For simulating failure evolution, it is challenging for the numerical methods to overcome the drawback of mesh-dependency due to local constitutive modelling in which the stress at a given material point only depends on the strain at that point. Because strain softening would lead to damage and macrocracking, ignoring the softening stage could make the simulation results inaccurate in evaluating the failure evolution process. Nonlocal softening models in terms of gradient or integral of strain field have been proposed to regularize softening with localization^[1][2]. An MPM (material point method) improved with smoothing operator which is originated from SPH (smoothed particle hydrodynamics) has been proposed to implement a nonlocal model via the gradient of plastic strain^[3]. The MPM is a continuum-based particle method for solving large-deformation and failure evolution problems. The smoothing operator is adopted on the material points to reduce the unphysical oscillations and facilitate the evaluation of strain gradient. Based on the recent work on simulating shear band evolution^[4] a comparative study via the MPM, SPH and MPM integrated with smoothing operator will be presented here, with a focus on the similarities and differences among the results obtained by the three numerical algorithms. It is demonstrated that the integrated MPM and SPH algorithm could inherit the advantages of both the MPM and SPH methods in softening problem. Future tasks will then be discussed accordingly.

REFERENCES

[1]      H.L. Schreyer and Z. Chen. One Dimensional Softening with Localization. Journal of Applied Mechanics, 53(4): 791-797, 1986.

[2]      Z. Chen and H.L. Schreyer. On nonlocal damage models for interface problems. International Journal of Solids and Structures, 31(9): 1241-1261, 1994.

[3]      L. He and Z. Chen. Study on one-dimensional softening with localization via integrated MPM and SPH. Computational Particle Mechanics, 6:629–636, 2019.

[4]      Y. Su, T. Sewell and Z. Chen. Comparative investigation of shear-band evolution using discrete and continuum-based particle methods. Acta Geotechnica, 16:2337–2354, 2021.