Scipedia: Videos of Plenary Lectures presented at the XIII International Conference on Computational Plasticity (COMPLAS 2015)

Computational Crystal Plasticity for the Design of Material and Processes

Complas Contents — Wed, 29 Jun 2016 11:58:11 +0200

The macroscale mechanical behaviour of crystalline materials, such as polycrystalline metals and single crystal semiconductors, is dictated by the anisotropic behaviour of individual crystals/grains and their interactions with neighboring crystals or other materials. Furthermore, the elastic-plastic response of individual crystals is associated with the underlying atomic lattice structure and phenomena of dislocation glide on the slip systems and dislocation multiplication and interactions. As a result, microstructural characteristics such as grain size, shape, and orientation, have a significant effect on the macroscale mechanical properties and performance. Moreover, these microstructural features are strongly affected by the thermal-mechanical process used to create a part. Because of this, tremendous effort has been made to develop crystal plasticity models that explicitly model the crystal (grain) scale behavior to predict the local macroscale response.

In this talk, a framework for computational modelling of discretized single or polycrystal grain structures subjected to thermal-mechanical loading conditions is presented. The model is general for finite deformations with the crystal plasticity model based on dislocation motion and interactions. A parallel finite element implementation is briefly described. Then, applications including predicting microstructure evolution during large deformation processing, fatigue crack initiation, and defect formation during single crystal AlN crystal growth will be presented

Linking Mesoscale Plasticity to Atomistics

Complas Contents — Wed, 29 Jun 2016 11:51:16 +0200

Dislocation interactions and failure mechanisms at mesoscopic length scales of metallic materials are usually out of reach of atomistic simulations, thus requiring effective continuum models to describe their collective behavior and the resulting constitutive response. Coarse-graining the crystalline atomic ensemble, e.g. by means of the quasicontinuum (QC) approximation combined with techniques to accelerate atomistic simulations, provides an avenue to locally retain atomistic accuracy while being applicable to larger scales. One such method, the fully-nonlocal energy-based QC technique allows us to simulate the response of crystalline solids solely based on interatomic potentials but at significantly larger length scales than conventional molecular dynamics (MD). Here, we will apply this approach to study defect mechanisms in representative copper and aluminum single- and polycrystals. Among others, we will demonstrate the importance of coarsegrained atomistic simulations to avoid modeling artifacts inherited from nanoscale MD simulations.

Void nucleation, growth and coalescence are important mechanisms responsible for spall and ductile failure. By simulating individual nano-voids and collections of voids under hydrostatic and multiaxial loading, we investigate (i) the nucleation of defects and the associated failure mechanisms at sufficiently-large loads, and (ii) the importance of coarse-grained atomistic techniques to avoid modeling artefacts and size effects in small representative volume elements treated by conventional atomistic methods.

Grain boundaries (GBs) play a central role in polycrystal plasticity through their interactions with lattice defects as well as through GB relaxation mechanisms. We will use the aforementioned coarsegrained atomistic technique to study the behavior of GBs in three-dimensional crystals with a particular focus on the GB strength and the interaction with dislocations. As in the case of void expansion, the QC simulations enable us to consider sample sizes outside the realm of conventional atomistic techniques.

The numerical solution of large scale dynamic soil-structure interaction problems

Complas Contents — Fri, 10 Jun 2016 12:04:28 +0200

In civil engineering, and more particularly in structural mechanics, computational tools are used to understand and predict the behaviour of complete structures (bridges, buildings, …) or their individual components (cables, floors, …) in several limit states. A major complexity lies in the fact that many civil engineering structures, if not all, are in direct contact with the surrounding soil domain. The dynamic interaction between the structure and its environment often plays a crucial role and should be accounted for in numerical models. An efficient solution of dynamic soil–structure interaction (SSI) problems is indispensable, for example, for the assessment of damage to structures (buildings, nuclear power plants, bridges, tunnels) caused by earthquakes, the evaluation of annoyance in the built environment due to vibrations originating from road and railway traffic, or the design of offshore structures (wind turbines, oil and gas platforms) subjected to wind and wave loadings. These problems are of large societal and economic importance but are challenging from a computational point of view. Despite the advance of high performance computers, the numerical solution of large scale dynamic SSI problems remains very challenging and in many cases beyond current computer capabilities.

