PSI - Issue 80

Haolin Li et al. / Procedia Structural Integrity 80 (2026) 23–30

27

Author name / Structural Integrity Procedia 00 (2023) 000–000

5

the Neo-Hookean hyperelasticity model used in the PINN (Eq. 7) is consistent with the one used in Abaqus, which facilitates validation.

Fig. 3. Finite-element models of metamaterial structures: (a) octet-truss metamaterial; (b) gyroid metamaterial; (c) spindoid metamaterial.

3.1. Single-axis strain deformation

First, we apply a macroscopic tensile strain purely in the z (vertical) direction as an example of single-axis strain. The resulting homogenised stresses are given in Table.1. It is seen from the table that The PINN achieves accuracy comparable to the FEM results. The deformed configurations are illustrated in Fig. 4 as a showcase.

P xx

P yy

P zz

P xy

P xz

P yz

Octet Truss

FEM PINN FEM PINN FEM PINN

0.087 0.089 0.327 0.328 1.153 1.152

0.087 0.089 0.327 0.328 1.153 1.157

1.344 1.344 4.712 4.724

0.0137 0.0101

0.223 0.223 0.720 0.721 0.846 0.845

0.223 0.224 0.720 0.723 0.846 0.850

Gyroid

0.134 0.137 0.292 0.292

Spindoid

17.740 17.788

Table 1. Placeholder caption for a table with three rows and seven columns.

3.2. Multiple-axis strain deformation

Second, we apply random macroscopic strains in all three axes, including both normal and shear components. The homogenised stresses are reported in Table.2. Again, the PINN yields results comparable with the FEM reference. The deformed configurations are shown in Fig. 5 for illustration.

P xx

P yy

P zz

P xy

P xz

P yz

Octet Truss

FEM PINN FEM PINN FEM PINN

1.170 1.175 1.845 1.890 4.728 4.738

1.210 1.217 2.753 2.742

0.722 0.743 3.385 3.399

0.124 0.125 2.133 2.142 7.747 7.749

0.183 0.184 2.153 2.154 7.602 7.609

0.162 0.163 2.905 2.911 6.112 6.116

Gyroid

Spindoid

20.134 20.277

12.134 12.135

Table 2. Placeholder caption for a table with three rows and seven columns.