Thermodynamically consistent physics-informed neural network approach for thin films with nonstandard boundary conditions


TARIQ A., DELİKTAŞ B., Voyiadjis G. Z.

Thin-Walled Structures, cilt.225, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 225
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.tws.2026.114743
  • Dergi Adı: Thin-Walled Structures
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC
  • Anahtar Kelimeler: Energetic hardening, Micro/nano structure, Nonlocal model, Physics-informed neural network, Strain gradient plasticity, Thin films
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

Recent advances have revealed that classical strain gradient plasticity (SGP) theories often struggle to accurately capture size-dependent effects, primarily due to limitations in enforcing thermodynamic consistency. To address this, the present study employs a Physics-Informed Neural Network (PINN) framework built upon a thermodynamically consistent higher-order SGP model. The formulation explicitly incorporates multiple thermodynamic processes by splitting the internal state variables into dissipative and energetic constituents and introducing four distinct material length scales. This enables a more comprehensive understanding of the strengthening and hardening mechanisms in micro/nanostructured materials. The proposed PINN model is utilized to investigate several key phenomena: (i) energetic hardening associated with plastic strain and its gradients, (ii) dissipative strengthening governed by plastic strain rate gradients, (iii) interfacial hardening and yield strength, (iv) boundary layer effects, and (v) the influence of higher-order boundary conditions. An interface model is also integrated into the PINN to represent the internal boundary of the plastic zone and to capture the dislocation mechanics at the interface between two material phases. The formulation is applied to a benchmark problem involving a thin film on an elastic substrate subjected to uniaxial tension. The PINN model successfully satisfies the nonlocal microtraction and microforce balance conditions within the loss function, and the results demonstrate its ability to capture the underlying physical behavior. Furthermore, the proposed SGP formulation and its associated PINN framework were validated against experimental torsion data obtained from a thin wire. This approach provides enhanced predictive capabilities for modeling both bulk and interfacial responses in gradient-enhanced small-scale plasticity.