Homogenisation of Microheterogeneous Materials Considering Interfacial Delamination at Finite Strains

In modern engineering, composite materials gained importance because of their specific properties requested by the individual application. They consist of inclusions such as particles or fibres which are introduced into a binding matrix material in order to “design” special material behaviour. In case of particle inclusions, typical materials are concrete, aluminum-boron or rubber filled with carbon. Fibre reinforced composites are typically stiffened by glass-, carbon- or aramid fibres. Recently, fibre reinforced metals are also subject to detailed investigation and application. In all cases the mechanical behaviour on the micro level defines the resulting material behaviour on the macro scale, which is needed from an engineering point of view in an arbitrary design process. The effective properties of the overall material depend on the geometry of the microstructure and the material properties of the constituents. In case of finite strains one can observe interfacial degradation in a cohesive zone between the matrix material and the inclusions. In this paper we focus on the homogenisation process of such materials with interfacial delamination. Here the difficulties arise from the geometrical and material nonlinearities. Even for linear elasticity this homogenisation can hardly be done analytically. Therefore we apply the finite element method to get a numerical approximation for the mechanical behaviour of a representative volume element (RVE). The homogenisation then is done with a statistically representative set of RVEs. In order to increase the efficiency and accuracy of the computations the finite element meshes are refined adaptively using non-conforming elements

Computational Homogenisation of Polycrystalline Elastoplastic Microstructures at Finite Deformation

During sheet bulk metal forming processes, both flat geometries and three-dimensional structures change their shape while undergoing large plastic deformations. As for metal forming processes, FE-simulations are often done before in-situ experiments, a very accurate model for respective structures is required, performing well at small geometries possessing small curvatures as forms with wide as well as lateral characteristics.Because of the crystalline nature of metals, certain anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level.A crystal plasticity model for finite deformations is used to model the behaviour of polycrystalline materials in representative volume elements (RVEs) on the microstructure. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. Through homogenisation and optimisation techniques, effective stress-strain curves are determined and can be compared to results from real forming processes, leading to an effective elastoplastic material model which is suitable for processes in the sheet bulk metal forming field

Efficient multiscale modeling of heterogeneous materials using deep neural networks

Material modeling using modern numerical methods accelerates the design process and reduces the costs of developing new products. However, for multiscale modeling of heterogeneous materials, the well-established homogenization techniques remain computationally expensive for high accuracy levels. In this contribution, a machine learning approach, convolutional neural networks (CNNs), is proposed as a computationally efficient solution method that is capable of providing a high level of accuracy. In this work, the data-set used for the training process, as well as the numerical tests, consists of artificial/real microstructural images (“input”). Whereas, the output is the homogenized stress of a given representative volume element RVE . The model performance is demonstrated by means of examples and compared with traditional homogenization methods. As the examples illustrate, high accuracy in predicting the homogenized stresses, along with a significant reduction in the computation time, were achieved using the developed CNN model

A numerical framework for modelling tire mechanics accounting for composite materials, large strains and frictional contact

Presentation delivered by Alejandro Cornejo from CIMNE during the 17th International Conference on Computational Plasticity, Fundamentals and Applications (COMPLAS) taking place from 5 – 7 of September in Barcelona, Spain.The Fatigue4Light project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 10100684

Biocompatibility and degradation of the open-pored magnesium scaffolds LAE442 and La2

Porous magnesium implants are of particular interest for application as resorbable bone substitutes, due to their mechanical strength and a Young's modulus similar to bone. The objective of the present study was to compare the biocompatibility, bone and tissue ingrowth, and the degradation behaviour of scaffolds made from the magnesium alloys LAE442 (n= 40) and Mg-La2 (n= 40)in vivo. For this purpose, cylindrical magnesium scaffolds (diameter 4 mm, length 5 mm) with defined, interconnecting pores were produced by investment casting and coated with MgF2. The scaffolds were inserted into the cancellous part of the greater trochanter ossis femoris of rabbits. After implantation periods of 6, 12, 24 and 36 weeks, the bone-scaffold compounds were evaluated usingex vivo µCT80 images, histological examinations and energy dispersive x-ray spectroscopy analysis. The La2 scaffolds showed inhomogeneous and rapid degradation, with inferior osseointegration as compared to LAE442. For the early observation times, no bone and tissue could be observed in the pores of La2. Furthermore, the excessive amount of foreign body cells and fibrous capsule formation indicates insufficient biocompatibility of the La2 scaffolds. In contrast, the LAE442 scaffolds showed slow degradation and better osseointegration. Good vascularization, a moderate cellular response, bone and osteoid-like bone matrix at all implantation periods were observed in the pores of LAE442. In summary, porous LAE442 showed promise as a degradable scaffold for bone defect repair, based on its degradation behaviour and biocompatibility. However, further studies are needed to show it would have the necessary mechanical properties required over time for weight-bearing bone defects

A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete

A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility

Nonlinearity of Mechanochemical Motions in Motor Proteins

The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors - myosin V and kinesin KIF1A - and performed numerical investigations of their conformational relaxation properties within the coarse-grained elastic network approximation. We have found that the linearity assumption is deficient for ligand-induced conformational motions and can even be violated for characteristic thermal fluctuations. The deficiency is particularly pronounced in KIF1A where the normal mode description fails completely in describing functional mechanochemical motions. These results indicate that important assumptions of the theory of protein dynamics may need to be reconsidered. Neither a single normal mode, nor a superposition of such modes yield an approximation of strongly nonlinear dynamics.Comment: 10 pages, 6 figure

FitEM2EM—Tools for Low Resolution Study of Macromolecular Assembly and Dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top

The Mechanism of Ubiquitination in the Cullin-RING E3 Ligase Machinery: Conformational Control of Substrate Orientation

In cullin-RING E3 ubiquitin ligases, substrate binding proteins, such as VHL-box, SOCS-box or the F-box proteins, recruit substrates for ubiquitination, accurately positioning and orienting the substrates for ubiquitin transfer. Yet, how the E3 machinery precisely positions the substrate is unknown. Here, we simulated nine substrate binding proteins: Skp2, Fbw7, β-TrCP1, Cdc4, Fbs1, TIR1, pVHL, SOCS2, and SOCS4, in the unbound form and bound to Skp1, ASK1 or Elongin C. All nine proteins have two domains: one binds to the substrate; the other to E3 ligase modules Skp1/ASK1/Elongin C. We discovered that in all cases the flexible inter-domain linker serves as a hinge, rotating the substrate binding domain, optimally and accurately positioning it for ubiquitin transfer. We observed a conserved proline in the linker of all nine proteins. In all cases, the prolines pucker substantially and the pucker is associated with the backbone rotation toward the E2/ubiquitin. We further observed that the linker flexibility could be regulated allosterically by binding events associated with either domain. We conclude that the flexible linker in the substrate binding proteins orients the substrate for the ubiquitin transfer. Our findings provide a mechanism for ubiquitination and polyubiquitination, illustrating that these processes are under conformational control