Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.. Authors: Schaefferkoetter, Peter M. [University of Colorado, Boulder, CO (United States)]; Yoon, Young-Cheol [Myongji College, Seoul (South Korea)] (ORCID:0000000330175533); Song, Jeong-Hoon [University of Colorado, Boulder, CO (United States)] (ORCID:000000022932440X). DOE Contract: NA0003962. Subjects: Compressible neo-Hookean materials; Meshfree collocation; St. Venant Kirchhoff materials; Strong form; Three-dimensional large deformation