P W. Dondl, J. Zimmer/J. Mech. Phys. Solids 52(2004)2057-2077 The article is further organized as follows: in Section 2, it is shown how the phase transition can be analyzed in a two-dimensional framework; and in Section 3, an energ. function is derived and fitted to the elastic moduli of the different phases. Numerical simulations using this energy are presented in Section 4. We close with a discussion in Section 5 2. Planar phase transformation We follow Truskinovsky and Zanzotto(2002)and consider a transformation path in Zirconia g the tetragonal phase and certain orthorhombic and monoclinic phases. We show that these phase transformations can be described as an in-plane tran formation, thus motivating the restriction to two space dimensions in the simulations in Section 4 As usual, we take the high symmetry phase as reference configuration. (This is jus- tified by the observation that one can define a so-called Ericksen-Pitteri neighborhood (Ericksen, 1980; Pitter, 1984 )of the lattice with the maximal symmetry in such a way that it comprises the lattices with a subgroup symmetry. For Zirconia, the tetragonal phase, denoted T3, is the high symmetry phase. To fix the notation, we list the elements of T3(Truskinovsky and Zanzotto(2002); the axes c1, c2, c3 are shown in Fig. 2; Ra tands for the rotation with angle a and axis a ) T3={1,R1,R2,R2,R1+e,R-,R2,R2 The orthorhombic subgroups of T3 are O,23:={1,RG,R2,R2} see Truskinovsky and Zanzotto (2002). Both orthorhombic groups form their own gacy class in T3 There are three conjugacy classes of monoclinic subgroups, from which we list one representative each M:={1,R,M1+2:={1,R+},M3:={1,R Of course, there is also the trivial triclinic subgroup (Id]. A schematic representation of the point groups is given by Truskinovsky and Zanzotto(2002, Fig 3) We assume that the symmetry breaking in ZrO2 occurs along the path This path, as we consider it, is different from the one usually studied for the tetragonal- monoclinic transformation(Fabris et al., 2000). Our path was first suggested by Truskinovsky and Zanzotto (2002 ); Fadda et al.(2002)based on experimental evi- dence collected thereP.W. Dondl, J. Zimmer / J. Mech. Phys. Solids 52 (2004) 2057 – 2077 2061 The article is further organized as follows: in Section 2, it is shown how the phase transition can be analyzed in a two-dimensional framework; and in Section 3, an energy function is derived and 3tted to the elastic moduli of the diIerent phases. Numerical simulations using this energy are presented in Section 4. We close with a discussion in Section 5. 2. Planar phase transformation We follow Truskinovsky and Zanzotto (2002) and consider a transformation path in Zirconia as joining the tetragonal phase and certain orthorhombic and monoclinic phases. We show that these phase transformations can be described as an in-plane trans￾formation, thus motivating the restriction to two space dimensions in the simulations in Section 4. As usual, we take the high symmetry phase as reference con3guration. (This is jus￾ti3ed by the observation that one can de3ne a so-called Ericksen–Pitteri neighborhood (Ericksen, 1980; Pitteri, 1984) of the lattice with the maximal symmetry in such a way that it comprises the lattices with a subgroup symmetry.) For Zirconia, the tetragonal phase, denoted T3, is the high symmetry phase. To 3x the notation, we list the elements of T3 (Truskinovsky and Zanzotto (2002); the axes c1; c2; c3 are shown in Fig. 2; R a stands for the rotation with angle and axis a): T3 = {1; R c1 ; R c2 ; R c3 ; R c1+c2 ; R c1−c2 ; R=2 c3 ; R3=2 c3 }: The orthorhombic subgroups of T3 are O1;2;3 := {1; R c1 ; R c2 ; R c3 } and O3;1±2 := {1; R c3 ; R c1+c2 ; R c1−c2 }; see Truskinovsky and Zanzotto (2002). Both orthorhombic groups form their own conjugacy class in T3. There are three conjugacy classes of monoclinic subgroups, from which we list one representative each M1 := {1; R c1 }; M1+2 := {1; R c1+c2 }; M3 := {1; R c3 }: Of course, there is also the trivial triclinic subgroup {Id}. A schematic representation of the point groups is given by Truskinovsky and Zanzotto (2002, Fig. 3). We assume that the symmetry breaking in ZrO2 occurs along the path T3 → O1;2;3 → M3: This path, as we consider it, is diIerent from the one usually studied for the tetragonal￾monoclinic transformation (Fabris et al., 2000). Our path was 3rst suggested by Truskinovsky and Zanzotto (2002); Fadda et al. (2002) based on experimental evi￾dence collected there