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Shear banding modelling in cross-anisotropic rocks Pardoen, Benoît ; ; Collin, Frédéric in International Journal of Solids and Structures (2015), 72 Sedimentary geomaterials such as rocks frequently exhibit cross-anisotropic properties and their behaviour depends on the direction of loading with respect to their microstructure. As far as material ... [more ▼] Sedimentary geomaterials such as rocks frequently exhibit cross-anisotropic properties and their behaviour depends on the direction of loading with respect to their microstructure. As far as material rupture is concerned, localised deformation in shear band mode appears generally before cracks and material failure. The influence of cross-anisotropy on the shear strain localisation remains an important issue and is investigated in the present study. To do so, a constitutive elastoplastic cross-anisotropic model that includes anisotropy both on the elastic and plastic characteristics is defined. For the plastic part of the model, the anisotropy of a strength parameter is introduced with a microstructure fabric tensor. Then, the fractures are modelled with finite element methods by considering the development of shear strain localisation bands and an enriched model is used to properly reproduce the shear banding. The cross-anisotropy influence on shear banding is studied through numerical applications of small and large-scale geotechnical problems that engender fractures. The two considered applications are a plane-strain biaxial compression test and an underground gallery excavation. The numerical results provide information about the influence of cross-anisotropy on the appearance and development of shear bands. It has been noticed, among other observations, that the material strength vary with the loading direction and that the development and the shape of the excavation fractured zone that develops around a gallery is strongly influenced by the material anisotropy. [less ▲] Detailed reference viewed: 49 (13 ULg)Computational homogenization of cellular materials Nguyen, Van Dung ; Noels, Ludovic in International Journal of Solids and Structures (2014), 51(11-12), 2183-2203 In this work we propose to study the behavior of cellular materials using a second–order multi–scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin ... [more ▼] In this work we propose to study the behavior of cellular materials using a second–order multi–scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin components, such as cell walls or cell struts, can occur. Even if the behavior of the materials of which the micro–structure is made remains elliptic, the homogenized behavior can lose its ellipticity. In that case, a localization band is formed and propagates at the macro–scale. When the localization occurs, the assumption of local action in the standard approach, for which the stress state on a material point depends only on the strain state at that point, is no–longer suitable, which motivates the use of the second-order multi–scale computational homogenization scheme. At the macro–scale of this scheme, the discontinuous Galerkin method is chosen to solve the Mindlin strain gradient continuum. At the microscopic scale, the classical finite element resolutions of representative volume elements are considered. Since the meshes generated from cellular materials exhibit voids on the boundaries and are not conforming in general, the periodic boundary conditions are reformulated and are enforced by a polynomial interpolation method. With the presence of instability phenomena at both scales, the arc–length path following technique is adopted to solve both macroscopic and microscopic problems. [less ▲] Detailed reference viewed: 268 (149 ULg)Numerical study of shear band instability and effect of cavitation on the response of a specimen under undrained biaxial loading ; ; Collin, Frédéric in International Journal of Solids and Structures (2014), 51(9), 16861696 Detailed reference viewed: 15 (1 ULg)An implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage Wu, Ling ; Noels, Ludovic ; et al in International Journal of Solids and Structures (2013), 50(24), 38433860 This paper presents an incremental-secant mean- field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the ... [more ▼] This paper presents an incremental-secant mean- field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the proposed method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme. When strain softening of materials is involved, classical fi nite element formulations lose solution uniqueness and face the strain localization problem. To avoid this issue the model is formulated in a so-called implicit gradient-enhanced approach, with a view toward macro-scale simulations. The method is then used to predict the behavior of composites whose matrix phases exhibit strain softening, and is shown to be accurate compared to unit cell simulations and experimental results. Then the convergence of the method upon strain softening, with respect to the mesh size, is demonstrated on a notched composite ply. Finally, applications consisting in a stacking plate, successively without and with a hole, are given as illustrations of the possibility of the method to be used in a multiscale framework. [less ▲] Detailed reference viewed: 100 (30 ULg)A multiaxial constitutive model for concrete in the fire situation: Theoretical formulation. Gernay, Thomas ; ; Franssen, Jean-Marc in International Journal of Solids and Structures (2013), 50(22-23), 3659-3673 This paper aims to develop a multiaxial concrete model for implementation in finite element softwares dedicated to the