A two-level strain smoothing regularized meshfree approach with stabilized conforming nodal integration for elastic damage analysis

A two-level strain smoothing regularized meshfree formulation with stabilized conforming nodal integration is proposed for elastic damage analysis. This method is furnished by the non-local strain smoothing operation defined within a nodal representative domain. The one-level and two-level smoothing strain measures and the related smoothed nodal gradients of meshfree shape function are consistently formulated by selecting different kernel functions in the non-local operation. It is shown that both one-level and two-level smoothed nodal gradients of meshfree shape function can exactly meet the linear reproducing conditions and this provides a theoretical foundation for the employment of the smoothed nodal gradients in Galerkin meshfree formulation. Within the assumed strain framework, a regularized Galerkin meshfree method using the two-level smoothing strain measure is presented to deal with the dicretization sensitivity issue associated with the strain softening of elastic damage analysis. The discrete formulation is fulfilled by the nodal integration with the two-level smoothed nodal gradients of meshfree shape function. Numerical results of typical elastic damage examples evince that the proposed regularized meshfree method can effectively resolve the discretization sensitivity problem.