This talk gives an overview of computational techniques that have been developed within the frame of the first author’s doctoral research for solving large dynamic SSI problems. A domain decomposition approach is employed, where finite elements for the structure(s) are coupled to boundary elements for the soil, accounting for the soil’s stratification. A fast boundary element method is developed, resulting in a significant reduction of the required memory and CPU time with respect to traditional formulations. This allows for an increase of the problem size by at least one order of magnitude. Furthermore, innovative algorithms for an efficient coupling of finite and boundary elements are presented, considering three–dimensional as well as two–and–a–half– dimensional formulations. The computational performance of the proposed procedures is assessed and their suitability is illustrated through numerical examples.

The novel techniques are subsequently employed for the solution of challenging problems related to the prediction of railway induced ground vibrations. In particular, the efficiency of a stiff wave barrier for impeding the propagation of Rayleigh waves from the railway track to the surrounding buildings is studied in detail, providing fundamental insight in the underlying physical mechanism. The numerical results are validated by means of a full scale experimental test, confirming the efficacy of the proposed type of barrier.

Computation on dislocation-based crystal plasticity at micron-nano scales

Complas Contents — Fri, 10 Jun 2016 11:59:04 +0200

Plastic flow in crystal at micron-nano scales involves many new interesting issues. Some results are obtained for uniaxial compression experiments conducted on FCC single crystal micro-pillars, e.g. size effect and strain burst, etc.. In these experiments, the surfaces are transmissible and loading gradients are absent. Therefore, the strain gradient theory could not well explain these new mechanical behaviors. This in turn has led to several hypotheses based on intuitive insights, classical theory and dislocation plasticity in order to study the size effect at submicron scale. In the model proposed, mobile dislocations may escape from the free surface leading to the state of dislocation starved whereby an increase in the applied stress is necessary to nucleate or activate new dislocation sources. By performing in-situ TEM, the dislocation motion affected the material properties is observed. However, the atypical plastic behavior at submicron scales cannot be effectively investigated by either traditional crystal plastic theory or large-scale molecule dynamics simulation.

Accordingly, the discrete dislocation dynamics (DDD) coupling with finite element method (FEM), so a discrete-continuous crystal plastic model (DCM) is developed. Three kinds of plastic deformation mechanisms for the single crystal pillar at submicron scale are investigated. (1) Single arm dislocation source (SAS) controlled plastic flow. It is found that strain hardening is virtually absent due to continuous operation of stable SAS and weak dislocation interactions. When the dislocation density finally reaches stable value, a ratio between the stable SAS length and pillar diameter obeys a constant value. A theoretical model is developed to predict DDD simulation results and experimental data. (2) Confined plasticity in coated micropillars. Based on the simulation results and stochastic distribution of SAS, a theoretical model is established to predict the upper and lower bounds of stress-strain curve in the coated micropillars. (3) Dislocation starvation under low amplitude cyclic loading. This work argued that the dislocation junctions can be gradually destroyed during cyclic deformation, even when the cyclic peak stress is much lower than that required to break them under monotonic deformation. The cumulative irreversible slip is found to be the key factor of leading to junction destruction and promoting dislocation starvation under low amplitude cyclic loadings. Based on this mechanism, a proposed theoretical model successfully reproduces dislocation annihilation behavior observed experimentally for small pillar and dislocation accumulation behavior for large pillar. The predicted critical conditions of dislocation starvation agree well with the experimental data.

Computational modeling of ductile fracture processes

Complas Contents — Fri, 10 Jun 2016 11:55:58 +0200

Two fundamental questions in the mechanics and physics of fracture are: (i) What is the relation between observable features of a material’s microstructure and its resistance to crack growth? (ii) What is the relation between observable features of a material’s microstructure and the roughness of the fracture surface? An obvious corollary question is: What is the relation, if any, between a material’s crack growth resistance and the roughness of the corresponding fracture surface? 3D finite element calculations of mode I ductile crack growth aimed at addressing these questions will be discussed. In the calculations, ductile fracture of structural metals by void nucleation, growth and coalescence is modeled using an elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid. A material length scale is introduced via a discretely modeled microstructural feature, such as the spacing of inclusions that nucleate voids or the mean grain size. A particular focus will be on the use of such analyses to suggest the design of material microstructures for improved fracture resistance.

