Mathematics of the Masonry–Like model and Limit Analysis

摘要: These notes present a brief introduction to the mathematics of equilibrium no–tension (masonry–like) materials. We first review constitutive equations using idea that stress material must be always negative semidefinite. The strain tensor is naturally split into sum elastic and fracture strain. depends linearly on via fourth–order elasticities. Then we consider body made material, introduce loads total energy deformation with internal loads. examine question whether bounded from below. That brings us important notion strong compatibility are strongly compatible if they can equilibrated (in sense principle virtual work) by square integrable semidefinite field. below only compatible. central in limit analysis strengthened form theory existence states. Roughly speaking, compatible, then safe, while otherwise incompatible lead collapse body. To determine it not necessary solve full displacement problem, suffices find field, which independent theory.