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Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models are employed in failure analyses. In this contribution the governing field equations are regularized by adding rotational degrees‐of‐freedom to the conventional translational degrees‐of‐freedom. This so‐called elasto‐plastic Cosserat continuum model, for which an efficient and accurate integration algorithm and a consistent tangent operator are also derived in this contribution, warrants convergence of the load—deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone. This is demonstrated for an infinitely long shear layer and a biaxial test of a strain‐softening elasto‐plastic von Mises material.

The behaviour of cracked finite elements is investigated. It is shown that spurious kinematic modes may emerge when softening type constitutive laws are employed. These modes are not always suppressed by surrounding elements. This is exemplified for a double‐notched concrete beam and for a Crack‐Line‐Wedge‐Loaded Double‐Cantilever‐Beam (CLWL—DCB). The latter example has been analysed for a large variety of finite elements and integration schemes. To investigate the phenomenon in greater depth an eigenvalue analysis has been carried out for some commonly used finite elements.

The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy.

In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy.

The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena.

A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.

Fire analysis of precast segmental tunnels involves several problems, mainly related to the soil-structure interaction during fire exposure, coupled with material degradation. Temperature increase in the tunnel is the cause of thermal expansion of the lining, which is resisted by the soil pressure. Furthermore, the increase of temperature in the lining leads to severe damage to the reinforced concrete precast elements, which can jeopardise structural safety.

This problem has been analysed using an ideal case of a precast segmental tunnel excavated in a stratified soil. The analysis has been conducted with a commercial nonlinear FE element code. Initially, excavation of the tunnel was modelled in order to predict stresses in the lining due to the soil pressure and eventually fire exposure was considered. The reinforced concrete lining was modelled with a crack model in order to simulate the actual behaviour.

Results show the importance of considering the interaction with the soil and the degradation of the concrete lining.