Articles de revista
http://hdl.handle.net/2117/4002
2015-11-26T12:43:59ZAnalytical procedure for the design of PFRP-RC hybrid beams including shear interaction effects
http://hdl.handle.net/2117/79278
Analytical procedure for the design of PFRP-RC hybrid beams including shear interaction effects
Neagoe, Catalin Andrei; Gil Espert, Lluís
Hybrid beams made of pultruded fiber-reinforced polymer (PFRP) shapes connected to reinforced concrete (RC) slabs are regarded as novel cost-effective and structurally-efficient elements. The current study addresses the need for a robust analytical procedure for the design of such members considering the structural implications of shear interaction effects. The discussed analytical procedure is based on the Timoshenko beam theory and on the elastic interlayer slip model extended from steel-concrete and timber-concrete composite beams, and presents the necessary mathematical tools for evaluating deflections, flexural capacities and stress distributions of hybrid beams. Partial interaction effects are quantified by using a proposed dimensionless parameter that depends mainly on the connection's stiffness. The analytical equations were validated successfully against available experimental data and conclusions indicate that the simplified model for partial interaction is viable and should be used even for specimens with full interlayer shear capacity
2015-11-15T11:21:23ZNeagoe, Catalin AndreiGil Espert, LluísHybrid beams made of pultruded fiber-reinforced polymer (PFRP) shapes connected to reinforced concrete (RC) slabs are regarded as novel cost-effective and structurally-efficient elements. The current study addresses the need for a robust analytical procedure for the design of such members considering the structural implications of shear interaction effects. The discussed analytical procedure is based on the Timoshenko beam theory and on the elastic interlayer slip model extended from steel-concrete and timber-concrete composite beams, and presents the necessary mathematical tools for evaluating deflections, flexural capacities and stress distributions of hybrid beams. Partial interaction effects are quantified by using a proposed dimensionless parameter that depends mainly on the connection's stiffness. The analytical equations were validated successfully against available experimental data and conclusions indicate that the simplified model for partial interaction is viable and should be used even for specimens with full interlayer shear capacityExperimental study of GFRP-concrete hybrid beams with low degree of shear connection
http://hdl.handle.net/2117/79275
Experimental study of GFRP-concrete hybrid beams with low degree of shear connection
Neagoe, Catalin Andrei; Gil Espert, Lluís; Pérez Martínez, Marco Antonio
Recent developments in the design of advanced composite materials for construction have led researchers to create novel high-performance structural elements that combine fiber-reinforced polymer (FRP) shapes with traditional materials. The current study analyzes the experimental structural response of eight hybrid beams made of pultruded glass FRP (GFRP) profiles mechanically connected to reinforced concrete (RC) slabs, suitable for building floors as well as footbridge and marine pier superstructures. The influence of partial interaction is studied by considering a low degree of shear connection and an analytical assessment of the whole response is carried out using previous formulations, highlighting a good accuracy. The behavior of the hybrid beams is further evaluated against that of equivalent reinforced concrete beams and single GFRP profiles, thus proving the feasibility of the solution.
2015-11-15T10:33:40ZNeagoe, Catalin AndreiGil Espert, LluísPérez Martínez, Marco AntonioRecent developments in the design of advanced composite materials for construction have led researchers to create novel high-performance structural elements that combine fiber-reinforced polymer (FRP) shapes with traditional materials. The current study analyzes the experimental structural response of eight hybrid beams made of pultruded glass FRP (GFRP) profiles mechanically connected to reinforced concrete (RC) slabs, suitable for building floors as well as footbridge and marine pier superstructures. The influence of partial interaction is studied by considering a low degree of shear connection and an analytical assessment of the whole response is carried out using previous formulations, highlighting a good accuracy. The behavior of the hybrid beams is further evaluated against that of equivalent reinforced concrete beams and single GFRP profiles, thus proving the feasibility of the solution.On the equivalence between traction- and stress-based approaches for the modeling of localized failure in solids
http://hdl.handle.net/2117/78534
On the equivalence between traction- and stress-based approaches for the modeling of localized failure in solids
Wu, Jian-Ying; Cervera Ruiz, Miguel
This work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in solids. Two complementary methodologies, i.e., discontinuities localized in an elastic solid and strain localization of an inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity and the orientation is determined from Mohr's maximization postulate. If the displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity. Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness and continuity upon strain localization is established for general inelastic softening solids. Application to a unified stress-based elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, Le., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded and smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion are determined consistently from the kinematic constraint rather than given a priori. The bidirectional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form results under plane stress condition are also given. A generic failure criterion of either elliptic, parabolic or hyperbolic type is analyzed in a unified manner, with the classical von Mises (J(2)), Drucker-Prager, Mohr-Coulomb and many other frequently employed criteria recovered as its particular cases.
