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• Strain injection techniques for modeling 3D crack propagation

  I. Dias, J. Oliver, O. Lloberas-Valls

  Key engineering materials (2018). Vol. 774, pp. 547-552

  
  

  Abstract

  This work presents some novel results obtained by using the strain injection techniques for modeling crack propagation in challenging 3D benchmark tests. The techniques were already tested and validated by static and dynamic simulations in 2D [1-4], so the main goal of this paper is to verify if the most important advantages of the method, low computational cost and independence of the results on the finite element mesh, are kept in 3D. The methodology, implemented in the finite element framework, consists essentially in injecting those elements that are going to capture the cracks with some enhanced strain modes for improving the performance of the elements for modeling propagating material failure

  Abstract
  This work presents some novel results obtained by using the strain injection techniques for modeling crack propagation in challenging 3D benchmark tests. The techniques were [...]

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

  I. Dias, J. Oliver, O. Lloberas-Valls

  International journal of fracture (2018). Vol. 212 (1), pp. 67-87 (Preprint)

  
  

  Abstract

  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 scenarios

  Abstract
  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 [...]

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

  D. Roca, O. Lloberas-Valls, J. Cante, J. Oliver

  Computer Methods in Applied Mechanics and Engineering (2018). Vol. 330, pp. 415-446 (Preprint)

  
  

  Abstract

  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 attenuation

  Abstract
  A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic [...]

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• Computational material design for acoustic cloaking

  C. Méndez, J. Podestá, O. Lloberas-Valls, S. Toro, A. Huespe, J. Oliver

  International Journal for Numerical Methods in Engineering (2017). Vol. 112 (10), pp. 1353-1380

  
  

  Abstract

  A topology optimization technique based on the topological derivative and the level set function is utilized to design/synthesize the micro-structure of a pentamode material for an acoustic cloaking device. The technique provides a micro-structure consisting of a honeycomb lattice composed of needle-like and joint members. The resulting metamaterial shows a highly anisotropic elastic response with effective properties displaying a ratio between bulk and shear moduli of almost 3 orders of magnitude. Furthermore, in accordance with previous works in the literature, it can be asserted that this kind of micro-structure can be realistically fabricated. The adoption of a topology optimization technique as a tool for the inverse design of metamaterials with applications to acoustic cloaking problems is one contribution of this paper. However, the most important achievement refers to the analysis and discussion revealing the key role of the external shape of the prescribed domain where the optimization problem is posed. The efficiency of the designed micro-structure is measured by comparing the scattering wave fields generated by acoustic plane waves impinging on bare and cloaked bodies

  Abstract
  A topology optimization technique based on the topological derivative and the level set function is utilized to design/synthesize the micro-structure of a pentamode material [...]

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• The domain interface method in non-conforming domain decomposition multifield problemsdomain decomposition multifield problems

  O. Lloberas-Valls, M. Cafiero, J. Cante, A. Ferrer, J. Oliver

  Computational Mechanics (2017). Vol. 59 (4), pp. 579-610 (Preprint)

  
  

  Abstract

  The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the non-conforming domain decomposition technique consists in a discretization of a fictitious zero-thickness interface as in the original methodology and continuity of the solution fields across the domains is satisfied by incorporating the corresponding Lagrange Multipliers. The multifield DIM inherits the advantages of its irreducible version in the sense that the connections between non-matching meshes, with possible geometrically non-conforming interfaces, is accounted by the automatic Delaunay interface discretization without considering master and slave surfaces or intermediate surface projections as done in many established techniques, e.g. mortar methods. The multifield enhancement identifies the Lagrange multiplier field and incorporates its contribution in the weak variational form accounting for the corresponding consistent stabilization term based on a Nitsche method. This type of constraint enforcement circumvents the appearance of instabilities when the Ladyzhenskaya–Babuška–Brezzi (LBB) condition is not fulfilled by the chosen discretization. The domain decomposition framework is assessed in a large deformation setting for mixed displacement/pressure formulations and coupled thermomechanical problems. The continuity of the mixed field is studied in well selected benchmark problems for both mixed formulations and the objectivity of the response is compared to reference monolithic solutions. Results suggest that the presented strategy shows sufficient potential to be a valuable tool in situations where the evolving physics at particular domains require the use of different spatial discretizations or field interpolations

  Abstract
  The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the non-conforming [...]

