Multi-scale Modelling of Fracture in Open-Cell Metal Foams (original) (raw)
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Multiscale modelling of damage and failure in two-dimensional metallic foams
Journal of the Mechanics and Physics of Solids, 2011
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A plasticity-damage theory for large deformation of solidsI. Theoretical formulation
International Journal of Engineering Science, 1992
A coupled theory of continuum damage mechanics and finite strain plasticity (with small elastic strains) is formulated in the Eulerian reference system. The yield function used is of the von Mises type and incorporates both isotropic and kinematic hardening. An explicit matrix representation is derived for the damage effect tensor for a general state of deformation and damage. Although the theory is applicable to anisotropic d.-unage, the matrix representation is restricted to isotropy.
Recent finite element studies in plasticity and fracture mechanics
Computer Methods in Applied Mechanics and Engineering, 1979
The paper reviews recent work on fundamentals of elastic-plastic finite-element analysis and its applications to the mechanics of crack opening and growth in ductile solids. The presentation begins with a precise formu~tion of incremental equilibrium equations and their finite-element forms in a marines valid for deformations of arbitrary magnitude. Special features of computational procedures are outlined for accuracy in view of the near-incompressibility of elastic-plastic response. Applications to crack mechanics include the analysis of large plastic deformations at a progressively opening crack tip, the determination of J integral values and of limitations to I characterizations of the intensity of the crack tip field, and the determination of crack tip fields in stable crack growth.
Mecánica Computacional, Volume XXIX. Number 28. Constitutive Modeling of Materials (A
cimec.org.ar
In the truss-like Discrete Element Method (DEM) masses are considered lumped at nodal points and linked by means of unidimensional elements with arbitrary constitutive relations. In previous studies of the tensile fracture behavior of concrete cubic samples, it was verified that numerical predictions of fracture of non-homogeneous materials using DEM models are feasible and yield results that are consistent with the experimental evidence so far available. Applications that demand the use of large elements, in which extensive cracking within the elements of the model may be expected, require the consideration of the increase with size of the fractured area, in addition to the effective stress-strain curve for the element. This is a basic requirement in order to achieve mesh objectivity. Note that the degree of damage localization must be known a priori, which is a still unresolved difficulty of the nonlinear fracture analysis of non-homogeneous large structures. Results of the numerical fracture analysis of 2D systems employing the DEM are reported in this contribution and compared with predictions based on the multi-fractal theory proposed by Carpinteri et al according to which a fractal dimension, contained in the interval (1,2), defines the fracture area for a unitary thickness. The assessment of the equivalence and ranges of validity of different approaches to account for size and strain rate effects appear today as one of the most urgent areas of study in the mechanics of materials. The influences of various parameters, such as the mesh size, the strain velocity and the shape of the fracture surface are assessed by means of numerical simulation. Methods employed in the homogenization of heterogeneous materials, in which damage is expected to occur with different level of stress localization, are also examined. Finally, conclusions on the performance of the numerical procedures employed in the reported studies are presented.
Elastic-plastic nonlinearities considering fracture mechanics
solution of fracture mechanics type problems including material and geometric nonlinearities along with time-independent and time-dependent constitutive relation8 is diatxwed. The effect of solution tolerance8 on a fracture type problem arc discussed and the uaa of Green'8 strain tensor and the Piola-Kirchhoff 8tres8 tensor is caamined in a 1-D analysis and a 2-D fracture problem. A comparison of large and small displacement analysis for a ccnter-crackcd panel with elastic-plastic material is made. Small displacement, viscoplastic analysis results also arc presented for a center-cracked panel.
2006
In this report we present the formulation of the physically-based Evolving Microstructural Model of Inelasticity (EMMI). The specific version of the model treated here describes the plasticity and isotropic damage of metals as being currently applied to model the ductile failure process in structural components of the W80 program. The formulation of the EMMI constitutive equations is framed in the context of the large deformation kinematics of solids and the thermodynamics of internal state variables. This formulation is focused first on developing the plasticity equations in both the relaxed (unloaded) and current configurations. The equations in the current configuration, expressed in non-dimensional form, are used to devise the identification procedure for the plasticity parameters. The model is then extended to include a porosity-based isotropic damage state variable to describe the progressive deterioration of the strength and mechanical properties of metals induced by deformation. The numerical treatment of these coupled plasticity-damage constitutive equations is explained in detail. A number of examples are solved to validate the numerical implementation of the model.
