Latin American Journal of Solids and Structures

Published by SciELO


Creating wave-focusing materials
  • Conference Paper

October 2008


30 Reads

Basic ideas for creating wave-focusing materials by injecting small particles in a given material are described. The number of small particles to be injected around any point is calculated. Inverse scattering problem with fixed wavenumber and fixed incident direction of the plane acoustic wave is formulated and solved.

Creating Wave-Focusing Materials

June 2008


22 Reads

Basic ideas for creating wave-focusing materials by injecting small particles in a given material are described. The number of small particles to be injected around any point is calculated. Inverse scattering problem with fixed wavenumber and fixed incident direction of the plane acoustic wave is formulated and solved.

Figure 2: Comparison of experimental data for central deflection with the response of nonlinear finite element model of laminated glass plate with the PVB shear modulus 400 kPa or 689.5 kPa 
Figure 3: Comparison of experimental data for maximum principal stress at the center of the bottom surface of the bottom layer (left) and for minimum principal stress at the center of the top surface of the top layer (right) with the response of nonlinear finite element model of laminated glass plate with the PVB shear modulus 400 or 689.5 kPa. The two extreme principal stresses in two orthogonal directions should coincide at the center of the individual surfaces, because of square geometry of the unit. Therefore, two sets of experimental data appear in each graph. Latin American Journal of Solids and Structures 12 (2015) 1158-1181
Figure 9: Comparison of maximum deflection and stress at the center of the simply supported plate obtained by semi-analytical solution (AM) and geometrical linear and nonlinear finite element model (FEM).
Finite element model based on refined plate theories for laminated glass units
  • Article
  • Full-text available

May 2015


303 Reads

Laminated glass units exhibit complex response as a result of different mechanical behavior and properties of glass and polymer foil. We aim to develop a finite element model for elastic laminated glass plates based on the refined plate theory by Mau. For a geometrically nonlinear description of the behavior of units, each layer behaves according to the Reissner-Mindlin kinematics, complemented with membrane effects and the von K\'{a}rm\'{a}n assumptions. Nodal Lagrange multipliers enforce the compatibility of independent layers in this approach. We have derived the discretized model by the energy-minimization arguments, assuming that the unknown fields are approximated by bi-linear functions at the element level, and solved the resulting system by the Newton method with consistent linearization. We have demonstrated through verification and validation examples that the proposed formulation is reliable and accurately reproduces the behavior of laminated glass units. This study represents a first step to the development of a comprehensive, mechanics-based model for laminated glass systems that is suitable for implementation in common engineering finite element solvers.

An adaptive continuum/discrete crack approach for meshfree particle methods

June 2003


76 Reads

A coupled continuum/discrete crack model for strain softening materials is implemented in a meshfree particle code. A coupled damage plasticity constitutive law is applied until a certain strain based threshold value - this is at the maximum tensile stress of the equivalent uniaxial stress strain curve - is reached. At this point a discrete crack is introduced and described as an internal boundary with a traction crack opening relation. Within the frame-work of meshfree particle methods it is possible to model the transition from the continuum to the discrete crack since boundaries and particles can easily be added and removed. The EFG method and an explicit time integration scheme is used. The integrals are evaluated by nodal integration, an integration with stress points and also a full Gauss quadrature. Some results are compared to experimental data and show good agreement. Additional comparisons are made to a pure continuum constitutive law.

Figure 2: Dimensionless density of cracks vs. dimensionless time for three different Weibull moduli m when n = 3.
Figure 3: Tensile strength normalized by σ w vs. stress rate normalized by • σ t. The dots and error bars represent results obtained by Monte-Carlo simulations (500 realizations/point) and their standard deviation when m = 9.5 and n = 3. The curves are obtained by using Eqns. (13) and (15).
Figure 5: One quarter of an edge-on impact configuration with dynamic confinement.
Probabilistic-deterministic transition involved in a fragmentation process of brittle materials: Application to a high performance concrete

January 2005


103 Reads

Dynamic loadings produce high stress waves leading to the fragmentation of brittle materials such as ceramics, concrete, glass and rocks. The main mechanism used to explain the change of the number of fragments with the stress rate is a shielding phenomenon. However, under quasi static loading conditions, a weakest link hypothesis may be applicable. Therefore, depending on the local strain or stress rate, different fragmentation regimes are observed. One regime corresponds to single fragmentation for which a probabilistic approach is needed. Conversely, the multiple fragmentation regime may be described by a deterministic approach. The transition between the two fragmentation regimes is discussed. A damage model describing dynamic fragmentation is applied to a high performance concrete.

