Limit state analysis of RC structures

The inelastic static pushover analysis has become a popular tool for evaluating the seismic capacity of structures. It is able of predicting the seismic force and deformation demands by accounting in an approximate manner for the inelastic redistribution of internal forces. Though approximate in nature and based on static loading, if properly used the pushover analysis can provide many significant insights into the structural behaviour and also put forward the design weaknesses that may be hidden in the elastic analysis. The main features of the conventional pushover analysis are well described in [1], where are also emphasized limitations and possible causes that may produce loss of accuracy of the method. A basic prerequisite for successful applications of the method is an adequate knowledge of the inelastic behaviour of structural elements. This is particularly true for those structures containing shear walls that, if not properly described, may render the results of the analysis completely meaningless. In this work we show how, under appropriate hypotheses, one can introduce steel reinforcement into shear walls by appealing to a semi-analytical multi-scale approach. In particular, reinforcements are taken into account using an embedded beam approach, the usual conventional material behaviour, i.e. the the so-called parabolic-rectangular stress block for concrete and ideal elastic-plastic for steel as of Eurocode 2, and a fiber-free integration, that provides the exact solution for stress resultants over the cross section of the beam itself. Representative numerical simulations are shown that illustrate the capabilities of the proposed approach, that allows one to carry out accurate nonlinear analyses of full-scale reinforced concrete structures with relatively reduced computational effort

GRADIENT OF DAMAGE ENHANCEMENT FOR A COHESIVE MODEL

International audienceGradient enhancements have become increasingly popular in the last decades for dealing with problems in mechanics suffering from spurious mesh sensitivity induced by strain softening. Many proposals exist in this sense and various regularization techniques have been presented and successfully applied to study localization and fracture. In short, the idea underlying almost all such techniques is that of using some extended con-stitutive equations in which information about the material microstructure is represented through a length scale-related parameter. The physical interpretation of this quantity on a micromechanical basis is still the object of an open debate, whereby its interpretation as a mere numerical regularization parameter is certainly more appropriate. From a computational standpoint, once spatial gradients and/or length scales are introduced in the constitutive equations the latter are no longer defined at the local (quadra-ture point) level but they are established at a larger scale, i.e. the scale of the structural model, in a form that could be rephrased in an integral format. Basically, for usual local models stresses, strains and internal variables are defined in a point-wise fashion whereby, as outlined in [1], their values can be regarded as the parameters of a piece-wise constant interpolation. Hence, variables computed at the Gauss point level in classical displacement-based finite element methods can be understood as fields that are in general discontinuous across elements boundaries and inside elements as well. This discontinuous pattern is indeed one of the most striking consequences of the strictly local character of the constitutive law

Use of kriging to surrogate finite element models of bonded double cantilever beams

An algorithm based on kriging statistical interpolation for computing the surrogate response of a Finite Element model is presented. The interpolation model is calibrated via computation of Finite Element responses at a set of random occurrences of a material parameter. Such random generation concentrates at locations where the numerical model requires a higher amount of data to get the desired accuracy. As a model problem a standard fracture propagation test is analyzed. The proposed procedure is shown to be robust and accurate since responses obtained via a direct computation and use of the surrogate model turn out to be undistinguishable

Only thickness is essential in the Thick Level Set approach

Regularized damage formulations have become increasingly popular in the last decades for dealing with problems inMechanics suffering from spurious mesh sensitivity induced by strain softening [1]. In short, the idea underlying almost all such models is that of using some extended constitutive equations in which a length scale parameter brings to the macro level information about material microstructure. Classical regularized constitutive relationships are formulated via gradient or averaging operators. They provide globally smoothed solutions by enforcing a greater regularity either on strains or internal variables that are no longer defined at the quadrature point level but are established at a larger scale, i.e. the scale of the structural model. The same concepts are present into the so-called Thick Level Set (TLS) approach to quasi-brittle fracture [2], whereby progressive damage that takes place in a region of finite thickness is defined as an explicit function of the distance to the undamaged portion of the domain under consideration. Within this framework one possible way to follow the evolution of damage in the structure amounts to continuously tracking the position of the moving layer where the transition between the damaged material and the undamaged one occurs. In the original implementation of the model [2] this was achieved based on distance functions and level sets, which basically amounts to solve the eikonal equation. In the present contribution the eikonal-based approach to the TLS modeling is abandoned in favor of an implicit representation of the damage field and tools of convex analysis [3]. This allows to drop out the level sets from the formulation and to achieve a greater flexibility in the implementation of the model that is recast in the format of a non-local Generalized Standard Model in which the damage field is subject to convex constraints. Numerical results for representative test cases will be presented to demonstrate the capabilities of the proposed approach

A Damage-Friction Formulation for the De-Cohesion Analysis of Adhesive Joints

An interface model for the analysis of adhesively bonded assemblies accounting for damage as well as irreversible frictional sliding is presented. Decohesion at bonded interfaces is simulated via the damage mechanics-based approach developed by the authors whereas stick-slip motion is introduced after complete separation by analogy with plasticity theory. Numerical results for a typical test problem are shown that demonstrate the main features of the proposed approach

A gradient-enhanced cohesive model

International audienceA novel implementation of the cohesive zone concept that makes use of the gradient enhancement is discussed. The model can be shown to fit in the non-local generalized standard approach, whereby the framework of standard materials is extended to include the gradients of internal variables. A representative numerical example is shown that demonstrates the capabilities of the proposed approach

A damage model for simulating decohesion in adhesively bonded assemblies

In this work use is made of a cohesive-zone approach for the simulation of adhesive damage in adhesively bonded joints. The interface relationship relating tractions to displacement discontinuities is derived within the framework of damage mechanics and the constitutive model is formulated in a way that the advancement of the decohesion front takes place when the absorbed traction-separation work equals a critical fracture energy. For the mixed-mode case two interaction criteria expressed in terms of material parameters measurable in single mode delamination tests are adopted for determining the onset and growth of decohesion. Numerical simulations are presented for a typical test problem in which the adhesive layer is modelled via interface elements

A gradient-enhanced cohesive model

International audienceA novel implementation of the cohesive zone concept that makes use of the gradient enhancement is discussed. The model can be shown to fit in the non-local generalized standard approach, whereby the framework of standard materials is extended to include the gradients of internal variables. A representative numerical example is shown that demonstrates the capabilities of the proposed approach