Development of the distinct lattice spring model for large deformation analyses

G.-F. Zhao

Large deformations and geometrically nonlinearity are crucial components of many engineeringproblems. Many numerical methods have been developed to tackle the problem of solving them, suchas the finite element method (FEM) [1–8], the boundary element method (BEM) [9–11], the meshlessmethod [12–14], the Lagrangian integration point FEM [15], the natural element method (NEM) [16],the local Kriging method [17], the nearest-nodes FEM [18], and the B spline-based method [19].Various approaches have been developed to implement a numerical method for large deformationanalyses, including the total Lagrangian (TL) approach [1,2,19], the updated Lagrangian (UL)approach [3,4,14,18], the arbitrary Lagrangian–Eulerian (ALE) technique [5,20], the corotationalapproach [8], and the remeshing and interpolation technique with small strain model (RITSS)method [6]. Each method has its own advantages—for example, the meshless method is free ofmeshing requirements (e.g. [12–14]), whereas the RITSS FEM by Hu and Randolph [6] is robust andeasy to implement. It has also been found that different approaches and methods can produce verysimilar results (e.g. [14,17,19]), and large-deformation FEM has usually been adopted as the referencemethod for benchmarking. The development of a specific numerical method for large deformationanalysis is an essential extension of this method to the area of nonlinear analysis, which can usually beclassified as geometric nonlinearity and material nonlinearity. Large deformation problems may involveboth geometric and material nonlinearity, but this work considers only geometric nonlinearity