Continuum Theory for Strain‐Softening

Abstract

In heterogeneous materials such as concretes or rocks, failure occurs by progressive distributed damage during which the material exhibits strain‐softening, i.e., a gradual decline of stress at increasing strain. It is shown that strain‐softening which is stable within finite‐size regions and leads to a nonzero energy dissipation by failure can be achieved by a new type of nonlocal continuum called the imbricate continuum. Its theory is based on the hypothesis that the stress depends on the change of distance between two points lying a finite distance apart. This continuum is a limit of a discrete system of imbricated (regularly overlapping) elements which have a fixed length,