FeynAmpDenominatorSimplify[exp] tries to simplify each PropagatorDenominator in a canonical way. FeynAmpDenominatorSimplify[exp, q1] simplifies all FeynAmpDenominators in exp in a canonical way, including momentum shifts. Scaleless integrals are discarded.
FDS\text{FeynAmpDenominatorSimplify}
The cornerstone of dimensional regularization is that \int d^n k f(k)/k^4 = 0
FeynAmpDenominatorSimplify[f[k] FAD[k, k], k]0
This brings some loop integrals into a standard form.
FeynAmpDenominatorSimplify[FAD[k - Subscript[p, 1], k - Subscript[p, 2]], k]\frac{1}{k^2.(k-p_1+p_2){}^2}
FeynAmpDenominatorSimplify[FAD[k, k, k - q], k]\frac{1}{\left(k^2\right)^2.(k-q)^2}
FeynAmpDenominatorSimplify[f[k] FAD[k, k - q, k - q], k]\frac{f(q-k)}{\left(k^2\right)^2.(k-q)^2}
FeynAmpDenominatorSimplify[FAD[k - Subscript[p, 1], k - Subscript[p, 2]] SPD[k, k], k]
ApartFF[%, {k}]
TID[%, k] // Factor2\frac{2 \left(k\cdot p_2\right)+k^2+p_2{}^2}{k^2.(k-p_1+p_2){}^2}
\frac{2 \left(k\cdot p_2\right)+p_2{}^2}{k^2.(k-p_1+p_2){}^2}
\frac{p_1\cdot p_2}{k^2.(k-p_1+p_2){}^2}
FDS[FAD[k - p1, k - p2] SPD[k, OPEDelta]^2, k]\frac{(k\cdot \Delta +\Delta \cdot \;\text{p2})^2}{k^2.(k-\text{p1}+\text{p2})^2}