Mechanical properties of materials can be derived from the force-displacement relationship through instrumented indentation tests. Complications arise when establishing the full elastic-plastic stress-strain relationship as the accuracy depends on how the material's and indenter's parameters are incorporated. For instance, the effect of the material work-hardening phenomenon such as the pile-up and sink-in effect cannot be accounted for with simplified analytical indentation solutions. Due to this limitation, this paper proposes a new inverse analysis approach based on dimensional functions analysis and artificial neural networks (ANNs). A database of the dimensional functions relating stress and strain parameters of materials has been developed. The database covers a wide range of engineering materials that have the yield strength-to-modulus ratio (σy/E) between 0.001 to 0.5, the work-hardening power (n) between 0-0.5, Poisson's ratio (v) between 0.15-0.45, and the indentation angle (θ) between 65-80 degrees. The proposed algorithm enables determining the nanomechanical stress-strain parameters using the indentation force-displacement relationship, and is applicable to any materials that the properties are within the database range. The obtained results are validated with the conventional test results of steel and aluminum samples. To further demonstrate the application of the proposed algorithm, the nanomechanical stress-strain parameters of ordinary Portland cement phases were determined.