A Phase‐Field‐Smoothed Learning Method for Nonlinear Hyperelasticity Interface Problems

ABSTRACT

This article develops a phase‐field‐smoothed learning method for finite‐deformation hyperelasticity interface problems. In the considered problems, different material phases meet at internal interfaces, the elasticity tensor is discontinuous across the interface, and the displacement field is generally only globally regular. These features make standard strong‐form physics‐informed neural networks (PINNs) difficult to train, since automatic differentiation is applied across low‐regularity solution fields and discontinuous material coefficients. The proposed method, denoted by PFS‐PINN, combines phase‐field smoothing with a displacement–stress mixed PINN. The phase‐field network represents the sharp material interface by a continuous order parameter and constructs a smooth approximation of the discontinuous elasticity tensor. The original nonlinear interface problem is thereby converted into a smooth‐coefficient hyperelastic equilibrium problem. The mixed PINN then treats the first Piola–Kirchhoff stress as an independent network output, so that the equilibrium residual contains the first‐order divergence of the stress rather than second‐order derivatives of the displacement. For the phase‐field‐smoothed problem with continuous coefficients, the convergence of the system energy of the mixed PINN approximation is proved, and an ‐error bound for the displacement is also obtained. Numerical tests cover constant and continuously varying coefficients as baseline cases, and several hyperelastic interface problems with regular, high‐curvature, and multiple interfaces. The numerical results demonstrate that the proposed method possesses superior accuracy, computational efficiency, and robustness, which constitutes a valuable attempt for addressing complex hyperelasticity interface problems.