The local point interpolation–boundary element method (LPI–BEM) applied to the solution of mechanical 3D problem of a microdilatation medium

•A simple numerical strategy: coupled isotropic BEM with local point collocation.•Non-conventional material modelling: microdilatation.•Taking microstructure into account in the behaviour law.

A numerical solution procedure of three-dimensional constrained microstretch (microdilatation) elastic problem is presented. The approach called local point interpolation–boundary element method (LPI–BEM) uses a partition of the kinematical variables into complementary and particular parts. The complementary fields are obtained by isotropic boundary element method. The particular integrals are determined by solving the corresponding strong form differential equations using local radial point interpolation. The effectiveness and accuracy of the approach are proven on some simple examples. The latter are also used in order to highlight some peculiarities and potentialities of such extended continuum mechanical approach.