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This paper presents a novel approach concerning the development of an orthotropic damage model for composite materials, based on the original plane stress Tsai–Wu failure criterion. In its original formulation, the Tsai–Wu is a mode-independent criterion only capable of acknowledging the existence of damage in a certain point of a composite material. It is not capable of identifying if the damage is located in the fibre, matrix or interlaminar zone. This study aims at filling this gap in knowledge by providing a simple method, based on equivalent stresses and strains, that identifies the relevant failure modes when the Tsai–Wu failure criterion is at the onset of damage. Using this novel methodology, it is possible to implement classical damage evolution constitutive laws based on the fracture energy regularization. At present, the proposed damage formulation is based on the consideration of a plane stress space and Mode I fracture, but its generalization to a full 3D damage model is expected to be defined in the near future. The damage model is implemented in the commercial finite element software ABAQUS through a user-defined material (UMAT) subroutine, and all numerical models are compared with experimental results available in the literature.

Silicone breast implants are commonly used, even for reconstruction after mastectomy in malignant disease. In this setting, the presence of suspicious lymphadenopathy should be investigated, because it could represent disease progression. A case of a woman with left breast cancer (more than 20 years ago) and prosthesic reconstruction is reported. She developed a second breast cancer on the opposite side. During follow up, a suspicious lymphadenopathy was seen in the computed tomography scan, but the final diagnosis corresponded to a siliconoma. Silicone granuloma is a difficult diagnosis in these cases, but must be considered.

This paper presents and discusses the numerical performance of a set of physically non-linear models applied together with Carrera’s Unified Formulation (CUF) for the analysis of beams. The main objective of this work is to assess the numerical efficiency of CUF when non-linear material analysis is applied to 1D elements using the equivalent single layer (ESL) formulation. To model material behaviour this work considers three different alternative approaches: (i) the classical isotropic plasticity with no hardening, (ii) the Mazars isotropic concrete damage model, and (iii) the composite orthotropic Hashin damage model. To validate the models proposed, the numerical solutions are compared both with analytical results and experimental data. The results obtained show that it is possible to provide accurate results with CUF when physically non-linear analysis is performed, even when considering approximations involving a small number of degrees of freedom.

This paper presents some numerical investigations related to the use of a new approximation function to be applied in Carrera's Unified Formulation (CUF). The main objective is to study and assess the efficiency of the CUF, when Legendre approximation functions are used at the section level, on 1D element, using an equivalent single layer (ESL) formulation. Previous experimental and analytical results, obtained in the case of GFRP composite bridge decks and sandwich panels, are used to further validate the numerical results being reported. 3D finite elements are also used, in order to compare and validate the numerical structural outputs. The main conclusion is that the classical Legendre polynomial functions are suitable and provide accurate results. The use of this type of functions does not require any stabilization procedure of the resulting governing system for the case of 1D elements, in clear contrast to what typically happens when other approximation functions are used with an equivalent single layer formulation.

This paper presents a modified Mazars damage model, based on a strain formulation, for the physically nonlinear analysis of concrete structures. The main objective is to propose a modified damage model, in which both tension and compression damage evolution laws are regularized using a classical fracture energy methodology. The original loading functions are maintained, including their thermodynamic consistencies. The most relevant modification of the model is introduced in the damage evolutions laws, which are updated in order to produce similar stress-strain relations to those presented in fib Model Code 2010. The softening branch under both compressive and tensile strains is regularized with fracture energy. The damage model is then benchmarked with classical experimental and numerical tests considering monotonic loadings. The new constitutive relation was implemented in the commercial software ABAQUS via user subroutine UMAT. Research needs towards a definition of a generalized damage model with energy regularization are discussed and presented.

