Summary
To solve large deformation geotechnical problems, a novel strain‐smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge‐based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node‐based smoothed PFEM when lower‐order triangular element is used. Compared with the node‐based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super‐convergent and very accurate solutions due to the implementation of edge‐based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.
Particle finite element method (PFEM) is an effective numerical tool for solving large-deformation problems in geomechanics. By incorporating the node integration technique with strain smoothing into the PFEM, we proposed the smoothed particle finite element method (SPFEM). This paper extends the SPFEM to three-dimensional cases and presents a SPFEM executed on graphics processing units (GPUs) to boost the computational efficiency. The detailed parallel computing strategy on GPU is introduced. New computation formulations related to the strain smoothing technique are proposed
Computational modeling in geotechnical engineering frequently needs sophisticated constitutive models to describe prismatic behavior of geomaterials subjected to complex loading conditions, and meanwhile faces challenges to tackle large deformation in many geotechnical problems. The study presents a multiscale approach to address both challenges based on a hierarchical coupling of the smoothed particle finite element method (SPFEM) and the discrete element method (DEM) (coined SPFEM/DEM). In the approach, SPFEM serves as K E Y W O R D S footing, large deformation, multiscale modeling, slope failure, SPFEM/DEM 1 INTRODUCTION Numerical modeling plays an increasingly important role in geotechnical analysis and design today, and meanwhile, it faces ever growing challenges arising from many aspects of the material behavior and complexity of practical problems. Specifically, geomaterials are composed of discrete particles varying in mineralogical composition, morphology, and size, and exhibit inherent multiscale nature that dictates many macroscopic mechanical responses of these materials. Mathematical formulations of their mechanical behaviors, i.e., constitutive models, have been the backbone for numerical analysis. It remains a formidable task to propose a mathematical model general and robust enough to account for a wide spectrum of material behaviors, ranging from critical state and anisotropy 1,2 to non-coaxiality 3,4 and cyclic hysteresis, and 648
Particle finite element method (PFEM) is an effective numerical tool for solving large-deformation problems in geomechanics. By incorporating the node integration technique with strain smoothing into the PFEM, we proposed the smoothed particle ?nite element method (SPFEM). This paper extends the SPFEM to three-dimensional cases and presents a SPFEM executed on graphics processing units (GPUs) to boost the computational efficiency. The detailed parallel computing strategy on GPU is introduced. New computation formulations related to the strain smoothing technique are proposed to save memory space in the GPU parallel computing. Several benchmark problems are solved to validate the proposed approach and to evaluate the GPU acceleration performance. Numerical examples show that with the new formulations not only the memory space can be saved but also the computational efficiency is improved. The computational cost is reduced by 70% for the double-precision GPU parallel computing with the new formulations.
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