Select Maxwell, Kelvin-Voigt, or Standard Linear Solid (SLS) model to calculate creep, stress relaxation, and dynamic viscoelasticity (E', E'', tan δ) in real time. Includes model schematic for intuitive understanding of viscoelastic behavior.
Model & Parameters
Model Selection
E₁ (MPa)
MPa
η (MPa·s)
MPa·s
E₂ (MPa) [SLS]
MPa
Input Value (σ₀ or ε₀)
Results
—
Relaxation Time τ (s)
—
Instantaneous Modulus E₀
—
Long-Term Modulus E∞
—
Peak tanδ
Time
Time response for creep (blue: strain ε) and stress relaxation (red: stress σ).
Model
Schematic of the selected model and how the elastic spring and viscous dashpot are connected.
Dyn
Angular-frequency dependence of E' (storage modulus), E'' (loss modulus), and tanδ.
What exactly is "viscoelasticity" as a property? I can't really picture what it means for elasticity and viscosity to be "mixed"...
🎓
Think of it this way: a purely elastic material behaves like a spring. It deforms immediately under force and returns immediately when the force is removed. A purely viscous material behaves like water or oil: slow motion meets little resistance, fast motion meets more resistance. A viscoelastic material sits between those limits. Silicone gel, for example, can slowly deform under a steady load but bounce when struck quickly. Materials whose behavior depends on time scale are viscoelastic.
🙋
When I tried the Maxwell model in the "Creep" tab, the deformation keeps increasing over time. Doesn't it behave like real materials that "stop at some point"?
🎓
Exactly. In the Maxwell model the elements are in series, so the dashpot can continue deforming without limit, like a flowing liquid. That is useful for fluid-like resins but poor for many solid materials. Switching to the Kelvin-Voigt model shows creep approaching a final value. The SLS model is a useful middle ground because it improves both Kelvin-Voigt's missing instantaneous response and Maxwell's unbounded creep.
🙋
What do E' and E'' mean in the "Dynamic Viscoelasticity" tab? Why does E' increase when the angular frequency goes up?
🎓
E' is the elastic component that stores energy, while E'' is the viscous component that dissipates energy as heat. At low frequency, polymer chains have time to move and the material feels softer. At high frequency, the chains cannot follow the deformation, so the material behaves more like a stiff spring and E' rises. This is why a rubber mallet can feel hard under impact but soft when pressed slowly.
🙋
There's a peak in tanδ (tangent delta) at a specific frequency. What does that mean?
🎓
tanδ = E''/E' is the loss factor, a measure of how much vibration energy is converted into heat. The peak near ω=1/τ often corresponds to a material transition region. Engine mounts and tires use materials with high tanδ in their operating vibration range to absorb vibration. Precision equipment housings often use lower-loss materials when deformation must be minimized.
🙋
How can I use this kind of viscoelasticity in CAE finite element analysis?
🎓
In Ansys or Abaqus, this is usually entered as a viscoelastic material model using a Prony series. A Prony series is a generalized Maxwell model with multiple Maxwell branches in parallel, each with its own relaxation time τᵢ and modulus gᵢ. In practice, those parameters are fitted from DMA data by least squares and then entered into the material model. The graphs here give you an intuition for that fitting process.
Frequently Asked Questions
What is the difference between creep and stress relaxation?
Creep is the phenomenon where deformation increases over time under constant stress (e.g., a plastic shelf holding a heavy load for a long time). Stress relaxation is the phenomenon where stress decreases over time under constant deformation (e.g., the clamping force of a rubber gasket bolted down gradually decreases). Switch the "response type" in the simulator and observe the difference in the graphs.
Why is relaxation time τ important in material design?
τ defines the characteristic time scale of the material. If the product's service time is much longer than τ, the material behaves almost like a liquid (long-term creep issues). If the service time is much shorter than τ, it behaves elastically. In the design of seismic isolation rubber for earthquakes (on the order of seconds), damping materials are sometimes designed so that τ is comparable to the earthquake duration.
