Keywords: masonry structures, no tension material, incremental solutions, variable rate.

This paper focuses on the introduction of a special incremental formulation to treat the dynamics of masonry-like structures and numerical problems that may arise during the static analyses under ordinary loads. The paper deals with bodies whose constitutive material is unable to resist tensile stress (no-tension or NT material [1]) pointing to the specialization of some theorems formulated many years ago by Capurso [2,3] for incremental solutions of two and three-dimensional elastic-plastic problems. Some extremum properties of a suitably defined functional of the response variables, verified within each time step of the loading process are identified.

Despite a strong similarity between the plastic and the NT behaviour, the need for a re-formulation of the theorems is prompted by the circumstance that the fracture multipliers' rates are not semi-positive definite, as, by contrast, it happens for the plastic case. For non-holonomic materials the energy theorems can be only referred to stress and strain rates rather than to the instantaneous stress and strain fields, while, by contrast, in NT materials they depend only on the final load condition.

The incremental solution would not be necessary for treating static problems in elastic-no-tension bodies, since the solution does not depend on the loading path. Step solutions may be useful in the numerical solution of the problem in finite terms, when sometimes the solution is hidden in some narrow corner of the admissibility domain, and the incremental solution produces a path that helps with the convergence of the solution.

The potential of the original approach proposed in the paper, that leads to the identification of a suitable functional which is shown to be minimum in the solution. In the dynamic case, the displacements rates are usually known at the beginning of every time step since the accelerations at the previous step can be directly inferred by dynamic equilibrium, thus allowing the time step updating and the performance of step by step solutions.

1

A. Baratta, O. Corbi, "On Variational Approaches in NRT Continua", Intern. Journal of Solids and Structures, 42, 5307-5321, 2005.

2

M. Capurso, "Principi di minimo per la soluzione incrementale dei problemi elasto-plastici. Nota I", In Rendiconti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, VIII, vol. XLVI (4-5), 1969.

3

M. Capurso, "Principi di minimo per la soluzione incrementale dei problemi elasto-plastici. Nota II", In Rendiconti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, VIII, vol. XLVI (4-5), 1969.

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