Correction: Bennati et al. An Elastic Interface Model for the Delamination of Bending-Extension Coupled Laminates. Appl. Sci. 2019, 9, 3560

We, the authors, wish to make the following corrections to our paper [1].

Equations (26), (27), (28), and (41) were affected by some typos and should be substituted by the following ones (corrections are colored in red):

$$\begin{array}{cc}\hfill u_1\left(x\right)=& -\left({\mathsf{a}}_1+{\mathsf{b}}_1{h}_1\right)\left[\frac{f_5}{{\lambda }_5^2}exp\left(-{\lambda }_{5}x\right)+\frac{f_6}{{\lambda }_6^2}exp\left(-{\lambda }_{6}x\right)\right]+{\mathsf{b}}_1\sum _{i=1}^4\frac{f_i}{{\lambda }_i^3}exp\left(-{\lambda }_{i}x\right)+\hfill \\ & -\left[\left({\mathsf{a}}_1+{\mathsf{b}}_1{h}_1\right)f_7+{\mathsf{b}}_1{f}_{10}\right]\frac{x^2}{2}-\left({\mathsf{a}}_1{f}_8+{\mathsf{b}}_1{f}_{12}\right)x+f_{14},\hfill \\ \hfill w_1\left(x\right)=& \sum _{i=1}^4\left(\frac{{\mathsf{d}}_1}{{\lambda }_i^2}-{\mathsf{c}}_1\right)\frac{f_i}{{\lambda }_i^2}exp\left(-{\lambda }_{i}x\right)-\left({\mathsf{d}}_1{h}_1+{\mathsf{b}}_1\right)\left[\frac{f_5}{{\lambda }_5^3}exp\left(-{\lambda }_{5}x\right)+\frac{f_6}{{\lambda }_6^3}exp\left(-{\lambda }_{6}x\right)\right]+\hfill \\ & +\left[\left({\mathsf{d}}_1{h}_1+{\mathsf{b}}_1\right)f_7+{\mathsf{d}}_1{f}_{10}\right]\frac{x^3}{6}+\left({\mathsf{b}}_1{f}_8+{\mathsf{d}}_1{f}_{12}\right)\frac{x^2}{2}-\left(f_{16}+{\mathsf{c}}_1{f}_{10}\right)x+f_{15},\mathrm{and}\hfill \\ \hfill {\phi }_1\left(x\right)=& {\mathsf{d}}_1\sum _{i=1}^4\frac{f_i}{{\lambda }_i^3}exp\left(-{\lambda }_{i}x\right)-\left({\mathsf{d}}_1{h}_1+{\mathsf{b}}_1\right)\left[\frac{f_5}{{\lambda }_5^2}exp\left(-{\lambda }_{5}x\right)+\frac{f_6}{{\lambda }_6^2}exp\left(-{\lambda }_{6}x\right)\right]+\hfill \\ & -\left[\left({\mathsf{d}}_1{h}_1+{\mathsf{b}}_1\right)f_7+{\mathsf{d}}_1{f}_{10}\right]\frac{x^2}{2}-\left({\mathsf{b}}_1{f}_8+{\mathsf{d}}_1{f}_{12}\right)x+f_{16},\hfill \end{array}$$

(26)

