Modelling fracture in heterogeneous materials on HPC systems using a hybrid MPI/Fortran coarray multi-scale CAFE framework

A 3D multi-scale cellular automata finite element (CAFE) framework for modelling fracture in heterogeneous materials is described. The framework is implemented in a hybrid MPI/Fortran coarray code for efficient parallel execution on HPC platforms. Two open source BSD licensed libraries developed by the authors in modern Fortran were used: CGPACK, implementing cellular automata (CA) using Fortran coarrays, and ParaFEM, implementing finite elements (FE) using MPI. The framework implements a two-way concurrent hierarchical information exchange between the structural level (FE) and the microstructure (CA). MPI to coarrays interface and data structures are described. The CAFE framework is used to predict transgranular cleavage propagation in a polycrystalline iron round bar under tension. Novel results enabled by this CAFE framework include simulation of progressive cleavage propagation through individual grains and across grain boundaries, and emergence of a macro-crack from merging of cracks on preferentially oriented cleavage planes in individual crystals. Nearly ideal strong scaling up to at least tens of thousands of cores was demonstrated by CGPACK and by ParaFEM in isolation in prior work on Cray XE6. Cray XC30 and XC40 platforms and CrayPAT profiling were used in this work. Initially the strong scaling limit of hybrid CGPACK/ParaFEM CAFE model was 2000 cores. After replacing all-to-all communication patterns with the nearest neighbour algorithms the strong scaling limit on Cray XC30 was increased to 7000 cores. TAU profiling on non-Cray systems identified deficiencies in Intel Fortran 16 optimisation of remote coarray operations. Finally, coarray synchronisation challenges and opportunities for thread parallelisation in CA are discussed

Modelling artificial ground freezing subjected to high velocity seepage

Artificial ground freezing (AGF) is a ground improvement technique for en- suring the safety of underground construction works in water-bearing soils. High velocity water transport in coarse-grain soils can prevent the ice wall formation in brine-based ground freezing methods. This can be overcome by using expendable refrigerants such as solid carbon dioxide and liquid nitro- gen, which provide much lower temperatures. Presented here is a model for analysis and design of ground freezing by expendable refrigerants under high velocity seepage conditions. Non-local mathematical formulations of heat transfer and water flow in soils are developed within the framework of the Peridynamics theory. Their computational implementation uses an adaptive multi-grid peridynamic approach to analyse large domains efficiently. The simulations are tested successfully against several benchmarks. The devel- oped model enables reliable analyses of the effects of main geological and technological parameters on the ice-wall delivery in the presence of ground- water flow

Non-local modelling of freezing and thawing of unsaturated soils

A large part of the earth’s surface is covered by seasonally or permanently frozen soils. Considering the negative impact of climate change, future development of such regions can be underpinned by mathematical methods for accurate analysis of heat and moisture transport in freezing and thawing soils. Reported in this paper is a novel non-local formulation of water and heat transport in unsaturated soils. The formulation uses bond-based peridynamics (PD) and consists of a set of integral-difference formulations of energy and mass conservation. Specific features of freezing/thawing soils are incorporated by a combination of van Genuthcen and Clausius-Clapeyron relations. Computational results are compared with four sets of laboratory experiments to demonstrate the efficiency of the developed approach. The model can be used to analyse the effect of water flow on heat transfer in soils during thawing of permafrost soils. Further, it can be applied in modelling climate change effects, and can be used for construction of coupled physically justified models of frost heave

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.</p

Spatial variability in the mechanical properties of Gilsocarbon

The objective of this study is to investigate whether there is significant spatial variability in the mechanical properties of Gilsocarbon nuclear graphite at different sections of the billet; specifically the dynamic Poisson's ratio, dynamic shear modulus, dynamic Young's modulus and density. Similar studies have been done, usually in the context of manufacturing, to assess the quality of graphite components for nuclear reactors. In this new study, the measurements have been carried out at a much higher spatial resolution than previously. A Torness/Heysham B billet was machined into cubes so that measurements could be made across the circumference and height of the billet. ASTM standards were followed to assess the measurements of the samples. The spatial variability of material properties is described and analysed statistically. The study shows that material variability is present at different heights and circumferential locations of the billet. This discovery will have a significant impact on the structural integrity and through life performance predictions made in industry; both in current and future nuclear reactors. The computer modelling of graphite components may predict different outcomes to standard analyses (that use mean values) if this variability is incorporated into the analysis workflow; specifically through stochastic modelling