Meshfree Discretization Methods for Solid Mechanics

Abstract Meshfree methods are used for the spatial discretization of partial differential equations, but in contrast to finite element methods, they do not employ elements in the construction of the interpolants. Instead, a set of nodes is accompanied by a domain of influence for each node, whereby the overlap of domains of influence accounts for the interconnectivity between nodes. In this chapter, we will treat the formulation, implementation, and application to solid mechanics of meshfree methods. The focus will be on the element‐free Galerkin method but we will also provide an overview of other meshfree methods. As regards the applications, we will treat two major classes: firstly, incorporating discontinuities in meshless interpolations and secondly, exploiting the hypercontinuity of meshfree shape functions. Finally, we will discuss some urban myths surrounding meshfree methods, the relation with the new generation of node‐based finite element methods, and the future of meshfree methods.