Sandwich panels often need to be designed to sustain significant permanent loads, raising the need to accurately account for long-term creep deformation. However, the accurate prediction of creep in sandwich panels is not trivial, particularly owing to their composite multi-layered nature, the multitude of possible face and core material combinations, and the possible existence of through-thickness shear reinforcement (ribs/webs). This paper presents numerical investigations on the creep behaviour of composite sandwich panels produced by vacuum infusion with glass-fibre reinforced polymer (GFRP) faces and ribs, and polyurethane (PUR) and polyethylene terephthalate (PET) foam cores. Carrera Unified Formulation (CUF) is implemented, for the first time using 1D elements with an equivalent single layer (ESL) methodology, to model the creep response of simple and ribbed panels by adopting a Composite Creep Modelling (CCM) approach. Previous experimental results from creep tests carried out on such sandwich panels and their constituent materials are used to obtain time-dependent constitutive relations for the materials in various layers and validate the numerical results. Additionally, results from analytical beam models using Timoshenko beam theory (TBT) with multi-layered sections are used to further validate the numerical outputs obtained with CUF. The developed numerical models were able to predict the experimental creep behaviour of the full-scale sandwich panels with reasonable accuracy. Differences observed between the CUF and TBT models mainly stem from the inherent approximations concerning the shear correction factors used with TBT, which contrast with the solutions provided by CUF, where such factors do not need to be considered when higher degrees of approximation are used.

A field experiment was developed from May to September 2018 with the objective of evaluating the use of mulching in early garlic cultivars in semiarid conditions. Made available in DSpace on 2020-07-29T11:15:29Z (GMT). No. of bitstreams: 1 8998-Rev-Caatinga-54145-1-10-20200522-Marcio-Sinoia.pdf: 507902 bytes, checksum: 07251d165b7cd1ecf96204c202cecf74 (MD5) Previous issue date: 2020

This paper presents and discusses a hybrid-mixed stress (HMS) finite element model for the static and dynamic analysis of 2D reinforced concrete frame structures. It is assumed a physically non-linear behaviour for both concrete and steel. In this model, both the stress and the displacement fields are approximated in the domain of each element. Complete sets of orthonormal Legendre polynomials are used as approximation functions. The use of these functions makes possible the definition of analytical closed form solutions for the computation of all structural operators when a physically linear behaviour is assumed and leads to the development of very effective p- refinement procedures. Due to the nature of the HMS formulation, it is possible to consider the use of both inverse and direct integration schemes at the cross-section level. The time integration procedure uses classical step-by-step techniques, such as Newmark and α-HHT method. The latter is used in order to supress some numerical noise that may occur in the iterative procedure involved in the solution of dynamic non-linear problems. Three different types of damage models, with and without permanent strains, are used to model concrete behaviour. To validate the model, to illustrate its potential and to assess its accuracy and efficiency, several numerical examples are discussed, and comparisons are made with solutions provided by other numerical techniques.

This paper presents a numerical study on the mesh dependency of the Hashin Damage Model for 2D finite element simulations of orthotropic materials. The main objective is to study and assess the efficiency of energy regularization in preventing mesh dependency in orthotropic damage models. Initially, the thermodynamic laws used to validate a damage model are presented and applied to the specific Hashin damage model. An extensive parametric study is performed using various types of finite elements: with structured and squared-structured meshes; with linear and quadratic approximations; and with full and reduced integration schemes. To verify the mesh dependency, the results of a compact tension experimental test of glass fibre reinforced plastic (GFRP) material are compared to the numerical results; some conclusions are drawn regarding the force vs. displacement behaviour, with and without regular meshes.

A hybrid-mixed finite element model for the analysis of 3D structures is presented.Independent approximation of stress, strain and displacement fields.Legendre polynomials are used to define the approximation bases.Use of effective p-refinement procedures.Use of distinct approaches for the parallel solution of the global governing system. This paper reports the parallel implementation of a hybrid-mixed stress finite element model for the analysis of three-dimensional structures. The stress and the displacement fields in the domain and the displacement fields on the static boundary are independently approximated. All field equations are imposed in a weighted residual form and Legendre polynomials are used to define the approximation bases. The parallel implementation of the model uses a message passing scheme based on the MPI standard. For the parallel solution of the governing system, two distinct approaches are tested. The first corresponds to the use of a third-party parallel direct solver code, named MUMPS. The second uses an in-house developed hybrid solver inspired by the FETI method and designed to deal with the typical pattern of the hybrid-mixed stress model governing system. Some numerical examples are discussed to illustrate the effectiveness and performance of the adopted parallel approach.

This paper presents a new constitutive model for the simulation of reinforcing steel bars used in common reinforced concrete structures and it is designed to be used for general loading cases. The model includes the well-known Guiffre–Menegotto–Pinto softened branch, although new expressions are proposed for the evolutions of the curvature-related parameter and of the yield surface. The constitutive relation is enhanced with an innovative and simplified proposal for considering ultra-low-cycle fatigue effects. This phenomenon is particularly important for structures that undergo a small number of very large displacement cycles, e.g. when subjected to intense seismic events. It is known that in those situations the steel reinforcements experience a continuum and significant strength decrease that ultimately leads to premature failure induced by fatigue. The model’s mathematical description and some relevant implementation issues are described. Its accuracy is assessed by means of a series of validation tests using experimental data available in the bibliography.

