Abstract

A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters of non‐associated plasticity theory for frictional materials and a modified Mohr‐Coulomb yield surface is suggested. Onset and amount of cracking at a point are controlled by the values of the effective plastic strain and thus it can be studied by a posteriori postprocessing of numerical results. The accuracy and objectivity of the model is checked out with some examples of application.

Abstract

This paper extends the use of crack-tracking techniques within the smeared crack approach for the numerical simulation of cohesive–frictional damage on quasi-brittle materials. The mechanical behaviour is described by an isotropic damage model with a Mohr–Coulomb failure surface. The correct crack propagation among the two alternative fracture planes proposed by the Mohr–Coulomb theory is selected with the use of an energy criterion based on the total elastic strain energy. The simulation of three benchmark problems of mixed-mode fracture in concrete demonstrates that the proposed methodology can reproduce the material’s frictional characteristics, showing robustness, as well as mesh-size and mesh-bias independence.

Abstract

This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation and an isotropic damage constitutive model. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms. The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path and the force–displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data. Aspects related to the discrete solution, such as convergence regarding mesh resolution and mesh bias, as well as other related to the physical model, like structural size effect and the influence of Poisson’s ratio, are also investigated. The enhanced accuracy of the computed strain field leads to accurate results in terms of crack paths, failure mechanisms and force displacement curves. Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem.

Abstract

In the present paper, a new d+/d− damage model apt for quasi-brittle materials is described and its validation is carried out considering unreinforced concrete, reinforced concrete and masonry elements.

Two independent scalar damage variables, d+ and d−, in combination with the split of the reversible strain tensor into its positive and negative counterparts, are adopted in order to simulate the pronounced dissimilar response under tension and compression, typical of these materials. An energy-equivalent framework is considered for representing the orthotropy induced in the material by the degradation process, with the consequence that a thermodynamically consistent constitutive operator, positive definite, symmetric and strain-driven, is derived. In addition to the degradation parameters, the permanent strain tensor is also contemplated by the model and a modification of the exponential softening modulus is proposed in order to treat the evolution of the two causes of dissipation, damage and irreversible deformations, in a coupled way.

The formulation is integrated with a multidirectional damage procedure, addressed to extend the microcrack closure-reopening (MCR) capabilities of the model to shear cyclic conditions, characterized by orthogonal (or however intersecting) sets of cracks. Maintaining unaltered the dependence of the constitutive law from two scalar indeces, d+ and d−, this approach activates or deactivates a tensile(compressive) damage value on the base of the current maximum (minimum) principal strain direction. In correspondence with damage activation (crack opening) or deactivation (crack closure), a smooth transition is introduced, in order to avoid abrupt changes in stiffness and enhance the numerical performance and robustness of the multidirectional procedure. The adequacy of the proposed constitutive model in reproducing experimental results has been proven for both monotonic and cyclic loading conditions. The two examples of application involving cyclic loads, dominated by shear, constitute a validation of the multidirectional damage approach, showing how the suitable representation of unilateral effects and permanent deformations is essential to model the observed structural response in terms of maximum resistance, evolution of stiffness degradation and dissipation capacity.

Abstract

This paper discusses the modeling of cracking in quasi-brittle materials using isotropic and orthotropic damage constitutive laws. A mixed strain/displacement finite element formulation is used, taking advantage of its enhanced precision and its enforced interelemental strain continuity. On the one hand, this formulation avoids the spurious mesh dependency of the computed solution associated to standard elements and does not require the use of tracking techniques. On the other hand, it greatly alleviates the spurious stress locking associated to the use of orthotropic models on standard finite elements. The performance of several isotropic and orthotropic damage constitutive laws is assessed through an extensive comparison with analytical solutions, numerical tests and experimental evidence reported in the literature. The behavior of the different damage models in terms of crack surface, collapse mechanism and force displacement curves is investigated performing 3D analyses in several conditions including Mode I, Mixed Mode and Mode III fracture. When performing the appraisement of planar, bending and twisting cracks, the enhanced accuracy of the mixed formulation allows for a distinct assessment of the several damage models considered. Aspects related to the behavior of damage models, such as the influence of Poisson’s ratio, the shape of the damage surface and the adoption of isotropic and orthotropic models are investigated and noteworthy conclusions are drawn

Abstract

The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms. During the last years, a wide variety of numerical methods has been employed to assess the out-ofplane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh. Mixed strain/displacement finite elements have been recently proposed as a remedy to the above numerical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry structures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite elements.

Abstract

Experimental techniques usually employed in the characterization of conventional mixes are not able to clearly describe some specific properties of the recycled mixes, which are determinant in the material's mechanical response like cracking strength or tenacity. These new specific properties demands new methods of testing to know the really conditioning mechanical variables taking part in the process, so that being able to characterize and design new recycled mixes in an optimum way. In this paper, the direct tensile test is analyzed as a suitable method for evaluating the properties of recycled asphalt mixtures for different percentages of reclaimed asphalt pavement. A constitutive formulation has been developed to simulate the experimental results and can be used in conjunction with the experimental analysis of the recycled asphalt properties to provide an accurate characterization of the material.

Abstract

Abstract

Abstract

Starting from a discussion on the experimental results obtained from diagonal compression tests executed on in-situ masonry panels, the paper presents a constitutive model, together with a numerical formulation, to describe the cracking phenomena in rubble masonry structures. A classical finite element discretization is assumed with the hypothesis of a homogenous continuum material. The adopted constitutive model identifies three different phases: (i) the elastic phase; (ii) the micro-cracking phase, in which the formation of micro- cracks, spread in the structural members, is accounted assuming a plastic material with a strain hardening stable behavior; (iii) the macro-cracks phase, in which the formation of macro- cracks, developing along the edges of finite elements, are simulated by means of localized softening plastic deformation. While the numerical description of spread plasticity in the finite element framework is a topic that has been widely addressed in the past, the representation of localized plastic deformation and its implementation in a finite element code is an original contribution of the authors. From a computational point of view, the value of plastic deformations (i.e. crack openings) is found by solving a parametric linear complementarity problem (LCP) using mathematical programming algorithms. The main advantage of using an LCP method is its ability to deal also with configurations in which instability and a multiplicity of solutions are possible (e.g. softening behavior). The numerical simulation of a diagonal compression test and the comparison of the results with the experimental evidence are presented to validate the model