A meshfree model enhanced by NURBS-based Cartesian transformation method for cracks at finite deformation in hyperelastic solids

Abstract

This paper presents a numerical investigation of single and multiple cracks in hyperelastic solids by using an extended moving Kriging meshfree method. The behavior of crack such as jump of displacement field across crack surface is mathematically captured by enriched functions, which are selected based on asymptotic solution. For meshless numerical integration, the NURBS-enhanced Cartesian transformation method is proposed to evaluate domain integrals of geometries with curved boundaries, without the need for sub-division of problem domain into background cells. It is guaranteed that no discontinuity is located within integration domain, as crack surfaces are viewed as part of the boundaries. Thanks to the Kronecker’s delta property of the moving Kriging interpolation, direct imposition of boundary conditions can thus be made. The correlation parameter, which has certain effects on the accuracy of approximation, is not necessary to be pre-defined in this work. Instead, it is determined according to the characteristic nodal distance in every support domain. The accuracy and efficiency of the present approach are investigated in various examples and computed results are compared with available analytical solutions and/or other numerical methods.