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• Vademecum-based approach to multi-scale topological material design

  A. Ferrer, J. Oliver, J. Cante, O. Lloberas

  Advanced modeling and simularion in engineering sciences (2016). Vol. 3 (1), pp. 1-22 (Preprint)

  
  

  Abstract

  The work deals on computational design of structural materials by resorting to computational homogenization and topological optimization techniques. The goal is then to minimize the structural (macro-scale) compliance by appropriately designing the material distribution (microstructure) at a lower scale (micro-scale), which, in turn, rules the mechanical properties of the material. The specific features of the proposed approach are: (1) The cost function to be optimized (structural stiffness) is defined at the macro-scale, whereas the design variables defining the micro-structural topology lie on the low scale. Therefore a coupled, two-scale (macro/micro), optimization problem is solved unlike the classical, single-scale, topological optimization problems. (2) To overcome the exorbitant computational cost stemming from the multiplicative character of the aforementioned multiscale approach, a specific strategy, based on the consultation of a discrete material catalog of micro-scale optimized topologies (Computational Vademecum) is used. The Computational Vademecum is computed in an offline process, which is performed only once for every constitutive-material, and it can be subsequently consulted as many times as desired in the online design process. This results into a large diminution of the resulting computational costs, which make affordable the proposed methodology for multiscale computational material design. Some representative examples assess the performance of the considered approach

  Abstract
  The work deals on computational design of structural materials by resorting to computational homogenization and topological optimization techniques. The goal is then to minimize [...]

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• Model Order Reduction in Computational multiscale fracture mechanics

  M. Caicedo, J. Oliver, A. Huespe, O. Lloberas-Valls

  Key engineering materials (2016). Vol. 713, pp. 248-253 (Preprint)

  
  

  Abstract

  Nowadays, the model order reduction techniques have become an intensive research eld because of the increasing interest in the computational modeling of complex phenomena in multi-physic problems, and its conse- quent increment in high-computing demanding processes; it is well known that the availability of high-performance computing capacity is, in most of cases limited, therefore, the model order reduction becomes a novelty tool to overcome this paradigm, that represents an immediately challenge in our research community. In computational multiscale modeling for instance, in order to study the interaction between components, a di erent numerical model has to be solved in each scale, this feature increases radically the computational cost. We present a reduced model based on a multi-scale framework for numerical modeling of the structural failure of heterogeneous quasi-brittle materials using the Strong Discontinuity Approach (CSD). The model is assessed by application to cementitious materials. The Proper Orthogonal Decomposition (POD) and the Reduced Order Integration Cubature are the pro- posed techniques to develop the reduced model, these two techniques work together to reduce both, the complexity and computational time of the high-delity model, in our case the FE2 standard model

  Abstract
  Nowadays, the model order reduction techniques have become an intensive research eld because of the increasing interest in the computational modeling of complex phenomena [...]

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• Strain injection techniques in dynamic fracture modeling

  O. Lloberas-Valls, A. Huespe, J. Oliver, I. Dias

  Computer Methods in Applied Mechanics and Engineering (2016). Vol. 308, pp. 499-534 (Preprint)

  
  

  Abstract

  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

  Abstract
  A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injection techniques and Finite Elements with Embedded strong [...]

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• The domain interface method: a general-purpose non-intrusive technique for non-conforming domain decomposition problems

  M. Cafiero, O. Lloberas-Valls, J. Cante, J. Oliver

  Computational Mechanics (2016). Vol. 57 (4), pp. 555-581

  
  

  Abstract

  A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface and inserted in the formulation in the form of Lagrange multipliers. The final structure of the global system of equations resembles the dual assembly of substructures where the Lagrange multipliers are employed to nullify the gap between domains. A new approach to handle floating subdomains is outlined which can be implemented without significantly altering the structure of standard industrial finite element codes. The effectiveness of the developed algorithm is demonstrated through a patch test example and a number of tests that highlight the accuracy of the methodology and independence of the results with respect to the framework parameters. Considering its high degree of flexibility and non-intrusive character, the proposed domain decomposition framework is regarded as an attractive alternative to other established techniques such as the mortar approach.

  Abstract
  A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering [...]

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• Modeling tensile crack propagation in concrete gravity dams via crack-path-field and strain injection techniques

  I. Dias, J. Oliver, J. Lemos, O. Lloberas-Valls

  Engineering Fracture Mechanics (2016). Vol. 154, pp. 288-310 (Preprint)

  
  

  Abstract

  This work investigates tensile crack propagation in concrete gravity dams by using some recently developed numerical techniques (crack-path field and strain injection techniques). The work carefully addresses aspects related to mesh independence, robustness and computational cost, which are the main issues in fracture modeling. The novel technique consists of a procedure to insert, in the selected domain areas, specific strain fields for enhancing the performance of the underlying finite elements in modeling fracture. Representative numerical simulations of concrete dams show the accuracy and robustness of the methodology

  Abstract
  This work investigates tensile crack propagation in concrete gravity dams by using some recently developed numerical techniques (crack-path field and strain injection techniques). [...]

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