A thermodynamic model was constructed to analyze the negative capacitance effect in the presence of piezoelectricity. The model demonstrated that while piezoelectricity can lead to negative capacitance in principle, it is not strong enough in practice due to the unphysical amounts of charge and strain required. The inclusion of higher-order electromechanical coupling such as electrostriction can make the negative capacitance region accessible at a lower amount of charge. However, the required strains are still unphysical on the order of tens of percent. Furthermore, the material must possess a negative electrostriction coefficient, or else the negative capacitance effect will be suppressed by positive electrostriction. Most commonly used oxides, however, possess positive electrostriction coefficients. Finally, piezoelectricity, electrostriction, and ferroelectricity were analyzed together to show that a negative capacitance effect occurs but due to ferroelectricity and not piezoelectricity. The model ultimately demonstrates that for all practical purposes, pure electromechanical coupling is not strong enough to provide a negative capacitance effect.