Recent advances in non-intrusive coupling strategies

Complas Contents — Fri, 10 Jun 2016 11:52:12 +0200

In the last decade, many innovative modeling or solution techniques have been introduced in the field of computational mechanics. These techniques, such as enriched finite elements or multiscale modeling, enable performing complex simulations that are out of reach of conventional finite element analysis (FEA) tools, in terms of computational or human costs. Although these techniques have proved their performance by extensive testing on academic applications, they are scarcely applied on actual industrial problems because they cannot be conveniently implemented into commercial FEA software packages. Therefore a scientific and practical challenge is to allow realistic simulation of complex industrial problems including all their physical and technological complexity. The prerequisite of the proposed non-intrusive framework is to keep unchanged the global numerical model as well as the solver used for its treatment. Therefore two or several models are used concurrently, the untouched global model and locals ones which are iteratively substituted where needed. The exchanges between the two models are such that the data should be "natural" ones for the global model such as prescribed forces. Possible applications are numerous even though the approach as to be adapted depending on the context.

In this presentation we intend focusing on some recent works and associated possibilities and difficulties regarding:

the extension of the method in explicit and implicit-explicit coupling in dynamics
the coupling between plate and 3D models for bolted and multi-bolted plates
the treatment of complex non-linear visco-plastic structures

This work is partially funded by the French National Research Agency as part of project ICARE (ANR-12-MONU-0002-04).

Data-driven computational mechanics

Complas Contents — Fri, 10 Jun 2016 11:49:24 +0200

We develop a new computing paradigm, which we refer to as data-driven computing, according to which calculations are carried out directly from experimental material data and pertinent constraints and conservation laws, such as compatibility and equilibrium, thus bypassing the empirical material modeling step of conventional computing altogether. Data-driven solvers seek to assign to each material point the state from a prespecified data set that is closest to satisfying the conservation laws. Equivalently, data-driven solvers aim to find the state satisfying the conservation laws that is closest to the data set. The resulting data-driven problem thus consists of the minimization of a distance function to the data set in phase space subject to constraints introduced by the conservation laws. We motivate the data-driven paradigm and investigate the performance of data-driven solvers by means of two examples of application, namely, the static equilibrium of nonlinear three-dimensional trusses and linear elasticity. In these tests, the data-driven solvers exhibit good convergence properties both with respect to the number of data points and with regard to local data assignment. The variational structure of the data-driven problem also renders it amenable to analysis. We show that, as the data set approximates increasingly closely a classical material law in phase space, the data-driven solutions converge to the classical solution. We also illustrate the robustness of data-driven solvers with respect to spatial discretization. In particular, we show that the data-driven solutions of finite-element discretizations of linear elasticity converge jointly with respect to mesh size and approximation by the data set.

Numerical material and plate tests: Advantages and challenges

Complas Contents — Fri, 10 Jun 2016 11:46:23 +0200

The methods of two-scale analysis based on the method of numerical material testing (NMT) and plate testing (NPT) have indisputable superiority over FE2 -type micro-macro coupling schemes, though there are some issues to be resolved or examined. In particular, the decoupling of micro- and macroscopic analyses makes the homogenization-based two-scale analysis methods computationally law-cost and thus practical in view of industrial applications, but at the same time requires us to prepare reliable macroscopic constitutive models. To identify promising research directions for two-scale analyses, we introduce three selected topics described below to discuss the advantages and challenges of NMT and NPT.

A major advantage in the first topic is that macroscopic inelastic constitutive models for a variety of composite materials can easily be determined with reference to the material models assumed for periodic microstructures (unit cells), if the small strain assumption is valid. However, NMTs with finite deformation of resins often cause some trouble. That is, even though isotropic multiplicative finite visco-plastic models is originally developed and introduced for NMTs, the formulation of the corresponding anisotropic model for macroscopic analyses is not always possible.

The second topic arises from the method of NPT for composite plates, which enables us to evaluate the relationship between macroscopic resultant stresses and generalized strains. The originally formulated microscopic problem is featured by the in-plane periodic boundary conditions, which properly reproduces all the plate’s deformation modes. If we confine ourselves to linearly elastic material behavior, even the topology optimization of microscopic plate’s cross-sections is successfully conducted to maximize the performance at macro-scale. Nonetheless, we may not meet a macroscopic plate model that can accommodate the NPT results of nonlinear material behavior assumed for the in-plane unit cell.

The third subject of study is related to the method of isogeometric analyses (IGA) for NMT and NPT. Since the treatment of the combination of different materials in IGA models is not trivial especially along with periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex-full property of IGA and the in-plane periodicity. A promising coping technique is proposed and numerically demonstrated.

