Behavior of friction at material interfaces is inherently nonlinear causing variations and uncertainties in interfacial energy dissipation. A finite element model (FEM) of an elastic–plastic spherical contact subjected to periodic normal and tangential loads is developed to study fundamental mechanisms contributing to the frictional energy dissipation. Particular attention is devoted to three mechanisms: the elastic mismatch between contacting pairs, plastic deformations, and phase difference between the normal and tangential fluctuations in loading. Small tangential loads simulating mild vibrational environments are applied to the model and resulting friction (hysteresis) loops are used to estimate the energy loss per loading cycle. The energy losses are then correlated against the maximum tangential load as a power-law where the exponents show the degree of nonlinearity. Exponents increase significantly with in-phase loading and increasing plasticity. Although increasing elastic mismatch facilitates more dissipation during normal load fluctuations, it has negligible influence on the power-law exponents in tangential loading. Among all the configurations considered, out-of-phase loading with minimal mismatch and no plasticity lead to the smallest power-law exponents; promising linear frictional dissipation. The duration the contact remains stuck during a loading cycle is found to have a predominant influence on the power-law exponents. Thus, controlling that duration enables tunable degree of nonlinearity and magnitude in frictional energy dissipation.