A convected-particle tetrahedron interpolation technique in the material-point method for the mesoscale modeling of ceramics

Convected particle domain interpolation, which is known to boost the accuracy of the material-point method, is applied in a form called convected-particle tetrahedron interpolation (CPTI). CPTI exploits the efficiency of tetrahedral tessellations to represent complex structural geometries, while still solving field equations on a rectilinear background grid. Advantages include anti-locking and an ability to handle extremely large deformations without suffering typical Eulerian advection errors. CPTI is demonstrated to resolve long-standing errors caused by spuriously ragged (stair-stepped) surfaces, and it is also shown to accommodate mathematically rigorous evaluation of surface integrals in models for contact and friction. Benefits of this work are illustrated in mesoscale simulations of an aluminum oxynitride ceramic.