2015-10-29T18:22:36ZWu, Jian-YingCervera Ruiz, MiguelThis work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in solids. Two complementary methodologies, i.e., discontinuities localized in an elastic solid and strain localization of an inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity and the orientation is determined from Mohr's maximization postulate. If the displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity. Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness and continuity upon strain localization is established for general inelastic softening solids. Application to a unified stress-based elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, Le., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded and smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion are determined consistently from the kinematic constraint rather than given a priori. The bidirectional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form results under plane stress condition are also given. A generic failure criterion of either elliptic, parabolic or hyperbolic type is analyzed in a unified manner, with the classical von Mises (J(2)), Drucker-Prager, Mohr-Coulomb and many other frequently employed criteria recovered as its particular cases.An accurate FIC-FEM formulation for the 1D convection-diffusion-reaction equation
http://hdl.handle.net/2117/78518
An accurate FIC-FEM formulation for the 1D convection-diffusion-reaction equation
Oñate Ibáñez de Navarra, Eugenio; Miquel Canet, Juan; Nadukandi, Prashanth
In this paper we present an accurate stabilized FIC-FEM formulation for the 1D advection-diffusion-reaction equation in the exponential and propagation regimes using two stabilization parameters. Both the steady-state and transient solutions are considered.
The stabilized formulation is based on the standard Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method. The steady-state problem is considered first. The optimal value of the two stabilization parameters ensuring an exact (nodal) FEM solution using uniform meshes of linear 2-noded elements is obtained. In the absence of the absorption term the formulation simplifies to the standard one-parameter Petrov-Galerkin method for the advection-diffusion problem. For the diffusion-reaction case one stabilization parameter is just needed and the diffusion-type stabilization term is identical to that obtained by Felippa and Oñate (2007) using a variational FIC approach. A procedure for computing the stabilization parameters for the transient problem is proposed. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of steady-state and transient 1D advection-diffusion-radiation problems for a the range of physical parameters and boundary conditions. Finally we outline the procedure to extend the 1D FIC-FEM formulation to multidimensions.
2015-10-29T16:08:39ZOñate Ibáñez de Navarra, EugenioMiquel Canet, JuanNadukandi, PrashanthIn this paper we present an accurate stabilized FIC-FEM formulation for the 1D advection-diffusion-reaction equation in the exponential and propagation regimes using two stabilization parameters. Both the steady-state and transient solutions are considered.
The stabilized formulation is based on the standard Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method. The steady-state problem is considered first. The optimal value of the two stabilization parameters ensuring an exact (nodal) FEM solution using uniform meshes of linear 2-noded elements is obtained. In the absence of the absorption term the formulation simplifies to the standard one-parameter Petrov-Galerkin method for the advection-diffusion problem. For the diffusion-reaction case one stabilization parameter is just needed and the diffusion-type stabilization term is identical to that obtained by Felippa and Oñate (2007) using a variational FIC approach. A procedure for computing the stabilization parameters for the transient problem is proposed. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of steady-state and transient 1D advection-diffusion-radiation problems for a the range of physical parameters and boundary conditions. Finally we outline the procedure to extend the 1D FIC-FEM formulation to multidimensions.A stochastic model for soft tissue failure using acoustic emission data
http://hdl.handle.net/2117/77287
A stochastic model for soft tissue failure using acoustic emission data
Sánchez Molina, David; Martínez González, Eva; Velázquez Ameijide, Juan; Llumà Fuentes, Jordi; Rebollo Soria, María Carmen; Arregui Dalmases, Carlos
The strength of soft tissues is due mainly to collagen fibers. In most collagenous tissues, the arrangement of the fibers is random, but has preferred directions. The random arrangement makes it difficult to make deterministic predictions about the starting process of fiber breaking under tension. When subjected to tensile stress the fibers are progressively straighten out and then start to be stretched. At the beginning of fiber breaking, some of the fibers reach their maximum tensile strength and break down while some others remain unstressed (this latter fibers will assume then major stress until they eventually arrive to their failure point). In this study, a sample of human esophagi was subjected to a tensile breaking of some fibers, up to the complete failure of the specimen. An experimental setup using Acoustic Emission to detect the elastic energy released is used during the test to detect the location of the emissions and the number of micro-failures per time unit. The data were statistically analyzed in order to be compared to a stochastic model which relates the level of stress in the tissue and the probability of breaking given the number of previously broken fibers, i.e. the deterioration in the tissue). The probability of a fiber breaking as the stretch increases in the tissue can be represented by a non-homogeneous Markov process which is the basis of the stochastic model proposed. This paper shows that a two-parameter model can account for the fiber breaking and the expected distribution for ultimate stress is a Fréchet distribution.
