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In this paper, smoothed bond-based peridynamics (SBBPD) is proposed to simulate the large deformation. The governing equation of smoothed bond-based PD is obtained by incorporating the observed changes in the density field and long-range force reaction in Eulerian form. The Hencky stretch is introduced into smoothed bond-based PD to calculate the true strain because of the change in density (volume). The proposed method can achieve a more accurate result in solid mechanics compared with SPH and can well handle extremely large deformation problems compared with traditional bond-based PD. Numerical experiments are launched to test these modifies of smoothed bond-based PD method in solid mechanics.

The continuous smoothed particle hydrodynamics (CSPH) method is proposed to modify the kernel approximation in the smoothed particle hydrodynamics (SPH). The diffraction criterion is embedded in the framework of standard SPH. CSPH dramatically improves the computational ability in cracked bodies. Three numerical cases of cracked bodies, including dynamic stress intensity factor (DSIF) of a central crack, tensile fracture of brittle materials and Kalthoff’s experiment, are employed to verify the ability of the proposed method. It is found that the numerical results obtained by CSPH are in good agreement with the previous experimental and numerical results, implying the robustness and feasibility of the proposed method.

By means of computation and analysis of damage tolerance of composite laminates with hole or crack, the conclusion is brought forth that crack on laminates can’t be cut into hole to improve the residual strength; otherwise the damage will become more serious. The method and conclusion can be reference and basis for battle damage repair of airplane composite component.

In order to solve the fight problem of damaged airplane in war, based on linear elasticity, elastoplasticity and net section yield criterion, the calculation model for residual strength of plate with smooth circular hole is founded. Furthermore, the flexibility of calculation models using these three methods is analyzed through examples. All above can be basis for airplane battle damage assessment.