A new framework for crack tracking in elastodamaging materials based on the regularized extended finite element method
A new framework for crack tracking in elastodamaging materials based on the regularized extended finite element method
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We have formulated a new framework to track general crack paths in quasi-brittle materials in the regularized extended finite element method. Peculiarly, both the damaging process and the displacement discontinuities are captured through a unified framework. With respect to previous relevant authors’ contributions, a novel damage evolution law and an original crack tracking framework are proposed. We face mesh biases of various kind through suitable crack-direction-tracking algorithms, and demonstrate the accuracy of the computed crack paths and structural responses in several two-dimensional tests.
E. Benvenuti, N. Orlando. "A new framework for crack tracking in elastodamaging materials based on the regularized extended finite element method." submitted.
Extended virtual element method
Extended virtual element method
In this study, we have investigated the capability of the recently proposed extended virtual element method (X-VEM) to efficiently and accurately solve the problem of a cracked prismatic beam under pure torsion, mathematically described by the Poisson equation in terms of a scalar stress function. This problem is representative of a wide class of elliptic problems for which classic finite element approximations tend to converge poorly, due to the presence of singularities. The X-VEM is a stabilized Galerkin formulation on arbitrary polygonal meshes derived from the virtual element method (VEM) by augmenting the standard virtual element space with an additional contribution that consists of the product of virtual nodal basis functions with a suitable enrichment function. In addition, an extended projector that maps functions lying in the extended virtual element space onto linear polynomials and the enrichment function is employed. Convergence of the method on both quadrilateral and polygonal meshes for the cracked beam torsion problem is studied by means of numerical experiments. The computed results affirm the sound accuracy of the method and demonstrate a significantly improved convergence rate, both in terms of energy and stress intensity factor, when compared to standard finite element method (FEM) and VEM.
An Orthotropic Multi-surface Elastic-Damaging-Plastic Model with Regularized XFEM Interfaces for Wood Structures
An Orthotropic Multi-surface Elastic-Damaging-Plastic Model with Regularized XFEM Interfaces for Wood Structures
Wood is a natural composite exhibiting pronounced orthotropic behaviour, and markedly different properties along the parallel and transverse-to-the-fiber directions. It displays a strongly non-linear mechanical behavior, almost elasto-plastic at compressive loadings and elasto-damaging when subjected to tensile and shearing stresses.
We have developed a novel constitutive model for wood with a multi-surface failure domain resulting from a set of plastic laws for compressive failure modes and orthotropic damage laws for tensile/shear failure modes. The advantage over existing formulations is that the coexistence of anisotropic damage and plasticity constitutive laws allows to correctly capture brittle failure induced by strain localization as well as the possible occurrence of ductile plastic behavior. Furthermore, the present contribution shows how to numerically treat the simultaneous presence of anisotropic damage and plasticity in a general algorithmic multi-surface framework. It is shown that the obtained numerical results satisfactorily fit experimental data.
We investigate also the modelling capabilities offered by the multi-surface damage-plasticity FE-formulation when integrated with a regularized extended finite element model. The aim is to tackle discontinuous displacements and interfaces. In particular, we show how to embed a regularized discontinuity within an element, carry out the transition from the continuous to the regularized discontinuous regime and obtain physically consistent results. We present a wide set of applications ranging from brittle to ductile failure, displaying the effectiveness of the proposed FE-approach versus the experimental results.
Delamination of FRP plates from concrete beams in bending and shear tests
Delamination of FRP plates from concrete beams in bending and shear tests
The study focuses on a three-dimensional computational methodology aimed at modeling the detachment of FRP plates from Steel-Fiber-Reinforced-Concrete beams and standard reinforced concrete beams. Most finite element models introduce FRP-to-concrete bond-slip laws difficult to be derived, while simulating the cracks in the concrete with smeared crack models.
Conversely, the proposed approach is based on the regularized eXtended Finite Element Method with a mechanism-based detachment. It does not require bond-slip laws and makes use of standard material parameters.
The introduction of a regularization length and the adoption of a proper mechanical framework lead to an accurate and predictive methodology for smooth simulations of the FRP-detachment process.
Electromechamical behavior of CNTs
Electromechamical behavior of CNTs
We have simulated the electromechanical behavior of freestanding and clamped carbon nanotubes (CNTs) subjected to an electric potential and displaying charge end enhancements. In this case, CNT deformation is a consequence of the electrostatic pressure associated with the charge density. Whereas experiments investigate several micron long CNTs, computational models consider nanometer-sized CNTs. Hence, experimental and computational results, often, cannot be compared. Analytical solutions appear thus useful as reference solutions for finite element analysis, alternative to atomistic simulations, and complementary to experimental tests. In this work, the electromechanical behavior of CNTs is computed by using the nonlocal Poisson equation obtained extending the charge transport equations for spatially variable currents. Based on a certain equivalence between gradient and integral formulations, we solve the problem governing the electromechanical problem of CNTs regarded as cylinders subjected to electrostatic forces. The present procedure automatically captures charge end enhancements, thus overcoming the necessity of introducing suitable charge end correction factors. The analytical expressions of the radial displacement of freestanding CNTs, and the deflection of bent CNTs are obtained. For armchair single wall CNTs, the results obtained are consistent with experiments, and molecular mechanics and atomistic simulations. Size dependence of electric and mechanical properties is assessed.