2015-10-02T09:47:25ZSánchez Molina, DavidMartínez González, EvaVelázquez Ameijide, JuanLlumà Fuentes, JordiRebollo Soria, María CarmenArregui Dalmases, CarlosThe strength of soft tissues is due mainly to collagen fibers. In most collagenous tissues, the arrangement of the fibers is random, but has preferred directions. The random arrangement makes it difficult to make deterministic predictions about the starting process of fiber breaking under tension. When subjected to tensile stress the fibers are progressively straighten out and then start to be stretched. At the beginning of fiber breaking, some of the fibers reach their maximum tensile strength and break down while some others remain unstressed (this latter fibers will assume then major stress until they eventually arrive to their failure point). In this study, a sample of human esophagi was subjected to a tensile breaking of some fibers, up to the complete failure of the specimen. An experimental setup using Acoustic Emission to detect the elastic energy released is used during the test to detect the location of the emissions and the number of micro-failures per time unit. The data were statistically analyzed in order to be compared to a stochastic model which relates the level of stress in the tissue and the probability of breaking given the number of previously broken fibers, i.e. the deterioration in the tissue). The probability of a fiber breaking as the stretch increases in the tissue can be represented by a non-homogeneous Markov process which is the basis of the stochastic model proposed. This paper shows that a two-parameter model can account for the fiber breaking and the expected distribution for ultimate stress is a Fréchet distribution.A generalized finite-strain damage model for quasi-incompressible hyperelasticity using hybrid formulation
http://hdl.handle.net/2117/77100
A generalized finite-strain damage model for quasi-incompressible hyperelasticity using hybrid formulation
Comellas Sanfeliu, Ester; Bellomo, Facundo J.; Oller Martínez, Sergio Horacio
A new generalized damage model for quasi-incompressible hyperelasticity in a total Lagrangian finite-strain framework is presented. A Kachanov-like reduction factor (1 - D) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetric–isochoric split of the Helmholtz free energy. However, in the present work, it has been implemented in an in-house finite element code for neo-Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three-dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature.
This is the accepted version of the following article: [Comellas, E., Bellomo, F. J., and Oller, S. (2015) A generalized finite-strain damage model for quasi-incompressible hyperelasticity using hybrid formulation. Int. J. Numer. Meth. Engng, doi: 10.1002/nme.5118.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5118/abstract
2015-09-25T13:28:07ZComellas Sanfeliu, EsterBellomo, Facundo J.Oller Martínez, Sergio HoracioA new generalized damage model for quasi-incompressible hyperelasticity in a total Lagrangian finite-strain framework is presented. A Kachanov-like reduction factor (1 - D) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetric–isochoric split of the Helmholtz free energy. However, in the present work, it has been implemented in an in-house finite element code for neo-Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three-dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature.Computational modeling of high-performance steel fiber reinforced concrete using a micromorphic approach
http://hdl.handle.net/2117/77099
Computational modeling of high-performance steel fiber reinforced concrete using a micromorphic approach
Huespe, Alfredo Edmundo; Oliver Olivella, Xavier; Mora, Diego Fernando
A finite element methodology for simulating the failure of high performance fiber reinforced concrete composites (HPFRC), with arbitrarily oriented short fibers, is presented. The composite material model is based on a micromorphic approach. Using the framework provided by this theory, the body configuration space is described through two kinematical descriptors. At the structural level, the displacement field represents the standard kinematical descriptor. Additionally, a morphological kinematical descriptor, the micromorphic field, is introduced. It describes the fiber–matrix relative displacement, or slipping mechanism of the bond, observed at the mesoscale level. In the first part of this paper, we summarize the model formulation of the micromorphic approach presented in a previous work by the authors. In the second part, and as the main contribution of the paper, we address specific issues related to the numerical aspects involved in the computational implementation of the model. The developed numerical procedure is based on a mixed finite element technique. The number of dofs per node changes according with the number of fiber bundles simulated in the composite. Then, a specific solution scheme is proposed to solve the variable number of unknowns in the discrete model. The HPFRC composite model takes into account the important effects produced by concrete fracture. A procedure for simulating quasi-brittle fracture is introduced into the model and is described in the paper. The present numerical methodology is assessed by simulating a selected set of experimental tests which proves its viability and accuracy to capture a number of mechanical phenomenon interacting at the macro- and mesoscale and leading to failure of HPFRC composites.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-013-0873-4
