Correction: Kantaros et al. Smart Design Aided by Mathematical Approaches: Adaptive Manufacturing, Sustainability, and Biomimetic Materials. Designs 2025, 9, 102

In the published paper [1] there are two corrections that must take place. First, figures 4 and 5 and the equation appearing in Section 6 of the original manuscript are published (apart from the PhD Thesis from Kantaros, 2015, which was cited in the original manuscript) in the original literature work published in 2016 by Kantaros, Chatzidai and Karalekas, as cited in the newly inserted reference [2].

We changed the paragraph:

In this context, the figures below present an example of the aforementioned workflow from design to finite element simulation of a lattice scaffold structure used for biomedical applications, illustrating how stress and deformation fields can be visualized and refined before fabrication from a published literature work of the author [131].

With

In this context, the figures below present an example of the aforementioned workflow from design to finite element simulation of a lattice scaffold structure used for biomedical applications, illustrating how stress and deformation fields can be visualized and refined before fabrication from a published literature work by Kantaros, Chatzidai and Karalekas in 2016 [131] and PhD Thesis from Kantaros 2015 [132].

We have added citations to references 131 and 132 after this sentence in the revised manuscript.

• More specifically, Figure 4 presents the structure’s 3D design elements, comprising the initial subunit and views of the final 3D lattice design [131,132].
• The lattice scaffold structure design was subsequently 3D printed and subjected to mechanical experimental testing while in the same time a FEA computational analysis was also conducted [131,132]. Figure 5 depicts snapshots of this workflow indicating experimental and FEM generated scaffold snapshots with failure pattern and high stress value areas highlighted. The circular struts rupture and collapse of the first pore network row predicted in the computational analysis can be observed in the actual specimen [131,132].
• The aforementioned example drawn from published literature [131,132], showcases that the use of mathematical power laws for solids, combined with FEA computational analysis can be used to predict mechanical behavior of three-dimensional solid structures.

We added reference 131 after this sentence:

• Based on Ashby’s and Gibson’s formula [133] for cellular materials the effective modulus of a cellular structure can be obtained using the following equation [131]

We added a reference to 131 and 132 after the captions of Figures 4 and 5.

• Figure 4. (a) The subunit, (b) the side view, and (c) the plan view of the lattice scaffold structure design [131,132].
• Figure 5. Experimental and FEM generated scaffold snapshots with failure pattern and high stress value areas highlighted [131,132].

The previous reference 133 was incorrect and has been updated to the latest reference 134. In addition, the former reference 134 has been revised and is now updated to the latest reference 135.

With this correction, the order of some references has been adjusted accordingly.

The aforementioned equation is the following, according to the previously described published literature work [2], where the English symbol p is substituted with the Greek symbol $\mathrm{\rho }$:

$${\displaystyle \frac{{\mathit{E}}_{\mathit{e}\mathit{f}\mathit{f}}}{\mathit{E}}}={\mathit{C}}_{\mathbf{1}}{\left({\displaystyle \frac{{\mathit{\rho }}_{\mathit{s}\mathit{c}}}{{\mathit{\rho }}_{\mathbf{0}}}}\right)}^2$$

The second correction has to do with Equation (1) that appears in Table 4 of the original manuscript. Its correct form is the following, where the English symbol p is substituted with the Greek symbol $\mathrm{\rho }$:

$$E_{eff}=C_1{\left({\displaystyle \frac{{\rho }_{sc}}{{\rho }_0}}\right)}^{n}E$$

(1)

None of these changes affect the scientific results or the conclusions presented in [1]. The authors apologize to readers for any inconvenience these corrections may have caused. This correction was approved by the Academic Editor. The original publication has also been updated.