Figure 1: Main features of Langmuir circulations observed at surface layers of natural ecosystems. From [21].  
Table 1 : Main features of laboratory flows considered in simulations.
Three-dimensional Langmuir circulations and enhanced turbulence in upper mixed ocean layers

January 2005


107 Reads

Field and laboratory data confirm the presence of longitudinal billows in fluid flow under wind-wavy surfaces. In the ocean these vortices (called Langmuir cells) act by mixing nutrients and other biological material, and thus their role cannot be neglected in vertical transfer modelling. In this work non-dimensional mean velocity field equations are formulated with Craik & Leibovich theory including interaction terms between surface wave Stokes drift and mean current. A first order turbulence closure model (k,) is used to model the Reynolds stress tensor. The model is formulated in non-dimensional grounds, and numerical experiments are performed using a finit-volume technique. In the first set of simulations, model outputs are compared to measurements obtained at three different laboratory wind-water facilities (Cheung & Street, 1988; Thais & Magnaudet, 1996). Results suggest that the presence of secondary motions is necessary for explaining the observed channel flows. A second group of simulations involves field situations, when numerical results are compared to some typical environmental cases (Kitaigorodskii et al., 1983). Model results for this second group of experiments show ε()22*10Oukˆ= (k is the surface turbulent kinetic energy, and is the water friction velocity), representing the same order of magnitude currently found in situ for turbulence.

Formability of aluminum 1050A at high temperatures: Numerical modeling and experimental validation

August 2021


76 Reads

The sheet metals are prone to large plastic deformation during forming processes. The study purpose is to investigate 1050A aluminum sheets thermomechanical behavior with ductile damage. A modified Swift model coupled to isotropic ductile damage and thermal effects was used. The forming parameters are introduced using Swift model coefficients and Erichsen index. An inverse identification procedure is applied to nonhomogeneous Erichsen test results. Bulge test is then used to validate the identified parameters. Erichsen test (Punch force vs displacement) results were obtained by experimental testing and simulation to build the objective function. Aluminum 1050A plasticity flow parameters and ductile damage variables were identified using a part of Erichsen test results. The remaining part of Erichsen test and bulge test results were used for validation. The numerical approach allowed the detection of failure zones with respect to thermal gradient induced by heat exchange. Within the isothermal condition, equivalent stresses and strains for 1050A Aluminum were obtained by simulations and experimental data.

A mixed 3D-1D finite element formulation for analysis of geomaterial structures with embedded curvilinear inclusions: application to load transfer in mooring anchor systems

August 2018


245 Reads

A finite element model for structural analysis of media with embedded inclusions is presented. The “embedded element concept” is adopted to model the contact interaction of two medium components along the contact interface considering a mixed 3D-1D formulation. The Mohr-Coulomb interface model is employed to define the bond-stress and bond-slip relation and strains associated with bond-slip are assumed to remain infinitesimal along the interface. Nonlinear analysis is performed with a corotational kinematics description introduced in the context of embedded approach. The problem of load transfer in mooring anchor systems was investigated and reasonable results were obtained using the present model.