$$\begin{array}{cc}\hfill u_2\left(x\right)=& \left({\mathsf{a}}_2-{\mathsf{b}}_2{h}_2\right)\left[\frac{f_5}{{\lambda }_5^2}exp\left(-{\lambda }_{5}x\right)+\frac{f_6}{{\lambda }_6^2}exp\left(-{\lambda }_{6}x\right)\right]-{\mathsf{b}}_2\sum _{i=1}^4\frac{f_i}{{\lambda }_i^3}exp\left(-{\lambda }_{i}x\right)+\hfill \\ & +\left[\left({\mathsf{a}}_2-{\mathsf{b}}_2{h}_2\right)f_7+{\mathsf{b}}_2{f}_{11}\right]\frac{x^2}{2}+\left({\mathsf{a}}_2{f}_9+{\mathsf{b}}_2{f}_{13}\right)x+f_{17},\hfill \\ \hfill w_2\left(x\right)=& -\sum _{i=1}^4\left(\frac{{\mathsf{d}}_2}{{\lambda }_i^2}-{\mathsf{c}}_2\right)\frac{f_i}{{\lambda }_i^2}exp\left(-{\lambda }_{i}x\right)-\left({\mathsf{d}}_2{h}_2-{\mathsf{b}}_2\right)\left[\frac{f_5}{{\lambda }_5^3}exp\left(-{\lambda }_{5}x\right)+\frac{f_6}{{\lambda }_6^3}exp\left(-{\lambda }_{6}x\right)\right]+\hfill \\ & +\left[\left({\mathsf{d}}_2{h}_2-{\mathsf{b}}_2\right)f_7-{\mathsf{d}}_2{f}_{11}\right]\frac{x^3}{6}-\left({\mathsf{b}}_2{f}_9+{\mathsf{d}}_2{f}_{13}\right)\frac{x^2}{2}-\left(f_{19}-{\mathsf{c}}_2{f}_{11}\right)x+f_{18},\mathrm{and}\hfill \\ \hfill {\phi }_2\left(x\right)=& -{\mathsf{d}}_2\sum _{i=1}^4\frac{f_i}{{\lambda }_i^3}exp\left(-{\lambda }_{i}x\right)-\left({\mathsf{d}}_2{h}_2-{\mathsf{b}}_2\right)\left[\frac{f_5}{{\lambda }_5^2}exp\left(-{\lambda }_{5}x\right)+\frac{f_6}{{\lambda }_6^2}exp\left(-{\lambda }_{6}x\right)\right]+\hfill \\ & -\left[\left({\mathsf{d}}_2{h}_2-{\mathsf{b}}_2\right)f_7-{\mathsf{d}}_2{f}_{11}\right]\frac{x^2}{2}+\left({\mathsf{b}}_2{f}_9+{\mathsf{d}}_2{f}_{13}\right)x+f_{19},\hfill \end{array}$$

(27)

$$\begin{array}{c}{f}_{10}=-\frac{{\alpha }_3}{B{k}_x{\alpha }_4}{\mathsf{d}}_2{f}_7,f_{11}=\frac{{\alpha }_3}{B{k}_x{\alpha }_4}{\mathsf{d}}_1{f}_7,\hfill \\ f_{12}=-\frac{\left({\mathsf{a}}_1+{\mathsf{b}}_1{h}_1\right){\mathsf{d}}_2-\left({\mathsf{b}}_2-{\mathsf{d}}_2{h}_2\right){\mathsf{b}}_1}{{\alpha }_4}{f}_8-\frac{{\mathsf{a}}_2{\mathsf{d}}_2-{\mathsf{b}}_2^2}{{\alpha }_4}{f}_9,\hfill \\ f_{13}=\frac{{\mathsf{a}}_1{\mathsf{d}}_1-{\mathsf{b}}_1^2}{{\alpha }_4}{f}_8+\frac{\left({\mathsf{a}}_2-{\mathsf{b}}_2{h}_2\right){\mathsf{d}}_1-\left({\mathsf{b}}_1+{\mathsf{d}}_1{h}_1\right){\mathsf{b}}_2}{{\alpha }_4}{f}_9,\hfill \\ f_{14}=f_{17}-\left(h_1+h_2\right)f_{19}-\frac{1}{k_x}\left[\frac{1}{B}+\frac{{\alpha }_3}{B{\alpha }_4}\left({\mathsf{c}}_1{\mathsf{d}}_2-{\mathsf{c}}_2{\mathsf{d}}_1\right)h_1\right]f_7,\hfill \\ f_{15}=f_{18},\mathrm{and}{f}_{16}=f_{19}+\frac{{\alpha }_3}{B{k}_x{\alpha }_4}\left({\mathsf{c}}_1{\mathsf{d}}_2-{\mathsf{c}}_2{\mathsf{d}}_1\right)f_7,\hfill \end{array}$$

