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Athermal elastic moduli of soft sphere packings are known to exhibituniversal scaling properties near the unjamming point, most notably thevanishing of the shear-to-bulk moduli ratio $G/B$ upon decompression.Interestingly, the smallness of $G/B$ stems from the large nonaffinity ofdeformation-induced displacements under shear strains, compared toinsignificant nonaffinity of displacements under compressive strains. In thiswork we show using numerical simulations that the relative weights of theaffine and nonaffine contributions to the bulk modulus, and their dependence onthe proximity to the unjamming point, can qualitatively differ betweendifferent models that feature the same generic unjamming phenomenology. Incanonical models of unjamming we observe that the ratio of the nonaffine tototal bulk moduli $B_{na}/B$ approaches a constant upon decompression, while inother, less well-studied models, it vanishes. We show that the vanishing of$B_{na}/B$ in non-canonical models stems from the emergence of an invariance ofnet (zero) forces on the constituent particles to compressive strains at theonset of unjamming. We provide a theoretical scaling analysis that fullyexplains our numerical observations, and allows to predict the scaling behaviorof $B_{na}/B$ upon unjamming, given the functional form of the pairwiseinteraction potential.

Characterizing nonaffinity upon decompression of soft-sphere packings