A new hybrid-mixed stress finite element model for the static and dynamic non-linear analysis of concrete structures is presented and discussed in this paper. The main feature of this model is the simultaneous and independent approximation of the stress, the strain and the displacement fields in the domain of each element. The displacements along the static boundary, which is considered to include inter-element boundaries, are also directly approximated. To define the approximation bases in the space domain, complete sets of orthonormal Legendre polynomials are used. The adoption of these functions enables the use of analytical closed form solutions for the computation of all linear structural operators and leads to the development of very effective p-refinement procedures. To represent the material quasi-brittle behaviour, a physically non-linear model is considered by using damage mechanics. A simple isotropic damage model is adopted and to control strain localisation problems a non-local integral formulation is considered. To solve the dynamic non-linear governing system, a time integration procedure based on the use of the @a-HHT method is used. For each time step, the solution of the non-linear governing system is achieved using an iterative algorithm based on a secant method. The model being discussed is applied to the solution of two-dimensional structures. To validate the model, to illustrate its potential and to assess its accuracy and numerical efficiency, several numerical examples are discussed and comparisons are made with solutions provided by experimental tests and with other numerical results obtained using conventional finite elements (CFE).

This paper presents a new hybrid-mixed stress finite element model for the static analysis of concrete structures. A non-linear behaviour at the material level is assumed and to model the material’s quasi-brittle behaviour damage mechanics is considered. In this model, the stress, the strain and the displacement fields are independently approximated in the domain of each element. The displacements along the static boundary, which is considered to include inter-element boundaries, are also directly approximated. Complete sets of orthonormal Legendre polynomials are used to define all approximation bases required by the finite element model. The adoption of these functions enables the use of analytical closed form solutions for the computation of all linear structural operators and leads to the development of very effective p -refinement procedures. A simple isotropic damage model is adopted and to control strain localization problems a non-local integral formulation is considered. The model being discussed is applied to the solution of two-dimensional structures. To validate the model, to illustrate its potential and to assess its accuracy and numerical efficiency, several numerical examples are discussed and comparisons are made with solutions provided by experimental tests and with other numerical results obtained using conventional finite elements.

This paper introduces an original model to simulate the bond failure between concrete and reinforcing steel bars. The model was developed to be used in threedimensional analyses within the framework of the Finite Element Method and for general loading cases. It was designed using a hierarchical approach by combining what is called the base model, which acts as the skeleton of the model and introduces the basic response under monotonic and reversed loading, and four independent and optional sub-models used to enhance the simulation when needed, by considering the cyclic resistance degradation, the peak stress slip evolution, the reload slip evolution and the radial stress effect. The model implementation within the framework of the Finite Element Method is described and its accuracy is assessed using a series of validation tests. At the end, the main conclusions extracted from this work are presented.

The purpose of this work is to study the influence that the construction stage has on the distribution of stresses and strains in solid slabs. To that purpose, a numerical simulation framework for thermomechanical analysis has been implemented and deployed, with due account to the evolution of concrete properties at early ages. This framework was then used to simulate the behaviour of several alternative procedures to define the shoring system and scheduling that can be adopted in the construction phase, with the aim of identifying the best practices to control and reduce the residual stresses attained during the construction stage, which may in turn be responsible for less-than-optimum cracking behaviour in service. The results obtained confirmed that, for the particular case under study, delaying the shoring removal until concrete has reached its 28-day characteristic strength corresponds in fact to the best practice as it reduces the stresses and prevents cracking of the slab in the first 28 days. However, it was also seen that other more ambitious practices, leading to an early withdrawal of the shoring (before 28 days), are also perfectly acceptable in terms of stresses and deformations in the slab under study. Only in premature withdrawal schemes (before 7 days) the likelihood of early cracking is more significant, and so these situations can in fact demand a sophisticated study of stress history to adequately take into account the influence of the initial stresses on the service life behaviour of the slab., The authors gratefully acknowledge the support of the CERISICIST Research Institute, IST, University of Lisbon and the FCT (Foundation for Science and Technology). Funding provided by the Portuguese Foundation for Science and Technology (FCT) and COMPETE2020 to the Research Project PTDC/ECM-EST/1056/2014 (POCI-01-0145-FEDER-016841), as well to the Research Unit ISISE (POCI-01-0145-FEDER-007633) are gratefully acknowledged., info:eu-repo/semantics/publishedVersion

