In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For other, more complex and interesting situations, kinematic and kinetic hypotheses need to be invoked, and a constrained three-dimensional constitutive relation has to be employed at every point of the section in order to implement non-linear and dissipative constitutive laws into dimensionally reduced structural models. In this article we explain in which sense reduced constitutive models can be expressed as minimization problems, helping to formulate the global equilibrium as a single optimization problem. Casting the problem this way has implications from the mathematical and numerical points of view, naturally defining error indicators. General purpose solution algorithms for constrained material response, with and without optimization character, are discussed and provided in an open-source library.
Keywords: Structural models | Constitutive models | Variational method | Error estimation

This article presents a methodology for the experimental analysis of thin membranes using digital image processing techniques. The methodology is particularly suitable for structures that cannot be monitored using conventional systems, particularly those systems that involve contact with the structure. This methodology consists of a computer vision system that integrates the digital image acquisition and processing techniques online using special programming routines. Because the membrane analyzed is very thin and displays large displacements/strains, the use of any conventional sensor based on contact with the structure would not be possible. The methodology permits the measurement of large displacements at several points of the membrane simultaneously, thus enabling the acquisition of the global displacement field. The accuracy of the acquired displacement field is a function of the number of cameras and measured points. The second step is to estimate the strains and stresses on the membrane from the measured displacements. The basic idea of the methodology is to generate global two-dimensional functions that describe the strains and stresses at any point of the membrane. Two constitutive models are considered in the analysis: the Hookean and the neo-Hookean models. Favorable comparisons between the experimental and numerical results attest to the accuracy of the proposed experimental procedure, which can be used for both artificial and natural membranes. &2014 Elsevier Ltd. All rights reserved Keywords: Displacement measurement | Large displacements/strains | Digital image processing | Experimental analysis of structures | Nonlinear constitutive laws