Representative volume for elastic, hardening and softening materials

The objective of this study is to verify the existence of Representative Volume Elements (RVEs) in different regimes of loading and possibly to quantify the size of a RVE for brittle materials

Strain injection techniques in dynamic fracture modeling

A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injection techniques and Finite Elements with Embedded strong discontinuities (E-FEM). In the present research, classical strain localization and strong discontinuity approaches are considered by injecting discontinuous strain and displacement modes in the finite element formulation without an increase of the total number of degrees of freedom. Following the Continuum Strong Discontinuity Approach (CSDA), stress–strain constitutive laws can be employed in the context of fracture phenomena and, therefore, the methodology remains applicable to a wide number of continuum mechanics models. The position and orientation of the displacement discontinuity is obtained through the solution of a crack propagation problem, i.e. the crack path field, based on the distribution of localized strains. The combination of the above mentioned approaches is envisaged to avoid stress-locking and directional mesh bias phenomena. Dynamic simulations are performed increasing the loading rate up to the appearance of crack branching, and the variation in terms of failure modes is investigated as well as the influence of the strain injection together with the crack path field algorithm. Objectivity of the presented methodology with respect to the spatial and temporal discretization is analyzed in terms of the dissipated energy during the fracture process. The dissipation at the onset of branching is studied for different loading rate conditions and is linked to the experimental maximum velocity observed before branching takes place.Fil: Lloberas Valls, Oriol. Universidad Politecnica de Catalunya; España. Centre Internacional de Metodes Numerics en Enginyeria; EspañaFil: Huespe, Alfredo Edmundo. Centre Internacional de Metodes Numerics en Enginyeria; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Oliver, J.. Centre Internacional de Metodes Numerics en Enginyeria; España. Universidad Politecnica de Catalunya; EspañaFil: Dias, I.F.. Laboratório Nacional de Engenharia Civil; Portuga

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training energy snapshots. The outcome consists of a number of dominant strain modes integrated over a remarkably reduced number of integration points which provide the support to evaluate the constitutive behavior of the micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Strain-injection and crack-path field techniques for 3D crack-propagation modelling in quasi-brittle materials

This paper presents a finite element approach for modelling three-dimensional crack propagation in quasi-brittle materials, based on the strain injection and the crack-path field techniques. These numerical techniques were already tested and validated by static and dynamic simulations in 2D classical benchmarks [Dias et al., in: Monograph CIMNE No-134. International Center for Numerical Methods in Engineering, Barcelona, (2012); Oliver et al. in Comput Methods Appl Mech Eng 274:289–348, (2014); Lloberas-Valls et al. in Comput Methods Appl Mech Eng 308:499–534, (2016)] and, also, for modelling tensile crack propagation in real concrete structures, like concrete gravity dams [Dias et al. in Eng Fract Mech 154:288–310, (2016)]. The main advantages of the methodology are the low computational cost and the independence of the results on the size and orientation of the finite element mesh. These advantages were highlighted in previous works by the authors and motivate the present extension to 3D cases. The proposed methodology is implemented in the finite element framework using continuum constitutive models equipped with strain softening and consists, essentially, in injecting the elements candidate to capture the cracks with some goal oriented strain modes for improving the performance of the injected elements for simulating propagating displacement discontinuities. The goal-oriented strain modes are introduced by resorting to mixed formulations and to the Continuum Strong Discontinuity Approach (CSDA), while the crack position inside the finite elements is retrieved by resorting to the crack-path field technique. Representative numerical simulations in 3D benchmarks show that the advantages of the methodology already pointed out in 2D are kept in 3D scenariosPeer ReviewedPostprint (author's final draft

Strain-injection and crack-path field techniques for 3D crack-propagation modelling in quasi-brittle materials

This paper presents a finite element approach for modelling three-dimensional crack propagation in quasi-brittle materials, based on the strain injection and the crack-path field techniques. These numerical techniques were already tested and validated by static and dynamic simulations in 2D classical benchmarks [Dias et al., in: Monograph CIMNE No-134. International Center for Numerical Methods in Engineering, Barcelona, (2012); Oliver et al. in Comput Methods Appl Mech Eng 274:289–348, (2014); Lloberas-Valls et al. in Comput Methods Appl Mech Eng 308:499–534, (2016)] and, also, for modelling tensile crack propagation in real concrete structures, like concrete gravity dams [Dias et al. in Eng Fract Mech 154:288–310, (2016)]. The main advantages of the methodology are the low computational cost and the independence of the results on the size and orientation of the finite element mesh. These advantages were highlighted in previous works by the authors and motivate the present extension to 3D cases. The proposed methodology is implemented in the finite element framework using continuum constitutive models equipped with strain softening and consists, essentially, in injecting the elements candidate to capture the cracks with some goal oriented strain modes for improving the performance of the injected elements for simulating propagating displacement discontinuities. The goal-oriented strain modes are introduced by resorting to mixed formulations and to the Continuum Strong Discontinuity Approach (CSDA), while the crack position inside the finite elements is retrieved by resorting to the crack-path field technique. Representative numerical simulations in 3D benchmarks show that the advantages of the methodology already pointed out in 2D are kept in 3D scenario

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training energy snapshots. The outcome consists of a number of dominant strain modes integrated over a remarkably reduced number of integration points which provide the support to evaluate the constitutive behavior of the micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training energy snapshots. The outcome consists of a number of dominant strain modes integrated over a remarkably reduced number of integration points which provide the support to evaluate the constitutive behavior of the micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training energy snapshots. The outcome consists of a number of dominant strain modes integrated over a remarkably reduced number of integration points which provide the support to evaluate the constitutive behavior of the micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training energy snapshots. The outcome consists of a number of dominant strain modes integrated over a remarkably reduced number of integration points which provide the support to evaluate the constitutive behavior of the micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling

A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuations and their gradients are then accounted for in a saddle-point formulation of that variational principle in terms of Lagrange functionals. A physical interpretation of the involved Lagrange multipliers can then be readily obtained. The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuatio