Meaning
Mathematical expressions that calculate the current stress or strain state in a material by integrating its entire past load history govern the analysis of time-dependent deformation. The hereditary integral formulation is particularly useful for modeling viscoelastic polymers and composites that exhibit creep or relaxation. It scales the current response by considering both the magnitude of the applied load and the elapsed time since it was applied.
By continuous summation of these historical increments, the algorithm captures the complex behavior of plastics under variable thermal conditions.
Viscoelastic Response
Stress relaxation during a forming operation depends on how the material remembers past deformation steps. This memory is mathematically represented by a kernel function that decays over time. The solver evaluates this convolution at each increment to predict how the pressure decreases as the panel sits in the mold.
Material Characterization
Characterizing the material parameters for these equations requires experimental tests like stress relaxation or dynamic mechanical analysis. If these parameters are incorrect, the simulation will miscalculate the springback of the thermoformed part. This error directly affects the final geometry and can lead to assembly issues on the factory floor.
Production Calibration
In a high-volume manufacturing environment, predicting the exact relaxation behavior of polymers is necessary to optimize the cooling cycle time. If the cooling time is set too short based on incomplete simulations, the parts will deform when ejected from the tooling. Thus, the mathematical precision of these integrals is directly linked to the operational efficiency of the factory.