Preface to the special issue of the International Symposium on Solid Mechanics (MecSol 2017)

October 2018


135 Reads

The International Symposium on Solid Mechanics (MecSol) is a biennial conference which aims to provide a forum to discuss relevant issues associated with solid mechanics. The MecSol 2017 edition was held in the city of Joinville, Brazil, on 26-28 April 2017. Plenary lectures were delivered by researchers from five different countries. The main topics discussed in the conference are as follows: composite materials, optimization, constitutive modelling, fatigue, impact, nonlinear analyses, structural reliability, X-FEM, G-FEM, and BEM numerical methods. The participants were invited to submit full papers, which, after peer review, compound this special issue of the Latin American Journal of Solids and Structures. This article highlights the main topics addressed in the conference. © 2018, Brazilian Association of Computational Mechanics. All rights reserved.

Figure 4: Comparison of the yield stress directionality for Al 2090-T3: (a) uniaxial tensile yield stress; and (b) uniaxial compressive yield stress.
Figure 5: Comparison of the R-value directionality for Al 2008-T4.
Combination of Modified Yld2000-2d and Yld2000-2d in Anisotropic Pressure Dependent Sheet Metals

January 2015


754 Reads

In the current research to model anisotropic asymmetric sheet metals a new non-AFR criterion is presented. In the new model, Modified Yld2000-2d proposed by Lou et al. (2013) is considered as yield function and Yld2000-2d proposed by Barlat et al. (2003) is considered as plastic potential function. To calíbrate the presen-ted criterion, the yield function which is a pressure dependent criterion requiers ten directional yield stresses such as uniaxial tensile stresses in three directions of 0°, 45°, 90°, uniaxial com-pressive yield stresses in six directions of 0°, 15°, 30°, 45°, 75°, 90° from the rolling direction along with biaxial yield stress. Mo-reover, the plastic potential function which is a pressure indepe-dent criterion needs eight experimental data points such as tensile R-values in seven directions of 0°, 15°, 30°, 45°, 60°, 75°, 90° from the rolling direction and also biaxial tensile R-value. Finally with comparing the obtained results with experimental data points, it is shown that the presented non-AFR criterion predicts compressive yield stress, biaxial tensile yield stress and R-values more accura-tely than Modified Yld2000-2d and it would be considered as a new criterion for anisotropic asymmetric metals. © 2014 Brazilian Association of Computational Mechanics. All rights reserved.

2D Problem for a Long Cylinder in the Fractional Theory of Thermoelasticity

August 2016


64 Reads

In this manuscript, we solve an asymmetric 2D problem for a long cylinder. The surface is assumed to be traction free and subjected to an asymmetric temperature distribution. A direct approach is used to solve the problem in the Laplace transformed domain. A numerical method is used to invert the Laplace transforms. Graphically results are given and discussed. © 2016, Brazilian Association of Computational Mechanics. All rights reserved.

An enriched meshless finite volume method for the modeling of material discontinuity problems in 2D elasticity

April 2018


391 Reads

A 2D formulation for incorporating material discontinuities into the meshless finite volume method is proposed. In the proposed formulation, the moving least squares approximation space is enriched by local continuous functions that contain discontinuity in the first derivative at the location of the material interfaces. The formulation utilizes space-filling Voronoi-shaped finite volumes in order to more intelligently model irregular geometries. Numerical experiments for elastostatic problems in heterogeneous media are presented. The results are compared with the corresponding solutions obtained using the standard meshless finite volume method and element free Galerkin method in order to highlight the improvements achieved by the proposed formulation. It is demonstrated that the enriched meshless finite volume method could alleviate the expecting oscillations in derivative fields around the material discontinuities. The results have revealed the potential of the proposed method in studying the mechanics of heterogeneous media with complex micro-structures.

Isogeometric analysis applied to 2D Bernoulli-Euler beam model: imposition of constraints by Lagrange and Penalty methods

January 2020


308 Reads

The isogeometric analysis (IGA) consists of using the same shape functions, usually employed on Computer-Aided Design (CAD) technologies, on both geometric modelling and approximation of the fields of physical models. One issue that concerns IGA is how to make the connection or apply general constraints in the connection of structures described by different curves and surfaces (multi-patch structures), particularly when the shape functions are not interpolatory at the selected point for the imposition of the constraint or the desired constraint is not related directly to degrees of freedom, which may be an issue on Kirchhoff-Love shells and Euler-Bernoulli beams, since usually no rotational degrees of freedom are employed. In this context, the present contribution presents an isogeometric 2D curved beam formulation based on Bernoulli-Euler assumptions. An approach about the implementation of multi-patch structures enforcing constraints, such as same displacement or same rotation among neighbor paths, is developed based on Penalty and Lagrange methods. The applicability of the methods is verified by examples of application.

