Elementary Solutions for Equilibrium Problems of Masonry-Like Materials

Abstract

Certain features of the mechanical behaviour of materials such as masonry, which can withstand only low tension, are still far from being fully understood. Various authors have proposed that a non-linear elastic constitutive law should be used for such materials, with a negative semi-definite stress tensor and with the strain being considered as the sum of an elastic part and an inelastic part (Romano & Romano [1], Di Pasquale [2], Abruzzese et al. [3], Del Piero [4]). This constitutive law is relatively simple. However, although some progress has been made (Giaquinta & Giusti [5], Anzellotti [6], Del Piero [7]), the conditions for ensuring the existence of the solutions in a number of equilibium problems, even elementary ones, are still unknown, as are methods allowing us to determine them. Such difficulties can often be eluded by supposing the material to be linear elastic and by finding those structural shapes, if any, the interior of which is in a state of pure compression under the prescribed load conditions (Villaggio [8], Bennati & Lucchesi [9], Bennati et al. [10]). Nevertheless, it is clearly of some interest to find explicit solutions which, however elementary they may be, are obtained while still utilizing the hypothesis that the material does not support tension.