This paper presents a new approach to perform incremental dynamic analyses on reinforced concrete buildings using the so-called hybrid discretizations, taking advantage of parallelized computations and domain decomposition techniques to enhance the capability and performance for the analysis of large-scale problems. The concept of hybrid discretization consists in the combination of different modelling approaches for the three-dimensional structural elements. Where most of the non-linear phenomena are expected to occur, refined meshes and more complex constitutive relations are adopted. Elsewhere, simplified structural models are considered. Special attention is devoted to the definition of adequate techniques to treat the transition zones between different structural models. The efficiency and accuracy of alternative kinematic constraint techniques are studied and assessed. The paper ends with two validation examples that test the accuracy and the computational performance of the proposed methodology.

This paper presents and discusses a hybrid-mixed stress finite element model for the dynamic analysis of structures, assuming a physically and geometrically linear behavior. In this model, both the stress and the displacement fields are approximated in the domain of each element. The displacements along the static boundary are also independently approximated. Orthonormal Legendre polynomials are used as approximation functions. The use of these functions enables the use of analytical closed form solutions for the computation of all structural operators and leads to the development of very effective p-refinement procedures. The linear dynamic analysis is performed using time integration procedures. For this purpose, the classical Newmark, [email protected] and @a-HHT methods are implemented and tested. A recent and promising alternative approach, based on the definition of a mixed approximation in the time domain is also implemented and assessed. The model being discussed is applied to the solution of plane elasticity and Reissner-Mindlin plate bending problems. To validate the model, to illustrate its potential and to assess its accuracy and efficiency, several numerical examples are discussed and comparisons are made with analytical solutions and solutions provided by other numerical techniques.

This paper presents and discusses a hybrid-mixed stress finite element model based on the use of polynomial wavelets for the physically non-linear analysis of concrete structures. The effective stress and the displacement fields in the domain of each element and the displacements on the static boundary are independently approximated. As none of the fundamental equations is locally enforced a priori, the hybrid-mixed stress formulation enables the use of a wide range of functions. In the numerical model reported here, all approximations are defined using complete sets of polynomial wavelets. These bases present some important features. In one hand, the functions are orthogonal, which is an important issue when implementing hybrid-mixed stress elements as it ensures high levels of sparsity. On the other hand, the polynomial wavelet basis is defined through linear combinations of Legendre polynomials. This fact enables the use of closed-form solutions for the computation of the integrations involved in the definition of all linear structural operators. A simple isotropic damage model is adopted and a non-local integral formulation where the strain energy release rate is taken as the non-local variable is considered. The numerical model is both incremental and iterative and is solved with a modified Newton-Raphson method that uses the secant matrix. Classical benchmark tests are chosen to illustrate the use of the model under discussion and to assess its numerical performance.

The design of concrete structures reinforced with glass fibre reinforced polymer (GFRP) bars is influenced by their reduced stiffness and brittleness. In hyperstatic structures, the methodology used in force analysis depends on the ductility of the structural systems, which in this case, being essentially provided by the concrete, can be potentially increased by confining concrete in critical zones. This paper presents experimental and numerical investigations about the flexural behaviour of continuous beams reinforced with GFRP bars, namely of their service and failure responses, and the effect of increasing concrete confinement in critical cross-sections. A calculation procedure to quantify the confinement effect in beams due to the reduction of the spacing between shear stirrups is first presented. The experimental investigations comprised a comparative study in which two-span concrete beams reinforced with either GFRP or steel bars were tested in bending. In the former, the effect of reducing the shear stirrups spacing was analyzed together with the under- and over-reinforcement at the central support and midspan cross-sections, respectively. The development of a crack hinge in the continuity support zone highlighted the better performance of beams under-reinforced on the top layer with GFRP bars compared to “equivalent” beams reinforced with steel, namely at the resistance level. In addition, the confinement at critical zones increased significantly the strength and ductility. The numerical investigations included the development of non-linear finite element models for all beams tested – numerical results are in good agreement with test data and seem to confirm the confinement effect observed in the experiments.

