has less plasticiser, higher Tg, and higher modulus.
The Five Zones of Polymer Behaviour
When the modulus of an amorphous polymer is plotted against time (or temperature) on logarithmic scales, five characteristic zones appear:
- Glassy zone (T << Tg): G ≈ 109 Pa (1 GPa). Rigid, brittle. Chains are frozen.
- Transition zone (T ≈ Tg): G drops by 2–3 orders of magnitude. The glass transition occurs here. Loss tangent tan(δ) reaches 0.2 to 3.0.
- Rubber-elastic plateau (T > Tg): G ≈ 106 Pa (1 MPa). Chains are mobile but entangled.
- Terminal zone: G drops again as entanglements disentangle.
- Flow region: G → 0. The material behaves as a viscous liquid.
A critical practical relationship: a measurement at angular frequency ω is approximately equivalent to a measurement at time t ≈ 1/ω. This means a 3-second wind gust corresponds to ω ≈ 0.33 rad/s, while a 50-year permanent load corresponds to ω ≈ 6 × 10−10 rad/s — frequencies far below any laboratory measurement, which is why time-temperature superposition is needed.
From G(t,T) to Structural Design
The viscoelastic properties of the interlayer feed into structural glass design through a clear chain of calculations:
- G(t, T): The interlayer shear modulus at the design load duration and temperature — from DMA/relaxation data, represented by a Prony series with WLF shift factors.
- ω (omega): The shear transfer coefficient (0 to 1) — computed from G, the ply thicknesses, the interlayer thickness, and the panel span.
- heff: The effective thickness for deflection (hef,w) and stress (hef,σ) — computed from ω and the laminate geometry.
- σmax, wmax: The maximum stress and deflection in the panel — from plate theory using heff and the applied loads.
The accuracy bottleneck is the interlayer data. Research has shown that using simplified stiffness families (EN 16612) for G gives errors of approximately 61% versus experimental measurements. Using actual G(t,T) data from viscoelastic characterisation with time-temperature superposition reduces the error to approximately 3%. The plate theory and FEM solver make almost no difference — what matters is the quality of G.
Explore the Data
See how interlayer stiffness varies with temperature and load duration for all major interlayer types. Our free EN 16613 reference shows G values at all 11 standard conditions.
Launch EN 16613 Reference