Multiscale analysis applied to material modeling

Complas Contents — Fri, 10 Jun 2016 11:42:45 +0200

The presentation is aimed to cover areas related to modeling of material behaviour using different numerical schemes. Special emphasis is laid on homogenization procedures and multi- scale approaches that include inelastic microstructural deformations and development of inter- face cracks. In detail the inelastic responses of polycrystals is investigated including induced anisotropy and nonlinear hardening. The necessary numerical procedures will be discussed and examples from different areas are introduced.

Included in this presentation is the design of macroscopic constitutive equations with only few parameters that are obtained from homogenization of polycrystal assemblies. The results are validated at micro and macro scale by means of experiments. These include as well results from microstructural observation as from classical pullout tests. Typical and important industrial applications range from ceramic to ductile materials.

Efficient model order reduction in computational thermo-mechanics: Application to material forming processes

Complas Contents — Wed, 08 Jun 2016 14:59:57 +0200

Despite the impressive progresses attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional models, on which mesh-based approaches fail due to the exponential increase of degrees of freedom. Other challenging scenarios concern problems requiring many direct solutions (optimization, inverse identification, uncertainty quantification …) or those needing very fast solutions (real time simulation, simulation based control …).

We are developing a novel technique, called Proper Generalized Decomposition (PGD) based on the assumption of a separated form of the unknown fields that has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for addressing standard problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework opening new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of “Computational Vademecum”. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the “vademecum”, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.

Characterization of magneto-electric composites: product properties and multiscaling

Complas Contents — Tue, 07 Jun 2016 17:41:31 +0200

Coupling between electric and magnetic fields enables smart new devices and may find application in sensor technology and data storage. Materials showing magneto-electric (ME) coupling properties combine two or more ferroic characteristics and are known as multiferroics. Since singlephase materials show an interaction between polarization and magnetization at very low temperatures and at the best a too small ME coefficient at room temperature, composite materials become important. These ME composites consist of magnetically and electrically active phases and generate the ME coupling as a strain-induced product property. It has to be emphasized that for each of the two phases the ME coupling modulus is zero and the overall ME modulus is generated by the interaction between both phases. Here we distinguish between the direct and converse ME effect. The direct effect characterizes magnetically induced polarization, where an applied magnetic field yields a deformation of the magneto-active phase which is transferred to the electro-active phase. As a result, a strain-induced polarization in the electric phase is observed. On the other hand, the converse effect characterizes electrically activated magnetization. Several experiments on composite multiferroics showed remarkable ME coefficients that are orders of magnitudes higher than those of single-phase materials. Due to the significant influence of the microstructure on the ME effect, we derived a two-scale finite element (FE2) homogenization framework, which allows for the consideration of microscopic morphologies. A further major influence on the overall ME properties is the polarization state of the ferroelectric phase. With this in mind, a material model is implemented that considers the switching behavior of the spontaneous polarization and enables a more exact comparison to experimental measurements.

Computational design of engineering materials: an integrated approach for multiscale topological structure optimization

Complas Contents — Tue, 07 Jun 2016 17:02:28 +0200

Multiscale topological material design, aiming at obtaining optimal distribution of the material at several scales in structural materials is still a challenge. In this case, the cost function to be minimized is placed at the macro-scale (compliance function), but the design variables (material distribution) lie at both the macro-scale and the micro-scale. The large number of involved design variables and the multi-scale character of the analysis, resulting into a multiplicative cost of the optimization process, often make such approaches prohibitive, even if in 2D cases.

In this work, an integrated approach for multi-scale topological design of structural linear materials is proposed. The approach features the following properties:

The “topological derivative” is considered the basic mathematical tool to be used for the purposes of determining the sensitivity of the cost function to material removal. In conjunction with a level-set-based “algorithm” it provides a robust and well-founded setting for material distribution optimization.
The computational cost associated to the multiscale optimization problem is dramatically reduced by resorting to the concept of the online/offline decomposition of the computations. A “Computational Vademecum” containing the micro-scale solution for the topological optimization problem in a RVE for a large number of discrete macroscopic stress-states, is used for solving that problem by simple consultation.
Coupling of the optimization problem at both scales is solved by a simple iterative “fixedpoint” scheme, which is found to be robust and convergent.
The proposed technique is enriched by the concept of “manufacturability”, i.e.: obtaining sub-optimal solutions of the original problems displaying homogeneous material over finite sizes domains at the macrostructure: the “structural components”.