Fiber-matrix Contact Stress Analysis for Elastic 2D Composite Solids

March 2015


91 Reads

This paper presents a finite element formulation for the analysis of two dimensional reinforced elastic solids developing both small and large deformations without increasing the number of degrees of freedom. Fibers are spread inside the domain without the necessity of node coincidence. Contact stress analysis is carried out for both straight and curved elements via two different strategies. The first employs consistent differential relations and the second adopts a simple average calculation. The development of all equations is described along the paper. Numerical examples are employed to demonstrate the behavior of the proposed methodology and to compare the contact stress results for both calculations. © 2015, Brazilian Association of Computational Mechanics. All rights reserved.

Table 2 .
2D analysis of laminated composite and sandwich plates using a new fifth-order plate theory

September 2018


523 Reads

In the present paper, a new fifth-order shear and normal deformation theory (FOSNDT) is developed for the bi-directional bending analysis of laminated composite and sandwich plates subjected to transverse loads. This theory considered the effects of both transverse shear and normal deformations. In-plane displacements use a polynomial shape function expanded up to fifth-order in terms of the thickness coordinate to properly account the effect of transverse shear deformation. Transverse displacement is the function of x, y and z-coordinates to account the effect of transverse normal deformations i.e. thickness stretching. Hence, the present theory involves nine unknowns in the displacement field. The present theory does not require a problem dependent shear correction factor as it satisfies traction free boundary conditions at top and bottom surfaces of the plate. The governing differential equations and associated boundary conditions are obtained using the principle of virtual work. The plate is analysed for simply supported boundary conditions using Navier’s solution technique. To prove the efficiency of the present theory, the non-dimensional displacements and stresses obtained for laminated composite and sandwich plates are compared with existing exact elasticity solutions and other theories. It is observed from the comparision that the displacements and stresses obtained by the present theory are in excellent agreement with the results obtained by exact elasticity solutions compared to other higher-order plate theories available in the literature. © 2018, Brazilian Association of Computational Mechanics. All rights reserved.

2D moving element method for random vibration analysis of vehicles on Kirchhoff plate with Kelvin foundation

June 2009


253 Reads

W T Xu


J H Lin





F W Williams
Vehicle-pavement coupling systems may produce random vibration due to the road surface unevenness. In this paper, a Kirchhoff plate with Kelvin foundation is employed to model the pavement system and the one-dimensional moving element method proposed by Koh et al. is extended to deal with the random vibration of two-dimensional vehicle-pavement coupling systems. The plate element stiffness matrix is formulated in a coordinate system which moves with the load and the equation of motion of the coupled system is established. The pseudo excitation method is used to analyze random vibration of the coupled system and the influences on the responses both of the vehicle velocity and of the pavement damping are investigated by using numerical examples. Hence useful conclusions are drawn.

Figure 4: Work to fracture vs. location of the HAZ relative to the notch, as measured by the parameter x 2 c , for two different materials. (From [16], but with the work of fracture multiplied by a factor of two to correct an error in [16] in calculating the work from the force-deflection curve). 
Figure 5: Evolution of the maximum principal stress with applied displacement for various values of the specimen thickness. C 0 is the thickness of the standard Charpy specimen. The weld configuration is that shown in Fig. 2b and the initial temperature is −80 o C. (From [17]). 
Figure 6: Work to fracture versus the location of the HAZ for a specimen with the notched surface rotated 90 o from the surface of the welded piece. The notch location is measured by x 3c and the temperature is Θ init = 0 o C. (From [18]). 
Figure 4 of 4
Weld investigations by 3D analyses of Charpy V-notch specimens

