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.
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.
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.
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.
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.
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.
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 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.
This special issue contains selected papers first presented in a short format at the Congress CILAMCE 2018 (39th Ibero-Latin American Congress on Computational Methods in Engineering) held in Paris and in Compiègne, France, from 11 to 14 November 2018.
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.
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.
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.
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.
The present article deals with static and dynamic behavior of functionally graded skew plates based on the threedimensional 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 MoriTanaka 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.
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.
![Figure 1: Main features of Langmuir circulations observed at surface layers of natural ecosystems. From [21].](https://www.researchgate.net/profile/Philippe-Maurel-2/publication/27333992/figure/fig1/AS:340345909989388@1458156196300/Main-features-of-Langmuir-circulations-observed-at-surface-layers-of-natural-ecosystems_Q320.jpg)
![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).](https://www.researchgate.net/profile/Alan-Needleman/publication/277099291/figure/fig1/AS:649320713945088@1531821530350/Work-to-fracture-vs-location-of-the-HAZ-relative-to-the-notch-as-measured-by-the_Q320.jpg)
![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]).](https://www.researchgate.net/profile/Alan-Needleman/publication/277099291/figure/fig2/AS:649320713949185@1531821530365/Evolution-of-the-maximum-principal-stress-with-applied-displacement-for-various-values-of_Q320.jpg)
![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]).](https://www.researchgate.net/profile/Alan-Needleman/publication/277099291/figure/fig3/AS:649320713953282@1531821530381/Work-to-fracture-versus-the-location-of-the-HAZ-for-a-specimen-with-the-notched-surface_Q320.jpg)
