Mechanical Representation
Mathematical frameworks describe the time-dependent and temperature-dependent mechanical response of polymeric materials. This formulation, known as a viscoelastic constitutive model, combines spring and viscous dashpot elements to represent physical behavior. It allows engineers to predict how potting compounds and seals deform under load.
The model captures both the instant elastic reaction and the slow viscous drift that occurs over time.
Component Equations
The Maxwell and Kelvin-Voigt representations are the fundamental building blocks of these equations. The Maxwell model connects a spring and a dashpot in series, making it suitable for describing stress relaxation. The Kelvin-Voigt model places them in parallel, which is useful for modeling creep under a constant load.
Practical engineering analyses use a generalized Maxwell model, which uses multiple spring-dashpot pairs in parallel to represent complex polymers.
Material Characterization
Fitting the model parameters requires a series of dynamic and static laboratory tests. Technicians perform creep tests to measure deformation over time under a constant load, and stress relaxation tests to measure the decay of force at a fixed strain. Dynamic mechanical analysis determines the storage and loss moduli across a range of frequencies.
These data sets are used to calibrate the relaxation times and modulus coefficients of the model.
Numerical Application
Finite element software uses these models to simulate the structural behavior of sensor packages in stressful environments. By applying the calibrated equations, the software predicts the stress distribution on delicate electronic components when the sensor expands or contracts due to temperature changes. This simulation helps to identify potential failure points before the first prototypes are built.
It ensures the final product remains within its mechanical limits throughout its operating life. Designers use these results to select potting materials that will not damage delicate wire bonds or silicon sensor chips during rapid thermal cycling.