2015-09-25T13:02:52ZHuespe, Alfredo EdmundoOliver Olivella, XavierMora, Diego FernandoA finite element methodology for simulating the failure of high performance fiber reinforced concrete composites (HPFRC), with arbitrarily oriented short fibers, is presented. The composite material model is based on a micromorphic approach. Using the framework provided by this theory, the body configuration space is described through two kinematical descriptors. At the structural level, the displacement field represents the standard kinematical descriptor. Additionally, a morphological kinematical descriptor, the micromorphic field, is introduced. It describes the fiber–matrix relative displacement, or slipping mechanism of the bond, observed at the mesoscale level. In the first part of this paper, we summarize the model formulation of the micromorphic approach presented in a previous work by the authors. In the second part, and as the main contribution of the paper, we address specific issues related to the numerical aspects involved in the computational implementation of the model. The developed numerical procedure is based on a mixed finite element technique. The number of dofs per node changes according with the number of fiber bundles simulated in the composite. Then, a specific solution scheme is proposed to solve the variable number of unknowns in the discrete model. The HPFRC composite model takes into account the important effects produced by concrete fracture. A procedure for simulating quasi-brittle fracture is introduced into the model and is described in the paper. The present numerical methodology is assessed by simulating a selected set of experimental tests which proves its viability and accuracy to capture a number of mechanical phenomenon interacting at the macro- and mesoscale and leading to failure of HPFRC composites.Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
http://hdl.handle.net/2117/77059
Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
Toro, Sebastian; Sánchez, Pablo J.; Blanco, Pedro J.; de Souza Neto, E.; Huespe, Alfredo Edmundo; Feijóo, R.A.
This contribution presents a two-scale formulation devised to simulate failure in materials with heterogeneous micro-structure. The mechanical model accounts for the nucleation of cohesive cracks in the micro-scale domain. The evolution and propagation of cohesive micro-cracks can induce material instability at the macro-scale level. Then, a cohesive crack is nucleated in the macro-scale model which considers, in a homogenized sense, the constitutive response of the intricate failure mode taking place at the smaller length scale. The two-scale semi-concurrent model is based on the concept of Representative Volume Element (RVE). It is developed following an axiomatic variational structure. Two hypotheses are introduced in order to build the foundations of the entire theory, namely: (i) a mechanism for transferring kinematical information from macro-to-micro scale along with the concept of “Kinematical Admissibility”, and (ii) a Multiscale Variational Principle of internal virtual power equivalence between the involved scales of analysis. The homogenization formulae for the generalized stresses, as well as the equilibrium equations at the micro-scale, are consequences of the variational statement of the problem. The present multiscale technique is a generalization of a previous model proposed by the authors (Sánchez et al., 2013; Toro et al., 2014) and could be viewed as an application of a recent contribution (Blanco et al., 2014). The main novelty in this article lies on the fact that failure modes in the micro-structure involve a set of multiple cohesive cracks, connected or disconnected, with arbitrary orientation, conforming a complex tortuous failure path. Following the present multiscale modeling approach, the tortuosity effect is introduced as a kinematical concept and has a direct consequence in the homogenized mechanical response. Numerical examples are presented showing the potentialities of the model to simulate complex and realistic fracture problems in heterogeneous materials. In order to validate the multiscale technique in a rigorous manner, comparisons with the so-called DNS (Direct Numerical Solution) approach are also presented.