analysis of structures in fire. The need for proper concrete model remains a ... [more ▼] This paper aims to develop a multiaxial concrete model for implementation in finite element softwares dedicated to the analysis of structures in fire. The need for proper concrete model remains a challenging task in structural fire engineering because of the complexity of the concrete mechanical behavior characterization and the severe requirements for the material models raised by the development of performance-based design. A fully threedimensional model is developed based on the combination of elastoplasticity and damage theories. The state of damage in concrete, assumed isotropic, is modeled by means of a fourth order damage tensor to capture the unilateral effect. The concrete model comprises a limited number of parameters that can be identified by three simple tests at ambient temperature. At high temperatures, a generic transient creep model is included to take into account explicitly the effect of transient creep strain. The numerical implementation of the concrete model in a finite element software is presented and a series of numerical simulations are conducted for validation. The concrete behavior is accurately captured in a large range of temperature and stress states. A limitation appears when modeling the concrete post-peak behavior in highly confined stress states, due to the coupling assumption between damage and plasticity, but the considered levels of triaxial confinement are unusual stress states in structural concrete. [less ▲] Detailed reference viewed: 150 (38 ULg)Study of the geometrical inaccuracy on a SPIF two-slope pyramid by finite element simulations Guzmán Inostroza, Carlos Felipe ; ; et al in International Journal of Solids and Structures (2012), 49(25), 3594-3604 Single Point Incremental Forming (SPIF) is a recent manufacturing process which can give a symmetrical or asymmetrical shape to an undeformed metal sheet by using a relative small tool. In this article, a ... [more ▼] Single Point Incremental Forming (SPIF) is a recent manufacturing process which can give a symmetrical or asymmetrical shape to an undeformed metal sheet by using a relative small tool. In this article, a two-slope SPIF pyramid with two different depths, which suffers from large geometric deviations when comparing the intended and final shapes, is studied. The article goal is to detect if these divergences are due to new plastic strain while forming the second angle pyramid by using finite elements simulations. To validate the numerical results, both the shape and the forces are compared with experimental measurements. Then, an analysis of the material state is carried out taking the equivalent plastic strain, von Mises effective stress and yield stress distribution through a cut in the mesh. It is noticed that there is plastic deformation in the center of the pyramid, far from the tool neighbourhood. Also, high values of stresses are observed under the yield stress in other parts of the sheet. As a strong bending behaviour plus membrane tension is found in some sheet elements, these elastic stresses are due to a bending action of the tool. It is concluded that the main shape deviations come from elastic strains due to structural elastic bending, plus a minor contribution of localized springback, as no plastic deformation is observed in the angle change zone. Future developments in toolpath designs should eventually consider these elastic strains in order to achieve the intended geometry. [less ▲] Detailed reference viewed: 97 (38 ULg)Eulerian Formulation of Constrained Elastica Denoël, Vincent ; in International Journal of Solids and Structures (2011), 136 Detailed reference viewed: 32 (4 ULg)A two-scale model for subcritical damage propagation ; François, Bertrand ; in International Journal of Solids and Structures (2010), 47(3-4), 493-502 The failure behaviour of quasi-brittle materials is often time-dependent. This dependence is due to physical processes taking place at the level of the micro-structure. For a rigorous modeling of the time ... [more ▼] The failure behaviour of quasi-brittle materials is often time-dependent. This dependence is due to physical processes taking place at the level of the micro-structure. For a rigorous modeling of the time-dependent behaviour of that kind of solids, a two-scale approach is well suited. This paper investigates time-dependent damage which microscopic origin is the subcritical micro-crack growth. We present a two-scale time-dependent damage model completely deduced from small-scale descriptions of subcritical micro-crack propagation, without any macroscopic assumptions. The passage from the micro-scale to the macro-scale is done through an asymptotic homogenization approach. At the micro-scale, the tensile failure due to the subcritical propagation of cracks is the dominant mechanism of creep observed at the macro-scale. We consider microstructures with cracks evolving in different subcritical regimes. We assume a complex propagation law that considers three characteristic regimes of subcritical crack growth, corresponding to different physical processes at the crack tip level. Numerical simulations of constant strain rate, relaxation and creep tests illustrate the ability of the developed model to reproduce different regimes of time-dependent damage response. [less ▲] Detailed reference viewed: 58 (8 ULg)Analytical solutions for the thick-walled cylinder problem modeled with an isotropic elastic second gradient constitutive equation Collin, Frédéric ; ; in International Journal of Solids and Structures (2009), 46 Numerical modelling of localization phenomena shows that constitutive