Correction: Alfat et al. Phase Field Models for Thermal Fracturing and Their Variational Structures. Materials 2022, 15, 2571

Error in Equations

The authors were not aware of typographical errors made in the writing phase, and, hence, wish to make the following corrections to the original paper [1]. We apologize for these mistakes. There are four typo mistakes in the original paper, which are corrected as follows:

• Equation (1) is corrected as:

  $$\mathrm{div}\sigma \left[u\right]=\beta \nabla \mathsf{\Theta }\hspace{0.17em}\hspace{0.17em}\mathrm{in} \mathsf{\Omega }\times \left[0,T\right],$$
• The following equation

  $$-\mu \Delta u-(\lambda +\mu )\nabla \left(\mathrm{div}u\right)= \beta \nabla \mathsf{\Theta }.$$

  is corrected as:

  $$\mu \Delta u+(\lambda +\mu )\nabla \left(\mathrm{div}u\right)=\beta \nabla \mathsf{\Theta }.$$
• Equation (19a) is corrected as:

  $$\widetilde{\mathrm{div}}\tilde{\sigma }\left[\tilde{u}\right]=\tilde{\nabla }\tilde{\mathsf{\Theta }}\hspace{0.17em}\hspace{0.17em}\mathrm{in} \tilde{\mathsf{\Omega }}\times \left[0,\tilde{T}\right],$$
• Equation (39a) is corrected as:

  $$\mathrm{div}\left({\left(1-z\right)}^2\sigma \left[u\right]\right)={\left(1-z\right)}^2\nabla \mathsf{\Theta }\hspace{0.17em}\hspace{0.17em}\mathrm{in} \mathsf{\Omega }\times \left[0,T\right],$$

  The original article has been corrected.