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

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.

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.

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.

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). 

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. 

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.

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. 

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.

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.