Multiscale Modeling in Solid Mechanics (original) (raw)
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Fatigue modeling of materials with complex microstructures
Computational Materials Science, 2011
A new approach and method of the analysis of microstructure-lifetime relationships of materials with complex structures is presented. The micromechanical multiscale computational analysis of damage evolution in materials with complex hierarchical microstructures is combined with the phenomenological model of fatigue damage growth. As a result, the fatigue lifetime of materials with complex structures can be determined as a function of the parameters of their structures. As an example, the fatigue lifetimes of wood modeled as a cellular material with multilayered, fiber reinforced walls were determined for different parameters of wood microstructures. In so doing, 3D hierarchical finite element models of softwood, and a computational technique, including the repeating restart and model change procedures, have been employed to model the fatigue response of latewood.
A Time Multiscale Decomposition in Cyclic Elasto-Plasticity
For the numerical simulation of time-dependent problems, recent works suggest the use of a time marching scheme based on a tensorial decomposition of the time axis. This time-separated representation is straightforwardly introduced in the framework of the Proper Generalized Decomposition (PGD). The time coordinate is transformed into a multi-dimensional time through new separated coordinates, the micro and the macro times. From a physical viewpoint, the time evolution of all the quantities involved in the problem can be followed along two time scales, the fast one (micro-scale) and the slow one (macro-scale). In this paper, the method is applied to compute the quasi-static response of an elasto-plastic structure under cyclic loadings. The study shows the existence of a physically consistent temporal decomposition in computational cyclic plasticity. Such micro-macro characterization may be particularly appealing in high-cycle loading analyses, such as aging and fatigue, addressed in a future work in progress.
SPECIAL ISSUE MULTISCALE MECHANICAL MODELING OF COMPLEX MATERIALS AND ENGINEERING APPLICATIONS 2
2011
The present volume is a special issue of selected papers from the second edition of a special symposium session on Multiscale Mechanical Modelling of Complex Materials and Engineering Applications, organized within the frame-The early focus of the symposium was to bridge the gap between solid mechanics and material science, providing a forum for the presentation of fundamental, theoretical, experimental, and practical aspects of mechanical modelling of materials with complex microstructures and complex behaviour. This volume follows the issues already edited in connection with the THERMEC 2006 conference of the same symposium session held in Vancouver, Canada, in July 2006. 1 Each contribution has undergone a standard review process, and only papers that received positive reviews by at least two international referees have been included.
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.
Modelling of Anisotropic Fatigue
2016
A continuum approach for anisotropic fatigue is described. The approach is based on the idea of a moving endurance surface in the stress space where the movement is described by a back-stress type tensor. The evolution associated with the movement is described by a rate type equation. In addition, damage accumulation is governed by a rate type evolution equation, thus facilitating its use under arbitrary complex loading conditions. The main emphasis of this paper is to discuss the possible forms of the endurance surface and pertinent evolution equations to model high-cycle anisotropic fatigue. Suggestions towards a unified model capturing the low-cycle regime are also given.
A continuum mechanics model for mechanical fatigue analysis
Computational Materials Science, 2005
In this paper, a thermo-mechanical constitutive model for the predictions of fatigue in structures using the finite element method is formulated. The model is based on the damage mechanics of the continuous medium and allows the treatment in a unified way of coupled phenomena such as fatigue with damage, plasticity, viscosity and temperature effects. Basically it is gotten sensitive models to cyclic loads starting from classical non-linear constitutive formulations incorporating the special variable influenced by the characteristics of the cyclic load. A formulation based on the theories of damage and plasticity is developed. The necessary modifications of these theories are outlined in order to include the fatigue phenomena. A brief description of the finite element implementation is given. Finally, results of the performance of the proposed model are shown through the simple fatigue test and the fatigue analysis of an aluminium engine alternator support.
Use of constitutive equations for fatigue simulations
The mechanical phenomenon known as fatigue consists in the loss of material strength, and consequent failure, due to the effect of periodic loads. Fatigue is characterized, among other parameters, by the number of cycles, load amplitude and reversion index. Material failure is produced by an inelastic behavior, micro-cracking and crack coalescence, which lead to the final collapse of structural parts. This paper disseminates on the use of constitutive equations of plasticity and damage to numerically simulate the entire range of fatigue: high-cycle, low-cycle and ultra-low-cycle. The theoretical model will be presented as well as some numerical examples.
Physically based multiscale-viscoplastic model for metals and steel alloys: theory and computation
2005
The main requirement of large deformation problems such as high-speed machining, impact, and various primarily metal forming, is to develop constitutive relations which are widely applicable and capable of accounting for complex paths of deformation. Achieving such desirable goals for material like metals and steel alloys involves a comprehensive study of their microstructures and experimental observations under different loading conditions. In general, metal structures display a strong rate-and temperature-dependence when deformed non-uniformly into the inelastic range. This effect has important implications for an increasing number of applications in structural and engineering mechanics. The mechanical behavior of these applications cannot be characterized by classical (rate-independent) continuum theories because they incorporate no 'material length scales'. It is therefore necessary to develop a rate-dependent (viscoplasticity) continuum theory bridging the gap between the classical continuum theories and the microstructure simulations. Physically based vicoplasticity models for different types of metals (body centered cubic, face centered cubic and hexagonal close-packed) and steel alloys are derived in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the rate-dependent behavior. The concept of thermal activation energy, dislocations interactions mechanisms and the role of dislocations dynamics in crystals are used in the derivation process taking into consideration the contribution of the plastic strain evolution of dislocation density to the flow stress of polycrystalline metals. Material length scales are implicitly introduced into the governing equations through material rate-dependency (viscosity). The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh due to the successful incorporation of the material length scale in the model formulations. It is shown that the model predicted results compare very well with different experimental data over a wide range of temperatures (77K o-1000K o) and strain rates (10-3-10 4 s-1). It is also concluded from this dissertation that the width of localization zone (shear band) exhibits tremendous changes with different initial temperatures (i.e., different initial viscosities and accordingly different length scales).
Materials Science and Engineering: A, 2010
Forged components exhibit good mechanical strength, particularly in terms of high cycle fatigue properties. This is due to the specific microstructure resulting from large plastic deformation as in a forging process. The goal of this study is to account for critical phenomena such as the anisotropy of the fatigue resistance in order to perform high cycle fatigue simulations on industrial forged components. Standard high cycle fatigue criteria usually give good results for isotropic behaviors but are not suitable for components with anisotropic features. The aim is to represent explicitly this anisotropy at a lower scale compared to the process scale and determined local coefficients needed to simulate a real case. We developed a multi-scale approach by considering the statistical morphology and mechanical characteristics of the microstructure to represent explicitly each element. From stochastic experimental data, realistic microstructures were reconstructed in order to perform high cycle fatigue simulations on it with different orientations. The meshing was improved by a local refinement of each interface and simulations were performed on each representative elementary volume. The local mechanical anisotropy is taken into account through the distribution of particles. Fatigue parameters identified at the microscale can then be used at the macroscale on the forged component. The linkage of these data and the process scale is the fiber vector and the deformation state, used to calculate global mechanical anisotropy. Numerical results reveal an expected behavior compared to experimental tendencies. We proved numerically the dependence of the anisotropy direction and the deformation state on the endurance limit evolution.