March 2005


166 Reads

The Charpy impact test is a standard procedure for determining the ductile-brittle transition in welds. The predictions of such tests have been investigated by full three dimensional transient analyses of Charpy V-notch specimens. The material response is characterised by an elastic-viscoplastic constitutive relation for a porous plastic solid, accounting for adiabatic heating due to plastic dissipation and the resulting thermal softening. The onset of cleavage is taken to occur when the average of the maximum principal stress over a specified volume attains a critical value. Typically, the material parameters in the weld material differ from those in the base material, and the heat affected zone (HAZ) tends to be more brittle than the other material regions. The effect of weld strength undermatch or overmatch is an important issue. Some specimens, for which the notched surface is rotated relative to the surface of the test piece, have so complex geometry that only a full 3D analysis is able to account for the interaction of failure in the three different material regions, whereas other specimens can be approximated in terms of a planar analysis.

Figure 1 
Figure 2 
Figure 4 A comparison between through-the-thickness distributions of the lateral deflection of the central section of the homogeneous skew plate predicted by present results and ANSYS Workbench software
Dynamic and Static analysis of FGM Skew plates with 3D Elasticity based Graded Finite element Modeling

May 2014


335 Reads

The present article deals with static and dynamic behavior of functionally graded skew plates based on the three–dimensional theory of elasticity. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the equations of motion are derived in conjunction with the graded finite element approach. Solution of the resulted system of equations in time domain is carried out via Newmark's time integration method. Calculations are applied for fully clamped boundary condition. In the present paper, two different sets of distributions for material properties are considered. For the static analysis, material properties are considered to vary through the thickness direction according to an exponential law. In the case of dynamic analysis, variations of the volume fractions through the thickness are assumed to obey a power law function. Thus, the effective material properties at each point are determined by the Mori–Tanaka scheme. In case of dynamic analysis, the results are obtained for uniform step loadings. The effects of material gradient index and skew angle on displacement components and stress response are studied. Results of present formulations are verified by available results of a functionally graded rectangular plate for different boundary conditions and also compared with result of a homogenous skew plate by commercial FEM software.

3D Characterization of Mixed-Mode Fracture Toughness of Materials Using a New Loading Device

August 2016


1,749 Reads

In this paper, a new loading device was employed to conduct a mixed-mode fracture test. Therefore, disadvantages detected in the previous mixed-mode fracture toughness test methods can be avoided. The new fixture has perfect symmetry which provides a uniform stress state, creates the pure plane strain conditions and eliminates the unwanted mode-III loading conditions. The values of non-dimensional stress intensity factors for pure mode-I, pure mode-II, and pure mode-III were obtained using 3D models of new loading device and modified Arcan method in order to compare the results and investigate the variation of fracture parameters. Furthermore, the values of correction factors for pure mode-III in various loading angles were studied for both fixtures and it was resulted that in modified Arcan device there was a larger contribution of unwanted third mode loading conditions and therefore the values of mode-I and mode-II non-dimensional stress intensity factors were affected. In the present study, in order to compare the results, the fracture toughness values of ABS (Acrylonitrile butadiene styrene) polymeric material were determined experimentally for both fixtures and a full range of mixed-mode loading conditions including pure mode-I and pure mode-II loading were created and tested. The differences in critical stress intensity factors of the fixtures were found about 7.00% and 42.65% in mode-I and mode-II loading conditions, respectively. © 2016, Brazilian Association of Computational Mechanics. All rights reserved.

Structural shape optimization of 3D nearly-incompressible hyperelasticity problems

June 2008


57 Reads

This paper presents shape optimization of nearly incompressible hyperelastic structural problems. Initially, the Mooney-Rivlin hyperelastic model is reviewed. The finite element solution using a perturbed Lagrangian description and the Newton-Raphson method are discussed. The projected pressure method is used to solve the mixed problem using a standard one-field finite element procedure. The expressions of shape sensitivity are presented. Finally, the shape optimization of an engine mount geometry is considered using 2D and 3D finite element models.

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