2015-09-23T13:11:41ZToro, SebastianSánchez, Pablo J.Blanco, Pedro J.de Souza Neto, E.Huespe, Alfredo EdmundoFeijóo, R.A.This contribution presents a two-scale formulation devised to simulate failure in materials with heterogeneous micro-structure. The mechanical model accounts for the nucleation of cohesive cracks in the micro-scale domain. The evolution and propagation of cohesive micro-cracks can induce material instability at the macro-scale level. Then, a cohesive crack is nucleated in the macro-scale model which considers, in a homogenized sense, the constitutive response of the intricate failure mode taking place at the smaller length scale. The two-scale semi-concurrent model is based on the concept of Representative Volume Element (RVE). It is developed following an axiomatic variational structure. Two hypotheses are introduced in order to build the foundations of the entire theory, namely: (i) a mechanism for transferring kinematical information from macro-to-micro scale along with the concept of “Kinematical Admissibility”, and (ii) a Multiscale Variational Principle of internal virtual power equivalence between the involved scales of analysis. The homogenization formulae for the generalized stresses, as well as the equilibrium equations at the micro-scale, are consequences of the variational statement of the problem. The present multiscale technique is a generalization of a previous model proposed by the authors (Sánchez et al., 2013; Toro et al., 2014) and could be viewed as an application of a recent contribution (Blanco et al., 2014). The main novelty in this article lies on the fact that failure modes in the micro-structure involve a set of multiple cohesive cracks, connected or disconnected, with arbitrary orientation, conforming a complex tortuous failure path. Following the present multiscale modeling approach, the tortuosity effect is introduced as a kinematical concept and has a direct consequence in the homogenized mechanical response. Numerical examples are presented showing the potentialities of the model to simulate complex and realistic fracture problems in heterogeneous materials. In order to validate the multiscale technique in a rigorous manner, comparisons with the so-called DNS (Direct Numerical Solution) approach are also presented.A two-scale failure model for heterogeneous materials: numerical implementation based on the finite element method
http://hdl.handle.net/2117/77051
A two-scale failure model for heterogeneous materials: numerical implementation based on the finite element method
Toro, Sebastian; Sánchez, Pablo J.; Huespe, Alfredo Edmundo; Giusti, Sebastian Miguel; Blanco, Pedro J.; Feijóo, R.A.
In the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure-Oriented Multiscale Formulation (FOMF) devised for modeling failure in heterogeneous
materials is described. The proposed model considers two well separated physical length scales, namely: (i) the “macro” scale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the “micro” scale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, etc. These processes are modeled using the concept of Representative Volume Element (RVE). On the macro scale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the micro scale. The traction
separation response is obtained by a particular homogenization technique applied on specific RVE subdomains. Standard, as well as, Non-Standard boundary conditions are consistently derived in order to
preserve “objectivity” of the homogenized response with respect to the micro-cell size. In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two-scale model based on the Finite Element Method is presented. Special attention is devoted to the topics which are distinctive of the FOMF, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level. Finally, a set of numerical simulations is performed.
This is the accepted version of the following article: Toro, S., Sánchez, P.J., Huespe, A.E., Giusti, S.M., Blanco, P.J. and Feijóo, R.A. (2014), A two-scale failure model for heterogeneous materials: numerical implementation based on the finite element method. Int. J. Numer. Meth. Engng., 97: 313–351. doi: 10.1002/nme.4576, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.4576/abstract
2015-09-23T12:39:06ZToro, SebastianSánchez, Pablo J.Huespe, Alfredo EdmundoGiusti, Sebastian MiguelBlanco, Pedro J.Feijóo, R.A.In the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure-Oriented Multiscale Formulation (FOMF) devised for modeling failure in heterogeneous
materials is described. The proposed model considers two well separated physical length scales, namely: (i) the “macro” scale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the “micro” scale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, etc. These processes are modeled using the concept of Representative Volume Element (RVE). On the macro scale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the micro scale. The traction
separation response is obtained by a particular homogenization technique applied on specific RVE subdomains. Standard, as well as, Non-Standard boundary conditions are consistently derived in order to
preserve “objectivity” of the homogenized response with respect to the micro-cell size. In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two-scale model based on the Finite Element Method is presented. Special attention is devoted to the topics which are distinctive of the FOMF, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level. Finally, a set of numerical simulations is performed.On the numerical modeling of granular material flows via the Particle Finite Element Method (PFEM)
http://hdl.handle.net/2117/77026
On the numerical modeling of granular material flows via the Particle Finite Element Method (PFEM)
Dávalos, César; Cante Terán, Juan Carlos; Hernández Ortega, Joaquín Alberto; Oliver Olivella, Xavier
The aim of this work is to describe a numerical framework for reliably and robustly simulating the different kinematic conditions exhibited by granular materials while spreading ---from a stagnant condition, when the material is at rest, to a transition to granular flow, and back to a deposit profile. The gist of the employed modeling approach was already presented by the authors in a recent work (Cante et al., 2014), but no proper description of the underlying numerical techniques was provided therein. The present paper focuses precisely on the detailed discussion of such numerical techniques, as well as on its rigorous validation with the experimental results obtained by Lajeunesse, et al. in Ref. ( Lajeunesse et al., 2004).