The approach is tested by application to some engineering examples, involving minimum compliance design of material and structure topologies, which show the capabilities of the proposed framework.

Computational inelasticity at different scales - FE technology and beyond

Complas Contents — Tue, 07 Jun 2016 16:58:02 +0200

The necessity to provide physically reasonable and mathematically sound descriptions of mechanical behaviour at different scales is without discussion. Nevertheless, for engineering design quick estimations of important quantities such as stresses and strain are needed. This is not even enough. At a larger scale, information about the overall behaviour of complex systems has to be supplied. For this reason, we need to develop computational methods which on the one hand enable a detailed material description, on the other hand allow the bridging to coarser scales without losing too much information. In the present contribution, methods such as the phase field method are combined with FE technology, and, FE technology is combined with model reduction in order to reach this goal.

Isogeometric Phase-field Modeling of Brittle and Ductile Fracture

Complas Contents — Tue, 07 Jun 2016 16:49:19 +0200

The phase-field approach to predicting crack initiation and propagation relies on a damage accumulation function to describe the phase, or state, of fracturing material. The material is in some phase between either completely undamaged or completely cracked. A continuous transition between the two extremes of undamaged and completely fractured material allows cracks to be modeled without explicit tracking of discontinuities in the geometry or displacement fields. A significant feature of these models is that the behavior of the crack is completely determined by a coupled system of partial differential equations. There are no additional calculations needed to determine crack nucleation, bifurcation, and merging.
In this presentation, we will review our current work on applying second-order and fourth-order phase-field models to quasi-static and dynamic fracture of brittle and ductile materials, within the framework of isogeometric analysis. We will present results for several two- and three-dimensional problems to demonstrate the ability of the phase-field models to capture complex crack propagation patterns.

Plasticity for crushable granular materials via DEM

Complas Contents — Tue, 07 Jun 2016 13:07:29 +0200

The mechanical behavior of granular materials is characterized by strong non-linearity and irreversibility. These properties have been described by a variety of constitutive models, a large proportion of them are developed within an elasto-plastic framework. On top of the usual grain rearrangement mechanism, the presence of crushable grains adds one extra source of irreversibility to granular materials, a source that is frequently associated with instabilities. In his context, it is very instructive to obtain incremental responses of crushable granular materials but the experimental difficulties are formidable. This contribution describes a procedure to obtain incremental responses of this type of materials using the discrete element method.

The DEM model is calibrated to represent Fontaineblau sand. The resulting granular assembly is incrementally tested starting from an initial oedometric (no lateral deformation) condition. The incremental behavior of the numerical models is studied by performing axisymmetric stress probes of equal magnitude but varying direction. Recent advances to enhance the efficiency of the numerical procedure are adopted. The cascading nature of crushing events complicates stress probe control but damping is effectively used to overcome this problem.

The contribution of grain crushing to the incremental irreversible strain is identified and separately measured. Three components of the incremental strains are distinguished: elastic, plastic-unbreakable and plastic-crushing. Particular focus is placed on the effects of crushing on the direction of plastic flow.

Linking Process, Structure, and Property in Additive Manufacturing Applications through advanced materials modeling.

Complas Contents — Mon, 06 Jun 2016 16:56:21 +0200

Additive manufacturing (AM) processes have the ability to build complex geometries from a wide variety of materials. A popular approach for metal-based AM processes involves the deposition of material particles on a substrate followed by fusion of those particles together using a high intensity heat source, e.g. a laser or an electron beam, in order to fabricate a solid part. These methods are of high priority in engineering research, especially in applications for the energy, health, and defense sectors. The primary reasons behind the rapid growth in interest for AM include: (1) the ability to create complex geometries which are otherwise cost-prohibitive or difficult to manufacture, (2) increased freedom of material composition design through the adjustment of the ratios of the composing powders, (3) a reduction in wasted materials, and (4) the fast, low-volume, production of prototype and functional parts without the additional tooling and die requirements of conventional manufacturing methods. However, the highly localized and intense nature of these processes elicits many experimental and computational challenges. These challenges motivate a strong need for computational investigation, as does the need to more accurately characterize the response of parts built using AM. The present work will discuss these challenges and methods for creating multiscale material models that account for the complex phenomena observed in the AM production environment. The linkage between process, structure, and property of AM components, e.g., anisotropic plastic behavior combined anisotropic microstructural descriptors afforded through enhanced data compression techniques, will also be discussed.