A Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue
Hieber S.E., Koumoutsakos P., J. Computational Physics, 227, 9195-9215, 2008
We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue.Linear solids are represented by the Lagrangian formulation of the stress–strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce theboundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementinga particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions andthe results compare well with the results of respective finite elements simulations. In simulations of large solid deformationunder plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangianparticle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.