## 4 Conclusions  
This paper explores the influence of distance between indentation on the material properties for polystyrene through experimental nanoindentation and finite element method by using ABAQUS. Considering different depths and orientation, the results presented in Section 3 confirm that the properties are affected by the separation, and show little influence of orientation. The following conclusions can be drawn:  
1. The [PERSON]'s method allows to obtain the stress-strain through the loading-unloading curve from the nanoindentation experiment directly using the finite element method. The material properties will change according to the maximum indentation depth.
2. Berkovich tip orientation does not influence modulus or hardness values at separation above 5, thus removing the importance of the alignment.
3. Experimentally and through FEA, it was shown that for PS, the minimum required spacing to measure properties accurately is _d/h_ \(\sim\) 10-15, depending if indents are performed in a single line or matrix. When indents are executed in a single line or column, the nominal spacing of 10 is sufficient for separate indents to have similar hardness and modulus values and is independent on indentation depth. When a matrix set-up is used, _d/h_ \(>\) 15 is required for a depth of 1 \(\upmu\)m, and at least 10 for deeper indents.
4. At separations below 10-15, hardness and modulus values were lower when compared to those obtained at larger separations or with the first indent. PS tends to form pile-up and crazes when it is plastically deformed, as well as strain harden. The properties will depend on the location of the next indent: the areas having \"softer\" regions are those close to the pile-up, the \"hardest\" areas are close to the apex of the first indent. No or little difference in properties is observed when the indent takes place on optically undamaged surface, even though indents edges and plastic zones overlap.
5. Taking into account the viscoelastic nature of polymer materials and their time-dependent behavior that may increase the indent area for up to 40%, separation of at least 15 is recommended for polymers at all indentation depths for single line or column, or matrix arrangement. Overall, the required minimum spacing is lower than the original 30 times maximum depth rule.  
**Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/10/12/4262/s1](http://www.mdpi.com/2076-3417/10/12/4262/s1)]([http://www.mdpi.com/2076-3417/10/12/4262/s1](http://www.mdpi.com/2076-3417/10/12/4262/s1)), S1. Stress-Strain determination (Tables S1.1; S1.2; S1.3, Figures S1.1; S1.2; S1.3); S2. Mesh Convergence Study (Table S2, Figures S2.1, S2.2, S2.3); S3. Experiment Analysis of Indents in a Matrix for \(h=10\)\(\upmu\)m (Figures S3.1, S3.2); S4. Finite element analysis the maximum depth \(h=5\)\(\upmu\)m and 10 \(\upmu\)m with three different orientations (Figures S4.1, S4.2)  
**Author Contributions:** [PERSON]--investigation, FEA, formal data analysis, visualization, writing-original draft preparation; M.D.--optical and scanning images, graphical abstract, visualization, writing-proof read, and review; [PERSON]--project lead and administration, supervision, investigation, visualization, writing-review, and editing. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Conflicts of Interest:** The authors declare no conflict of interest.