CTMD's Calculation of the Materials' Responses to Forced Mechanical Stimuli

A method is proposed for evaluating the relative contributions of the various cluster size-dependent frequencies formulated by CTMD in Chap. 8 , to yield the system's response time distributionsResponse time distributions at equilibrium and non-equilibrium/forced conditions (such as to portray the clustersClusteringclusters' intermittencyIntermittency and the material's dynamic heterogeneityDynamic heterogeneity), which are shown to widen and shift to longer times upon cooling. Then the non-linear stress relaxationStress relaxation and creepCreep behaviors of an amorphous material are formulated at length from the individual primitive relaxorsRelaxorsprimitive relaxors' and clustersClusteringclusters' transition frequencies, to obtain the resulting stress relaxation moduli / creep compliances as functions of timeTime, temperatureTemperature, and overall applied strains/stresses (as generalized standard non-linear solids), such as to account for the non-affinityNon-affinity of the local strains and stresses relative to the overall average ones. The specific effects of cross-linking and crystallinity are then also formulated, followed by the frequency- and temperature-dependent dynamic responsesDynamic responses. The chapter then concentrates on showing that (1) CTMD yields the same classical approximate WLF and VTF behaviorWLF and VTF behavior even at constant volume conditionsConstant volume conditions, (2) predicts no divergence whatsoever of response times, (3) allows a universal formulation of the behavior of amorphous condensed matter, and (4) provides a simple quantitative model of tunable fragilityModel of tunable fragility.