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We provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of dilatation only. Such a model has many applications, e.g., to describe phenomena of interest in poroelasticity or in some situations where media with scalar microstructure are necessary. We present an extension of the previous results by Eremeyev et al. (2020 Z angew Math Phys 71 (6): 1–16) to the case of domains with edges and when external line forces are applied. Let us note that the interest paid to Lipschitz polyhedra-type domains is at least twofold. First, it is known that geometrical singularity of the boundary may essentially influence singularity of solutions. On the other hand, the analysis of weak solutions in polyhedral domains is of great significance for design of optimal computations using a finite-element method and for the analysis of convergence of numerical solutions. [ABSTRACT FROM AUTHOR]

Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided comparison of solutions obtained within the micropolar and classical elasticity shows the influence of micropolar properties on stress concentration in the vicinity of contact area. [ABSTRACT FROM AUTHOR]

• The collapse mechanisms of R.C. existing bridges piers subjected to corrosion effects has been analyzed considering static and dynamic loads. • An analytical approach has been considered to introduce the corrosion effects in the finite element model implementation. • Linear and non-linear numerical analyses have been carried out considering an existing R.C. bridge located in Northern Italy in order to evaluate its safety level under different load cases. • Different interventions have been proposed to prevent the collapse of the bridge. The evaluation of the structural behaviour of existing reinforced concrete (RC) bridges represents one of the most current structural engineering research topics due to their strategic importance, especially if they are subjected to corrosion effects which can lead to a significant reduction of load-bearing capacity of the main structural elements (e.g., the piers). In the last decades, different types of numerical approaches have been proposed for the evaluation of the structural behaviour of these strategic infrastructures, especially after the recent collapses that have affected this type of structures during last years. In this paper, the structural behaviour of an existing RC bridge subjected to corrosion effects due to carbonation is analysed by means of an efficient procedure based on the implementation of a Finite Element Model (FEM) where the main structural elements are implemented using only Timoshenko beam elements. The safety level of the bridge has been evaluated considering different load conditions (e.g. traffic load, seismic action, etc.) calculated according to the Italian Design Code (NTC2018). Finally, a retrofitting intervention is proposed in order to guarantee and adequate safety level of the bridge under the considered different load combinations. [ABSTRACT FROM AUTHOR]