Extending a radial point interpolation meshless method to non-local constitutive damage models

This work extends the radial point interpolation method (RPIM) to the analysis of concrete structures using an elastic continuum damage constitutive model. Here, the theoretical basis of the material model and the computational procedure are described with detail. Firstly, the plane stress meshless formulation is adapted to a rate-independent standard local damage criterion where both compressive and tensile damage evolution are settled respecting a Helmholtz free energy function. Afterwards, the non-local damage formalism is established based on the foregoing local model. Subsequently, the internal variable fields (such as local and non-local damage parameters) are obtained within the return-mapping damage algorithm. This study employs the Newton-Raphson algorithm to achieve the non-linear damage solution. The numerical stability and performance of the proposed standard and non-local models are assessed using the results of experimental tests available in the literature.