3D regularized XFEM for inclusions and interfaces
3D regularized XFEM for inclusions and interfaces
We have proposed an eXtended Finite Element Method convergent to the asymptotic solution of a thin interface problem for both planar and curved imperfect interfaces in three dimensions. The main advantage over standard cohesive-zone models is the bulk-mesh size independence. With respect to standard eXtended Finite Element Method, in the proposed procedure, blending and quadrature sub-domains are not required. The focus is on the evaluation of the accuracy of the proposed approach in solving three-dimensional benchmark tests. The numerical results are compared with those available from analytical solutions and spring-like interface models.
Equivalent eigenstrain approach
Equivalent eigenstrain approach
Several engineering applications rely on particulate composite materials, and numerical modelling of the matrix–inclusion interface is therefore a crucial part of the design process. The focus of this work is on an original use of the equivalent eigenstrain concept in the development of a simplified eXtended Finite Element Method. Key points are: the replacement of the matrix-inclusion interface by a coating layer with small but finite thickness, and its simulation as an inclusion with an equivalent eigenstrain. For vanishing thickness, themodel is consistent with a spring-like interface model. The problem of a spherical inclusion within a cylinder is solved. The results show that the proposed approach is effective and accurate.
Continuous-discontinuous transition for quasi brittle concrete-like materials
Continuous-discontinuous transition for quasi brittle concrete-like materials
Experimental tests carried out on concrete specimens show that a fracture process zone with finite width develops in front of the crack tip. Currently, the only way of modelling a finite-width process zone is to adopt a non-local continuum damage model. This choice, however, precludes the description of macro-cracks, which emerge during the late stage of the cracking process. The eXtended Finite Element Method is a powerful tool for modelling the cracking process. The proposed eXtended Finite Element approach can simulate in a unified and smooth way both the formation of a process zone with finite width and its subsequent collapse into a macro-crack. Weak points of existing formulations, such as the necessity of ad hoc strategies in order to get mesh-independent results, and the sudden loss of stiffness at the transition from the continuous to the discontinuous regime, are overcome. In the case of tensile cracking, effectiveness is tested through comparisons with numerical and experimental results.
Analytical and numerical solutions for nonlocal elasticity models
Analytical and numerical solutions for nonlocal elasticity models
The equivalence between nonlocal and gradient elasticity models has been investigated by making reference to one-dimensional boundary value problems equipped with two integral stress–strain laws proposed by Eringen (Nonlocal Continuum Field Theories (2002)). Corresponding closed-form solutions are derived through a procedure for the reduction of integral to differential equations. The reproduction of size effects in micro/nano rods is discussed. The differential formulation associated with the local/nonlocal model is shown to correspond to the strain-gradient formulation proposed by Aifantis (Mech. Mater. 35 (2003) 259–280).
Advanced approximation methods for nonlocal elasticity models
Advanced approximation methods for nonlocal elasticity models
We have investigated the application and performance of high-order approximation techniques to one-dimensional nonlocal elastic rods. Governing equations and corresponding discrete forms are derived for the integro-differential formulation proposed by Eringen and the laplacian-based strain gradient formulation developed by Aifantis and coworkers. Accuracy and convergence rate of the numerical solutions obtained with Lagrange, Hermite, B-spline finite elements and C∞ generalized finite elements are assessed against the corresponding analytical solutions.
joint work with Prof. A. Simone, M. Malagu', Prof A. Duarte, more details at
http://cm.strumech.citg.tudelft.nl/simone/software/HighOrderNonLocalGradientElasticity1D/nlgre.html
Downloadable software
http://sourceforge.net/projects/nonlocal-gradient-elasticity1d/
Nonlocal Damage for quasi brittle concrete-like materials
Nonlocal Damage for quasi brittle concrete-like materials
Structural elements made of quasi-brittle materials as concrete and geomaterials may exhibit degradation of their elasticproperties, and, eventually, a reduction of strength and stiffness after a certain threshold of stress or strain is reached. Materials presenting this kind of behavior are said to be of damaging type.Numerical approaches based on classical continuum mechanics models are not suitable for studying this class of materials.In fact, as the spatial discretization is refined, strain may localize into bands with zero volume. Consequently, the bulk energydissipated in the process zone tends to zero, and the objectivity of the numerical response is lost.To overcome these drawbacks, a number of regularization techniques has been proposed. Nonlocal models belong to thisclass of methods. If the principle of local action is not assumed, the behavior of the material at a prescribed point becomesnonlocal, i.e. depending on the behavior of the particles placed in a surrounding neighborhood. In this way, one (or more)constitutive length is introduced, and a process zone can be accounted for where material points undergoing damage interact.
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