Control of heat flux using computationally designed metamaterials

To gain control over the diffusive heat flux in a given domain, one has to design metamaterials with a specifc distribution of the generally anisotropic thermal conductivity throughout the domain. Until now, the appropriate conductivity distribution was usually determined using transformation thermodynamics. By this way, only a few particular cases of heat flux control in simple domains having simple boundary conditions were studied. As a more general approach, we propose to define the heat control problem as an optimization problem where we minimize the error in guiding the heat flux in a given way, taking as design variables the parameters that define the variable microstructure of the metamaterial. Anisotropic conductivity is introduced by using a metamaterial made of layers of two materials with highly dfferent conductivities, the thickness of the layers and their orientation throughout the domain are the current design variables. As an application example we design a device that thermally shields the region it encloses, while it keeps unchanged the flux outside it.Preprin

Métodos de continuación para el trazado de curvas de equilibrio primarias y secundarias en análisis de mecanismos

Describimos un método para el trazado de trayectorias de equilibrio en sistemas multicuerpos flexibles. Permite posicionarse en forma precisa en puntos límite y de bifurcación simples. El sistema de ecuaciones aumentado propuesto para ubicar los puntos singulares logra una tasa de convergencia cuadrática en ambos casos. Se muestran ejemplos de ilustración.We describe a methodology for tracing the nonlinear equilibrium path in flexible multibody systems. It allows to position accurately turning and simple bifurcation points. The augmented systems of equations proposed to position the singular points, give full quadratic convergence rate in both cases. Severa1 examples illustrating the approach are presented.Peer Reviewe

A study on finite elements for capturing strong discontinuities

The work focuses on the presently existing families of finite elements with embedded discontinuities and explores the possibilities of obtaining symmetric statically consistent finite elements that alleviate the stress-locking problem. For this purpose, mixed (reduced integration) and assumed enhanced strain techniques are applied to the basic symmetric four-noded element. Numerical simulations show the effectiveness of the proposed measures

A model of material failure for reinforced concrete via continuum strong discontinuity approach and mixing theory

In this work a two-dimensional formulation describing the fracture process in reinforced concrete is developed, implemented and validated. The cracks in the material are captured by means of continuum strong discontinuity approach (CSDA) (Oliver 1996) and the constitutive model of composite material is defined through mixing theory (Truesdell & Toupin 1960). The composite material consists of one or two groups of long fibers or steel bars embedded within a concrete matrix. Likewise, each component is characterized by a constitutive model. The concrete is described by a damage model with degradation in tension and compression (Oliver, Cervera et al. 1990). A uniaxial plasticity model (Simó & Hughes 1998) is used for the steel. Also, phenomena as bond-slip and dowel action (Park & Paulay 1975) are included and represented by additional models of interaction between concrete and steel. The initiation and propagation of cracks are understood as a strain localization process described by means of CSDA. A bifurcation analysis of composite material is proposed to establish the bifurcation time and direction of the crack. The model has been implemented in a two-dimensional analysis program using the finite element method (FEM), where it is assumed material non-linearity and infinitesimal strains. An implicit-explicit integration scheme for the constitutive equation (Oliver, Huespe et al. 2004; Oliver, Huespe et al. 2006) ensures a positive defined stiffness matrix of the problem and increases the robustness and stability of the solution. On the other hand, a strategy to tracking discontinuity paths (Samaniego 2002; Oliver & Huespe 2004), allows that the discontinuity paths correspond among the elements. According to the proposed formulation, on each point of solid, the strain and stress fields of the reinforced concrete are described as a composite material. This has the following advantages: first, the model facilitates the implementation on the finite element method, since many ingredients of standard numerical process remain, and secondly, the macroscopic scale of analysis avoids the discretization of each component material and the interaction effects, and consequently the computational cost is reduced. The model can reproduce two different stages of cracking in the reinforced concrete. Initially, the steel capacity and the adherence in the interface produce a stable stage of distributed cracking, where appear many cracks with constant spacing and opening. Afterward, a localization cracking stage is characterized by few cracks while the structural response decreases. Reinforced concrete members subjected to tension, bending and shear are simulated. The numerical results, mainly the structural response and the crack pattern, are compared with experimental test (Leonhardt 1965; Collins, Vecchio et al. 1985; Ouyang & Shah 1994; Ruiz, Elices et al. 1998). The correlation between numerical results using the proposed formulation and actual results is quantitative and qualitatively satisfactory

A finite strain, finite band method for modeling ductile fracture

We present a finite deformation generalization of the finite thickness embedded discontinuity formulation presented in our previous paper [A.E. Huespe, A. Needleman, J. Oliver, P.J. Sánchez, A finite thickness band method for ductile fracture analysis, Int. J. Plasticity 25 (2009) 2349–2365]. In this framework the transition from a weak discontinuity to a strong discontinuity can occur using a single constitutive relation which is of importance in a range of applications, in particular ductile fracture, where localization typically precedes the creation of new free surface. An embedded weak discontinuity is introduced when the loss of ellipticity condition is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. The methodology is illustrated through several example problems emphasizing finite deformation effects including the development of a cup-cone failure in round bar tensio

A phase-field/gradient damage model for brittle fracture in elastic-plastic solids

The formulation of a phase-field continuum theory for brittle fracture in elastic-plastic solids and its computational implementation are presented in this contribution. The theory is based on a virtual-power formulation in which two additional and independent kinematical descriptors are introduced, namely the phase-field and the accumulated plastic strain. Further, it incorporates irreversibility of both phase-field and plastic strain evolutions by introducing suitable constraints and by carefully heeding the influence of those constraints on the kinetics underlying microstructural changes associated with plasticity and fracture. The numerical implementation employs the finite-element method for spatial discretization and a splitting scheme with sub-stepping for the time integration. To illustrate its potential utility, we apply the model to a number of well known linear, as well as non-linear, fracture mechanics problems. The described phase-field model, coupled with plasticity, provides a feasible technique to analyzing crack initiation and the subsequent crack growth resistance only if the length scale parameter included in the phase-field model is finite and treated as a material parameter which should be properly characterized.Preprin

A finite thickness band method for ductile fracture analysis

We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffness of the material degrades. An embedded weak discontinuity is introduced when the condition for loss of ellipticity is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. Also since the constitutive relation for a progressively cavitation solid is used inside the band in the post-localization regime, the traction-opening relation across the band depends on the stress triaxiality. The methodology is illustrated through several example problems including mode I crack growth and localization and failure in notched bars. Various finite element meshes and values of the thickness of the localization band are used in the calculations to illustrate the convergence with mesh refinement and the dependence on the value chosen for the localization band thicknes

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 plac

On the strong discontinuity approach in finite deformation settings

Taking the strong discontinuity approach as a framework for modelling displacement discontinuities and strain localization phenomena, this work extends previous results in infinitesimal strain settings to finite deformation scenarios. By means of the strong discontinuity analysis, and taking isotropic damage models as target continuum (stress–strain) constitutive equation, projected discrete (tractions–displacement jumps) constitutive models are derived, together with the strong discontinuity conditions that restrict the stress states at the discontinuous regime. A variable bandwidth model, to automatically induce those strong discontinuity conditions, and a discontinuous bifurcation procedure, to determine the initiation and propagation of the discontinuity, are briefly sketched. The large strain counterpart of a non-symmetric finite element with embedded discontinuities, frequently considered in the strong discontinuity approach for infinitesimal strains, is then presented. Finally, some numerical experiments display the theoretical issues, and emphasize the role of the large strain kinematics in the obtained result

Model Order Reduction in Computational multiscale fracture mechanics

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 mode