equations with internal length scale are necessary to properly model the post-localization behaviour. Moreover, these models allow an ... [more ▼] Numerical modelling of localization phenomena shows that constitutive equations with internal length scale are necessary to properly model the post-localization behaviour. Moreover, these models allow an accurate description of the scale effects observed in some phenomena like micro indentation. This paper proposes some analytical results concerning a boundary value problem in a medium with microstructure. In addition to their own usefulness, such analytical solutions can be used in benchmark exercises for the validation of numerical codes. The paper focuses on the thick-walled cylinder problem, using a general small strain isotropic elastic second gradient model. The most general isotropic elastic model involving seven different constants is used and the expression of the analytical solutions is explicitly given. The influence of the microstructure is controlled by the internal length scale parameter. The classical macrostress is no more in equilibrium with the classical forces at the boundary. Double stresses are indeed also generated by the classical boundary conditions and, as far as the microstructure effects become predominant (i.e. the internal length scale is much larger than the thickness of the cylinder), the macrostresses become negligible. This leads to solutions completely different from classical elastic ones. [less ▲] Detailed reference viewed: 215 (10 ULg)Thermomechanical modeling of metals at finite strains: First and mixed order finite elements ; Ponthot, Jean-Philippe in International Journal of Solids and Structures (2005), 42(21-22), 5615-5655 The aim of this paper is to describe an updated EAS (Enhanced Assumed Strain) finite element formalism developed to model the thermomechanical behavior of metals submitted to large strains. We will also ... [more ▼] The aim of this paper is to describe an updated EAS (Enhanced Assumed Strain) finite element formalism developed to model the thermomechanical behavior of metals submitted to large strains. We will also expose the use of mixed order elements (first order mechanical elements strongly coupled with quadratic thermal elements) which, as we will show, is of particular interest for modeling fast processes inducing important temperature gradients. The features of this formalism, used jointly with an Updated Lagrangian approach and an hypoelastic anisothermal constitutive formulation, will be described. Three applications involving finite strains and important thermomechanical couplings will be studied. The results obtained will be compared with the results given by the now classical SRI (Selective Reduced Integration) formalism. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 28 (4 ULg)On the use of large time steps with an energy momentum conserving algorithm for non-linear hypoelastic constitutive models Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in International Journal of Solids and Structures (2004), 41(3-4), 663693 This paper presents an extension of the energy momentum conserving algorithm, developed by the authors for hypoelastic constitutive models. For such a material, contrarily to hyperelastic models, no ... [more ▼] This paper presents an extension of the energy momentum conserving algorithm, developed by the authors for hypoelastic constitutive models. For such a material, contrarily to hyperelastic models, no potential can be defined, and thus the conservation of the energy is ensured only if the elastic work of deformation can be restored by the scheme. In a previous paper, we proposed a new expression of internal forces at the finite element level which is shown to verify this property. We also demonstrated that the work of plastic deformation is positive and consistent with the material model. In this paper, the second order terms that were neglected in the previous work are now taken into account. Several numerical applications are presented to demonstrate the necessity of taking these terms into account once large time step sizes are used. The limitations of the Newmark algorithm in the non-linear range are also illustrated. (C) 2003 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 31 (2 ULg)An equilibrium model for plate bending Fraeijs de veubeke, Baudouin ; in International Journal of Solids and Structures (1968), 4 A conforming displacement model for plate bending was presented earlier. It is of intyerest to have also an equilibrium moàdel available in order to generate both upper and lower bounds to plate ... [more ▼] A conforming displacement model for plate bending was presented earlier. It is of intyerest to have also an equilibrium moàdel available in order to generate both upper and lower bounds to plate deflections. The theory of the triangular equilibriium model, which is presented here, takes advantage of oblique coordinates. Il allows to cover transvers loading modes. Because the numerical investigations required adaptibility of the model to a stiffness computer-program, only the elaboration of the stiffness matrix was aimed at. The element can nevertheless be recognised as the Southwell analogue of the plane stress model with quadratic displacement field. As such it can be handled efficiently by a force program. Numerical results show the monotonic convergence of deflections from above for the equilibrium model and from below for the conforming model. The convergence rate, in terms of generalized coordinates, is compâred with that of other plate bending elements. [less ▲] Detailed reference viewed: 66 (9 ULg) |
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