TY - JOUR

T1 - On the application of SPH to solid mechanics

AU - Shutov, Alexey

AU - Klyuchantsev, Vladislav

PY - 2019/7/16

Y1 - 2019/7/16

N2 - We analyze the applicability of the smooth particle hydrodynamics (SPH) to the solution of boundary value problems involving large deformation of solids. The main focus is set on such issues as the reduction of artificial edge effects by implementing corrected kernels and their gradients, accurate and efficient computation of the deformation gradient tensor, evaluation of the internal forces from the given stress field. For demonstration purposes, a hyperelastic body of neo-Hookean type and a visco-elastic body of Maxwell type are considered; the formulation of the Maxwell material is based on the approach of Simo and Miehe (1992). For the implementation of constitutive relations efficient and robust numerical schemes are used. A solution for a series of test problems is presented. The performance of the implemented algorithms is assessed by checking the preservation of the total energy of the system. As a result, a functional combination of SPH-techniques is identified, which is suitable for problems involving large strains, rotations and displacements coupled to inelastic material behaviour. The accuracy of the SPH-computations is assessed using nonlinear FEM as a benchmark.

AB - We analyze the applicability of the smooth particle hydrodynamics (SPH) to the solution of boundary value problems involving large deformation of solids. The main focus is set on such issues as the reduction of artificial edge effects by implementing corrected kernels and their gradients, accurate and efficient computation of the deformation gradient tensor, evaluation of the internal forces from the given stress field. For demonstration purposes, a hyperelastic body of neo-Hookean type and a visco-elastic body of Maxwell type are considered; the formulation of the Maxwell material is based on the approach of Simo and Miehe (1992). For the implementation of constitutive relations efficient and robust numerical schemes are used. A solution for a series of test problems is presented. The performance of the implemented algorithms is assessed by checking the preservation of the total energy of the system. As a result, a functional combination of SPH-techniques is identified, which is suitable for problems involving large strains, rotations and displacements coupled to inelastic material behaviour. The accuracy of the SPH-computations is assessed using nonlinear FEM as a benchmark.

KW - PARTICLE

KW - EQUATIONS

UR - http://www.scopus.com/inward/record.url?scp=85073899524&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1268/1/012077

DO - 10.1088/1742-6596/1268/1/012077

M3 - Conference article

AN - SCOPUS:85073899524

VL - 1268

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012077

T2 - All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019

Y2 - 13 May 2019 through 17 May 2019

ER -