(28)

$$\begin{array}{c}{g}_{10}=\left(-\frac{{\alpha }_3}{B{k}_x{\alpha }_4}{\mathsf{d}}_2+{\beta }_0\frac{{\mathsf{b}}_2-{\mathsf{d}}_2{h}_2}{B{\alpha }_4}\right)g_7,g_{11}=\left(\frac{{\alpha }_3}{B{k}_x{\alpha }_4}{\mathsf{d}}_1-{\beta }_0\frac{{\mathsf{b}}_1+{\mathsf{d}}_1{h}_1}{B{\alpha }_4}\right)g_7,\hfill \\ g_{12}=-\frac{\left({\mathsf{a}}_1+{\mathsf{b}}_1{h}_1\right){\mathsf{d}}_2-\left({\mathsf{b}}_2-{\mathsf{d}}_2{h}_2\right){\mathsf{b}}_1}{{\alpha }_4}{g}_8-\frac{{\mathsf{a}}_2{\mathsf{d}}_2-{\mathsf{b}}_2^2}{{\alpha }_4}{g}_9,\hfill \\ g_{13}=\frac{{\mathsf{a}}_1{\mathsf{d}}_1-{\mathsf{b}}_1^2}{{\alpha }_4}{g}_8+\frac{\left({\mathsf{a}}_2-{\mathsf{b}}_2{h}_2\right){\mathsf{d}}_1-\left({\mathsf{b}}_1+{\mathsf{d}}_1{h}_1\right){\mathsf{b}}_2}{{\alpha }_4}{g}_9,\hfill \\ g_{14}=g_{17}-\left(h_1+h_2\right)g_{19}-\left[\frac{1}{B{k}_x}+\frac{{\alpha }_3}{B{k}_x{\alpha }_4}\left({\mathsf{c}}_1{\mathsf{d}}_2-{\mathsf{c}}_2{\mathsf{d}}_1\right)h_1+{\beta }_0\frac{{\mathsf{b}}_1{\mathsf{c}}_2-{\mathsf{c}}_1{\mathsf{b}}_2+{\mathsf{c}}_1{\mathsf{d}}_2{h}_2+{\mathsf{c}}_2{\mathsf{d}}_1{h}_1}{B{\alpha }_4}{h}_1\right]g_7,\hfill \\ g_{15}=g_{18},\mathrm{and}{g}_{16}=g_{19}+\left[\frac{{\alpha }_3}{B{k}_x{\alpha }_4}\left({\mathsf{c}}_1{\mathsf{d}}_2-{\mathsf{c}}_2{\mathsf{d}}_1\right)+{\beta }_0\frac{{\mathsf{b}}_1{\mathsf{c}}_2-{\mathsf{c}}_1{\mathsf{b}}_2+{\mathsf{c}}_1{\mathsf{d}}_2{h}_2+{\mathsf{c}}_2{\mathsf{d}}_1{h}_1}{B{\alpha }_4}\right]g_7,\hfill \end{array}$$

(41)

Furthermore, we observe that the constant terms in the shear stress expressions (18) and (32) (corresponding to Jourawski’s solution for an unbroken beam) should not contribute to the Mode II energy release rate ${\mathcal{G}}_{\mathrm{II}}$. Thus, the peak values of the shear interfacial stress entering Equation (44) should be computed as ${\tau }_0=\tau \left(0\right)-f_7/B$ and ${\tau }_0=\tau \left(0\right)-g_7/B$ in the balanced and unbalanced cases, respectively. As a consequence, Equations (45) and (46) should be replaced by the following ones:

$${\mathcal{G}}_{\mathrm{I}}=\frac{\mathcal{H}\left({\sigma }_0\right)}{2k_z{B}^2}{\left(\sum _{i=1}^4{f}_i\right)}^2\mathrm{and}{\mathcal{G}}_{\mathrm{II}}=\frac{1}{2k_x{B}^2}{\left(\begin{array}{c}\hfill f_5+f_6\end{array}\right)}^2$$

(45)

and

$${\mathcal{G}}_{\mathrm{I}}=\frac{\mathcal{H}\left({\sigma }_0\right)}{2k_z{B}^2}{\left(\sum _{i=1}^6{g}_i\right)}^2\mathrm{and}{\mathcal{G}}_{\mathrm{II}}=\frac{1}{2k_x{B}^2}{\left(\begin{array}{c}\hfill k_x{\beta }_0{\displaystyle \sum _{i=1}^6}\frac{g_i}{{\mu }_i({\mu }_i^2-{\alpha }_3)}\end{array}\right)}^2.$$

(46)

The corrections do not affect the results and scientific conclusions of the paper. We apologize for any inconvenience caused.