What are typical τ values for real materials?
Typical values at room temperature: silicone rubber (τ ≈ 0.1–10 s), epoxy resin (τ ≈ several hours to days), adhesive tape (τ ≈ several seconds to minutes), concrete (τ ≈ several decades). As temperature increases, τ decreases significantly (Arrhenius law). This is why "creep problems in high-temperature environments" are important in engineering.
What are examples of materials with high loss factor tanδ?
Typical examples: adhesive in adhesive tape (tanδ ≈ 1–5), vibration-damping rubber (tanδ ≈ 0.3–1), asphalt (temperature-dependent: high tanδ at high temperatures), tire rubber (tanδ = 0.1–0.3 in the operating range). In general, materials with high tanδ excel at vibration absorption but generate more hysteresis heat, and in tires, this leads to increased rolling resistance (worse fuel economy).
What is the time-temperature superposition (WLF equation)?
For polymeric materials, the relationship "increasing temperature is equivalent to decreasing measurement frequency" (time-temperature superposition) holds. Behavior at low temperature and high frequency is equivalent to that at high temperature and low frequency. This allows obtaining data over a wide frequency range with fewer experiments (master curve). In CAE, it is used to predict temperature-dependent viscoelastic behavior.
How is the SLS model expressed as a Prony series?
The relaxation modulus of the SLS model can be written as G(t) = E₂ + E₁·exp(-t/τ). This corresponds to the one-term Prony series G(t) = G∞ + Σ Gᵢ·exp(-t/τᵢ). When inputting into Ansys or Abaqus, convert to ΔG₁=E₁, τ₁=η/E₁, G∞=E₂. For real materials, multi-term (n=5–20) Prony series are used, fitted to DMA data via least squares.
What is Spring Dashpot?
Spring Dashpot is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Spring-Dashpot Viscoelastic Model Simulator. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Spring-Dashpot Viscoelastic Model Simulator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.
Select your viscoelastic model: Maxwell (spring-dashpot in series), Kelvin-Voigt (parallel), or SLS (Standard Linear Solid with both).
Enter material parameters: E1 (elastic modulus in GPa), η (viscosity in Pa·s), and E2 (secondary modulus for SLS) using the input fields e1Val, etaVal, e2Val.
Define input type and magnitude (inp): step strain, ramp strain, or sinusoidal loading at specified frequency and amplitude.
Run simulation to compute time-domain creep curves, stress relaxation modulus, or frequency-dependent storage/loss moduli.
Worked Example
For a polymer composite using Kelvin-Voigt model with E1=3.5 GPa, η=1.2×10⁸ Pa·s, and step strain of 0.01 (1%), the creep compliance increases from D₀=1/(3.5×10⁹)=2.86×10⁻¹⁰ Pa⁻¹ toward steady-state at time constant τ=η/E=34,286 seconds. At t=100 seconds, strain reaches approximately 0.0115 under constant 3.5 MPa stress. For SLS at 10 Hz sinusoidal loading with E2=1.2 GPa, the storage modulus E' shifts from 4.5 GPa at 0.1 Hz toward E∞=2.7 GPa at 100 Hz.
Practical Notes
Maxwell models predict unbounded creep; use Kelvin-Voigt or SLS for real polymers, rubbers, and asphalts that stabilize under sustained load.
Viscosity units matter: convert poise (1 P=0.1 Pa·s) and use consistent SI. Epoxy: η≈10⁹–10¹⁰ Pa·s; silicone elastomer: η≈10⁷–10⁸ Pa·s.
Stress relaxation time τ=η/E governs response speed; materials with τ>1000 s (bitumen, PTFE) show slow recovery unsuitable for shock loads.
Compare model predictions to DMA (Dynamic Mechanical Analysis) data across temperature and frequency ranges to validate parameter fitting.