Yield design applied to a mechanically based non-local continuum

Abstract

Classical yield design theory provides upper and lower bounds of failure loads using local strength criteria. However, purely local formulations fail to reproduce size effects on failure loads of structures observed in quasi-brittle materials.

In this paper, a yield design formulation is developed for a mechanically based non-local continuum, in which long-range interactions between material points are introduced through central internal body forces. The formulation preserves classical Cauchy boundary conditions while enriching the internal power with a non-local contribution governed by an intrinsic length and a decay function. This work introduces a mechanically based non-local yield design approach that inherently accounts for size effects, offering a physically grounded extension of classical collapse analysis. Both kinematic (upper bound) and static (lower bound) approaches are established by defining local and non-local strength domains.

The exact solution is derived for a one-dimensional example with the same failure load derived by both approaches.  This illustrates how the proposed framework leads to size-dependent axial strength.

An upper-bound non-local yield design approach of a cubic specimen under compression is used to predict a volume-dependent size effect of quasi-brittle materials with a Mohr–Coulomb local criterion and to interpret the hourglass failure mechanism.