This paper addresses, for the first time, the buckling analysis of isotropic and laminated plates that are subjected to partial inplane edge loads by a first-order shear deformation theory. The numerical approach is based on collocation with wavelets. It is shown that the present method produces highly accurate critical loads and modes.

In recent years, some research effort has been devoted to the development of non-conventional finite element models for the analysis of concrete structures. These models use continuum damage mechanics to represent the physically non-linear behavior of this quasi-brittle material. Two alternative approaches proved to be robust and computationally competitive when compared with the classical displacement finite element implementations. The first corresponds to the hybrid–mixed stress model where both the effective stress and the displacement fields are independently modeled in the domain of each finite element and the displacements are approximated along the static boundary, which is considered to include the inter-element edges. The second approach corresponds to a hybrid–displacement model. In this case, the displacements in the domain of each element and the tractions along the kinematic boundary are independently approximated. Since it is a displacement model, the inter-element boundaries are now included in the kinematic boundary. In both models, complete sets of orthonormal Legendre polynomials are used to define all approximations required, so very effective p-refinement procedures can be implemented. This paper illustrates the numerical performance of these two alternative approaches and compares their efficiency and accuracy with the classical finite element models. For this purpose, a set of numerical tests is presented and discussed.

The most relevant aspects involved in the implementation of the stress model of the hybrid-mixed finite element formulation are presented and discussed. In this formulation, the stress and displacement fields in the domain of the element and the displacements on the boundary are simultaneously approximated. Digital Walsh functions are used in all three approximations. Due to the special properties of these functions, it is possible to obtain closed form solutions for the integrals involved in the computation of the structural operators. The governing system is usually very large in dimension, but also well structured and highly sparse. Consequently, the use of adequate algorithms to store and manipulate sparse matrices is essential to ensure the numerical efficiency of the model. The direct and iterative methods most used in the solution of large, sparse systems of linear equations are tested and assessed. Fast transform algorithms are used in the post-processing phase to perform the linear combinations of digital Walsh functions needed to construct the stress and displacement fields from their direct approximations. Linear elastostatic problems are used to illustrate the implementation of the Walsh-based hybrid-mixed stress elements.

A hybrid-mixed stress finite element formulation for the elastoplastic analysis of stretching plates is presented. This model is characterized by the simultaneous and independent approximation of both the stress and the displacement fields in the domain and of the displacement field on the static boundary. To model the local phenomena associated with plasticity, the plastic parameter increments are also directly approximated. The plastic flow and the kinematic boundary conditions are locally satisfied. The remaining fundamental equations are enforced in a weighted residual form so designed as to ensure that the discrete model presents all relevant properties of the continuous system, namely the static-kinematic duality, elastic reciprocity and associated plasticity. The orthogonal Legendre polynomials are used as approximation functions for the stress and the displacements fields. Dirac functions and non-negative polynomial functions are used to model the plastic parameter increments. The model presented here assumes a quasi-static and geometrically linear response. The elastoplastic constitutive relations are uncoupled into elastic and plastic deformation modes and both the Von Mises and the Drucker-Prager yield criteria have been implemented. The non-linear governing system is solved using the Newton-Raphson method. To validate the hybrid-mixed stress model and to assess its performance and accuracy, a set of numerical test cases is presented and discussed.

This paper reports the use of polynomial wavelets as approximation functions in hybrid-mixed stress finite element models applied to the solution of plane elasticity problems. The stress and displacement fields in the domain and the displacements on the static boundary are independently approximated. The kinematic boundary conditions are locally satisfied. All remaining equations are enforced in a weighted residual form so designed as to ensure that the discrete model embodies the relevant properties of continuum systems, namely the static-kinematic duality and elastic reciprocity. A set of numerical applications is presented to illustrate the use of the hybrid-mixed model and to assess its efficiency and accuracy. Copyright © 2009 John Wiley & Sons, Ltd.

This paper reports on the nonlinear static analysis of 2D concrete structures using a non-conventional finite element formulation. The nonlinear behavior of the material is modelled with a continuum non-local and isotropic damage model. While the material's behavior is linear elastic, a pure hybrid-displacement Trefftz formulation is adopted. From the point where the concrete assumes a nonlinear behavior, this approach degenerates into a hybrid-displacement formulation. The computational performance is tested by means of two numerical examples which show that the proposed model predicts correctly the global behavior of the structures.