On the coupling of anisotropic damage and plasticity models for ductile materials
International Journal of Solids and Structures, 2003
In this contribution various aspects of an anisotropic damage model coupled to plasticity are considered. The model is formulated within the thermodynamic framework and implements a strong coupling between plasticity and damage. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. The damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The model considers different interaction mechanisms between damage and plasticity defects in such a way that two-isotropic and twokinematic hardening evolution equations are derived, one of each for the plasticity and the other for the damage. An additive decomposition of the total strain into elastic and inelastic parts is adopted in this work. The elastic part is further decomposed into two portions, one is due to the elastic distortion of the material grains and the other is due to the crack closure and void contraction. The inelastic part is also decomposed into two portions, one is due to nucleation and propagation of dislocations and the other is due to the lack of crack closure and void contraction. Uniaxial tension tests with unloadings have been used to investigate the damage growth in high strength steel. A good agreement between the experimental results and the model is obtained.
Engineering Fracture Mechanics, 2011
Fracture toughness of open-cell foams consisting of tetrakaidecahedral unit cells is predicted by simulating crack propagation using a finite element (FE) based micromechanical model. The inputs to the model are the geometric parameters required to model the repeating unit cell and tensile strength of the foam ligament or strut. Cracks are created by removing certain number of cells pertaining to a crack length. The FE model consists of a local micro-scale region surrounding the crack tip. For an assumed stress intensity factor, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics for orthotropic materials. The stresses in the ligaments ahead of the crack tip calculated from this micro-model in conjunction with the tensile strength of the strut material are used to predict fracture toughness. A parametric study with different micro-model sizes and different crack lengths is performed to check for convergence of predicted Mode-I, Mode-II and mixed mode fracture toughness values. The effect of applying rotations as additional boundary conditions along with translational displacement boundary conditions on the predicted fracture toughness values is also studied.
Understanding the constraints and limitations of various potential hull structure materials and armor is paramount in design considerations of future civil and military vehicles. Developing and applying theoretical and computational models that guide the development of design criteria and fabrication processes of high-impact/ballistic-resistant materials are essential. Therefore, performing accurate computational modeling and simulation of the ballistic response of vehicles made of high-performance materials under impact/blast loading conditions is invaluable. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening (localization) and the finiteelement computations are affected considerably by the mesh size and alignment and gives non-physical descriptions of the damaged regions and failure of solids. This study is concerned with the development and numerical implementation of a novel coupled thermo-hypo-elasto, thermo-visco-plastic, and thermo-visco-damage constitutive model within the laws of thermodynamics in which implicit and explicit intrinsic material length-scale parameters are incorporated through the nonlocal gradient-dependent viscoplasticity and viscodamage constitutive equations. In this current model, the Laplacian of the effective viscoplastic strain rate and its coefficient, which introduces a missing length-scale parameter, enter the constitutive equations beside the local effective viscoplastic strain. It is shown through simulating plugging fracture in ballistic penetration of high-strength steel circular plates by hardened blunt-nose cylindrical steel projectiles that the Laplacian coefficient parameter plays the role of a localization limiter during the penetration and perforation processes allowing one to obtain meaningful values for the ballistic limit velocity (or perforation resistance) independent of the finite-element mesh density. For the corresponding local model, on the other hand, the ballistic limit continuously decreases as the mesh density increases and does not converge even for the finest mesh. KEY WORDS: nonlocal viscoplasticity, impact damage, length-scale effect, ballistic limit, mesh sensitivity, projectile perforation, adiabatic shear banding 1543-1649/12/$35.00 c ⃝ 2012 by Begell House, Inc. 503 504 Abu Al-Rub & Palazotto