A Numerical Model for Masonry-Like Materials
Masonry-like materials (as rock, concrete, bricks) are practically incapable of sustaining tensile stresses, and therefore the stress tensor σ(x) is usually assumed to belong to the convex cone Ko of negative semi-definite matrices. A special constitutive law for such materials can be obtained by specializing Hencky’s law (see , Ch.5, 6.1) for perfect plasticity (also in that case σ(x) must belong to a convex set). According to [l], for a given bounded set Ω⊂IR2. and displacement field u(x), we have: (1) ε(x) = A-1 σ (x) +β(x) A being a symmetrical positive definite operator; (2) β (x) ·[σ (x) - τ] ⩾ 0 for any τ ∈K0. Condition (1) means that the strain ε (x) is the sum of an elastic part A-1 σ(x) and another part β(x) which, according to (2), is positive semidefinite and orthogonal to the stress. Furthermore, this implies that the displacement field u(x) need not to be continuous.