The constitutive model is based on the concepts of large strains plasticity. The yield surface is defined in terms of the Drucker Prager yield function, endowed with a deviatoric plastic flow and the elastic part by a hypoelastic model. The plastic flow condition is assumed nearly incompressible, so a u - p mixed formulation, with a stabilization of the pressure term via the Polynomial Pressure Projection (PPP), is employed. The numerical scheme takes as starting point the Particle Finite Element Method (PFEM) in which the spatial domain is continuously redefined by a different nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM approximations ( Idelsohn et al., 2004), in which the free boundary is obtained by a geometrical technique (a-shape method), in this work the boundary is treated as a material surface, and the boundary nodes are removed or inserted by means of an error function. One of the novelties of this work is the use of the so-called Impl-Ex hybrid integration technique to enhance the spectral properties of the algorithmic tangent moduli and thus reduce the number of iterations and robustness of the accompanying Newton-Raphson solution algorithm (compared with fully implicit schemes respectively). The new set of numerical tools implemented in the PFEM algorithm – including new discretization techniques, the use of a projection of the variables between meshes, and the constraint of the free-surface instead using classic a-shape – allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of granular flows.
Finally, numerical results are compared with the experiments developed in Ref. (Lajeunesse et al., 2004), where a granular mass, initially confined in a cylindrical container, is suddenly allowed to spread by the sudden removal of the container. The study is carried out using different geometries with varying initial aspect ratios. The excellent agreement between computed and experimental results convincingly demonstrates the reliability of the model to reproduce different kinematic conditions in transient and stationary regimes.
2015-09-22T14:00:18ZDávalos, CésarCante Terán, Juan CarlosHernández Ortega, Joaquín AlbertoOliver Olivella, XavierThe aim of this work is to describe a numerical framework for reliably and robustly simulating the different kinematic conditions exhibited by granular materials while spreading ---from a stagnant condition, when the material is at rest, to a transition to granular flow, and back to a deposit profile. The gist of the employed modeling approach was already presented by the authors in a recent work (Cante et al., 2014), but no proper description of the underlying numerical techniques was provided therein. The present paper focuses precisely on the detailed discussion of such numerical techniques, as well as on its rigorous validation with the experimental results obtained by Lajeunesse, et al. in Ref. ( Lajeunesse et al., 2004).
The constitutive model is based on the concepts of large strains plasticity. The yield surface is defined in terms of the Drucker Prager yield function, endowed with a deviatoric plastic flow and the elastic part by a hypoelastic model. The plastic flow condition is assumed nearly incompressible, so a u - p mixed formulation, with a stabilization of the pressure term via the Polynomial Pressure Projection (PPP), is employed. The numerical scheme takes as starting point the Particle Finite Element Method (PFEM) in which the spatial domain is continuously redefined by a different nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM approximations ( Idelsohn et al., 2004), in which the free boundary is obtained by a geometrical technique (a-shape method), in this work the boundary is treated as a material surface, and the boundary nodes are removed or inserted by means of an error function. One of the novelties of this work is the use of the so-called Impl-Ex hybrid integration technique to enhance the spectral properties of the algorithmic tangent moduli and thus reduce the number of iterations and robustness of the accompanying Newton-Raphson solution algorithm (compared with fully implicit schemes respectively). The new set of numerical tools implemented in the PFEM algorithm – including new discretization techniques, the use of a projection of the variables between meshes, and the constraint of the free-surface instead using classic a-shape – allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of granular flows.
Finally, numerical results are compared with the experiments developed in Ref. (Lajeunesse et al., 2004), where a granular mass, initially confined in a cylindrical container, is suddenly allowed to spread by the sudden removal of the container. The study is carried out using different geometries with varying initial aspect ratios. The excellent agreement between computed and experimental results convincingly demonstrates the reliability of the model to reproduce different kinematic conditions in transient and stationary regimes.