The meshless simulation of the atherosclerotic plaque tissue using an elasto-plastic model

In this work, using meshless methods, the elasto-plastic response of human atherosclerotic plaque tissue is numerically analysed. The meshless method used in this work is the Natural Neighbour Radial Point Interpolation Method (NNRPIM). Within the NNRPIM the nodal connectivity is enforced with the Natural Neighbour concept. Using the constructed Voronoi diagram, it is possible to establish the influence-domains and to construct a node-depending background integration mesh used in the numerical integration of integro-differential equations governing the studied physic phenomenon. The NNRPIM interpolation functions, used as test functions in the Galerkin weak form, are constructed using the Radial Point Interpolators. In the construction of the NNRPIM interpolation functions no polynomial basis is required and the used Radial Basis Function (RBF) is the Multiquadric RBF. The natural and essential boundary conditions can be imposed by the direct imposition method since the NNRPIM interpolation functions possess the Kronecker delta property. In the literature, it is possible to find research works regarding the mechanical characterization of the human atherosclerotic plaque tissue. As the literature shows, it is possible to represent the nonlinear behaviour of such soft tissue using a classic "linear elastic-linear plastic" inelastic model. The non-linear solution algorithm considered in this work is the Newton-Raphson initial stiffness method. Additionally, the elasto-plastic behaviour of the human atherosclerotic plaque tissue is characterised with: the von-Mises yield surface; an associative flow rule; and an isotropic hardening rule. Here, the experimental tests performed in the literature are numerically reproduced and a numerical model of an artery with atherosclerotic plaque tissue is analysed. The results clearly show the importance of the inclusion of an elasto-plastic model for the atherosclerotic plaque tissue.