Xin Gu

Elastoplastic deformation in solids is often accompanied by strain localization, energy dissipation and, when localization further develops, crack initiation and propagation, posing challenges for local plasticity models and conventional fracture descriptions in naturally representing evolving displacement discontinuities and crack surfaces. This study develops a thermodynamically consistent nonlocal plasticity formulation for plastic evolution and its application to fracture problems, with particular emphasis on a kinematic hardening mechanism motivated by geometrically necessary dislocation (GND)-related incompatibility. Starting from nonlocal kinematics, nonlinear elastic and kinematic hardening force state constitutive relations are derived from the Saint-Venant–Kirchhoff (SVK) elastic energy and a hardening energy associated with incompatibility-induced internal deformation. The resulting hardening force state provides a nonlocal representation of the back stress and offers a physical basis for deriving thermodynamically consistent nonlocal yield functions. Based on Clausius–Duhem inequality, nonlocal J2 and Drucker–Prager (DP) yield criteria are derived with isotropic and kinematic hardening, leading to a unified thermodynamic formulation for ductile metals and pressure-dependent geomaterials. To integrate the resulting nonlinear system composed of the plastic flow rule, yield condition, and hardening evolution equations, a multivariable Newton return mapping (MNRM) algorithm with Wolfe line search is developed, in which the plastic multiplier and internal variables are solved simultaneously. A consistent tangent force state relation is further derived for the global equilibrium iteration. The proposed formulation is verified through benchmark problems involving monotonic and cyclic elastoplastic deformation, pressure-dependent plasticity, crack propagation and fatigue-like damage accumulation. The results show good agreement with the finite element (FEM) and experimental references, demonstrating the capability of the formulation to capture plastic strain localization, stress redistribution, hardening-induced path dependence, and fracture evolution within a unified nonlocal setting. This also offers a new perspective for simulating fatigue damage driven by plastic accumulation.

Fluid–structure interaction (FSI) involving free-surface flows remains challenging due to complex free-surface evolution, transient hydrodynamic pressure transfer, and structural deformation. This study develops a direct coupling framework between smoothed particle hydrodynamics (SPH) and non-ordinary state-based peridynamics (NOSBPD) to improve the accuracy, stability, and efficiency of free-surface FSI simulations. In the proposed framework, structural particles are directly treated as SPH boundary particles, and the FSI force is obtained through pressure interpolation and Newton's third law, avoiding additional virtual-particle generation. Flexible and independent spatial discretizations are allowed for the fluid and solid domains, so that their resolutions can be adjusted separately without simultaneous refinement of both domains. NOSBPD is used to describe structural deformation and directly calculate stress and strain fields. A condition-number-assisted particle shifting technique is introduced to improve the efficiency and stability of free-surface particle identification and particle distribution correction, reducing local pressure oscillations near the free surface and fluid–structure interface. The solver is accelerated using Taichi-based graphics processing unit computing with an optimized linked-list neighbor search, achieving more than 3 orders of magnitude speedup over single-core central processing unit computation. Benchmark tests show normalized root mean square error within 1% for structural deformation and below 3.5% for free-surface flow quantities. Compared with representative particle-based FSI results, the proposed model produces smoother pressure fields and more accurate structural displacement predictions. The last application simulation further demonstrates its capability to stably capture strong free-surface loading, large deformation of complex free-surface FSI simulations.

The simulation of frost cracking in cold-region soils involves the coupling of multiple physical processes, including heat transfer, water migration, phase change, and mechanical deformation, which presents significant challenges for traditional numerical methods. In this study, a thermo-hydro-mechanical (THM) coupled model based on classical frozen soil theory is combined with a hybrid peridynamics-finite element method (PD–FEM) to develop a numerical framework for simulating the damage and cracking behavior of soils during freezing. The PD method is used to describe the crack evolution process without requiring predefined crack paths, while the FEM is employed to solve the coupled temperature and water migration equations. The freeze-induced cracking process of a soil column under unidirectional freezing conditions was simulated. The simulation results agree well with experimental data, indicating that the proposed model can effectively capture damage, crack initiation, and propagation in soil during freezing while efficiently coupling multiple physical processes. Furthermore, this study explores the influence of crack propagation and the infilling material within the cracks on the freezing process.

Accurate and efficient modeling of thermomechanical failure in critical structures under extreme conditions remains a great challenge. Traditional local methods struggle with discontinuities, such as fractures, while peridynamics (PD) is computationally intensive. This study presents a rapid prediction framework that combines sequential PD thermomechanical coupling simulations with a deep learning (DL) surrogate model. The framework adopts bond-based PD to solve the deformation field, accounting for thermal expansion, whereas the temperature field is handled using the peridynamic differential operator to address boundary effects and enhance transient accuracy. The validation results show that the PD thermomechanical coupling model achieved high accuracy. For example, the cooling simulation results of a 2D plate using PD and FEM show that the results had a global error in temperature and displacement of less than 0.7%. In the Al₂O₃ ceramic quenching simulations, the crack propagation path is accurately reproduced using the PD model, which matches the experimental data well. To improve the computational efficiency, the DL surrogate model was trained on a large dataset generated by PD simulations. The inputs include the crack geometries and loads, and the outputs are the predicted crack openings, average radial displacement/strain, and circumference change rates. The optimized deep neural network (DNN) consisted of two hidden layers, each with nine neurons. The DNN model predicted complex multi-output responses in approximately 0.5 s, about 1200 times faster than direct PD simulation, maintaining high accuracy. The PD-DL framework offers a new direction for assessing the thermomechanical damage and structural integrity in engineering applications.