Invasive ductal carcinoma (IDC) is the most common histological type of breast cancer, accounting for up to 85% of all invasive breast carcinomas.1 In IDC, the most common areas of solitary metastasis are lung, liver, brain and bone. In a study published by Borst and Ingold,2 referring to the metastatic patterns of breast cancer in a group of 2246 patients with ICD, no one presented with adrenal metastasis. Adrenal metastases of breast cancer are usually associated with invasive lobular carcinoma (ILC), most …

This communication reports on the nonlinear analysis of 2D concrete structures using an hybrid-mixed stress formulation and continuum damage mechanics. The finite element model adopted is based on the direct and independent approximation of three fields: the stress and displacement fields in the domain of each element and the displacement field on the static boundary. The nonlinear behavior of the material is modelled using both a local and nonlocal isotropic damage model. Two numerical examples are presented to illustrate and validate the use of such numerical technique.

The objective of this paper is to present the application of wavelets in the implementation of the stress model of the hybrid-mixed finite element formulation. Independent wavelet bases are used to approximate the stresses in the domain and the displacements both in the domain and on the boundary of elastostatic finite elements. Except for the kinematic boundary conditions, which are enforced directly, all the remaining equations of elastostatics are enforced in a weighted residual form so designed as to ensure that the discrete model embodies the relevant properties of the continuum fields they represent, namely static-kinematic duality and elastic reciprocity. Numerical examples are used to illustrate the characteristics of the numerical model being presented and to assess its accuracy and efficiency.

The static deformations and the natural frequencies of doubly-curved composite shells are computed by the first-order theory of Donnell. A meshless method based on wavelet collocation is used for discretization of the equations of motion and the boundary conditions. Several examples demonstrate the high accuracy of the present method in the prediction of the static deformations and the natural frequencies.

A study of bending deformations of sandwich plates using a layerwise theory of laminated or sandwich plates is presented. The analysis is based on a wavelet collocation technique to produce highly accurate results. Numerical results for symmetric laminated composite and sandwich plates are presented and discussed.

A study of static deformations and free vibrations of shear flexible isotropic and laminated composite plates with a first-order shear deformation theory is presented. The analysis is based on collocation with a Deslaurier Dubuc interpolating basis to produce highly accurate results. Numerical results for isotropic and symmetric laminated composite plates are presented and discussed for various thickness-to-length ratios. The high order collocation method presented in this paper proved to be very accurate for this type of problems and the numerical efficiency is as good as other numerical schemes for first-order shear deformation theories, such as finite element solutions.

The conforming displacement elements are nowadays dominant in standard finite element applications. Nevertheless, they present some known limitations, particulary in what concerns accuracy and safety in stress estimates. With computational development and the motivation to model increasingly more complex structural problems, several alternative numerical techniques have been proposed to substitute or complement the tradicional displacement formulation, e.g. the boundary elements, meshless models and hybrid and mixed formulations. The hybrid and mixed finite element formulations adopted in this work [2] are developed from first-principles of Mechanics, namely, equilibrium, compatibility and constitutive relations. Recently, these formulations have been tested with continuum damage models in order to correctly simulate the behavior of softening materials such as concrete [3], [5], [6], [4]. The most promising formulations are the hybrid-mixed stress formulation, with an independent approximation of the effective stress field instead of an approximation of the stress filed [6], and the hybrid displacement formulation [4].

This paper discusses three hybrid-displacement finite element formulations for the simulation of strain localization based on nonlocal damage theory. An isotropic integral nonlocal damage model is chosen. The hybrid finite element formulations adopted in this work are developed from first principles of Mechanics. The first one defines the domain approximations using the Trefftz functions derived for the linear elastic regime. When damage appears the hybrid-Trefftz displacement formulation degenerates into an hybrid-displacement formulation. The second formulation uses an enriched Trefftz basis with the consideration of local Heaviside functions. The third formulation uses orthonormal Legendre polynomials for the domain approximations. A set of benchmark tests is presented and discussed in order to compare the performance and accuracy of the different models. It is shown that the proposed hybrid-Trefftz formulation allows the reproduction of the general behavior of the structure but does not lead to a correct simulation of the strain tensor evolution. The hybrid-displacement formulation that uses orthonormal Legendre polynomials gives coherent results, so it appears to be a promising field of investigation.