Nonlinear analysis of thin-walled structures based on tangential differential calculus with FEniCSx

We present an approach to implement the Tangential Differential Calculus (TDC) for a variety of thin-walled structures (beams, membranes, shells) in the framework of nonlinear kinematics and/or material behaviour. In contrast to classical formulations the TDC describes kinematics, equilibrium and constitutive relation of the thin structure (as two-dimensional manifold) on the basis of a full three-dimensional deformation state. This allows to introduce the undeformed configuration of e.g. a shell directly in terms of a mesh of topological dimension 2 and geometrical dimension 3. Of particular interest is the use of finite elements of higher-order geometrical order to capture the (interpolated) curvature of the manifold with high accuracy. Numerical examples and reference implementations of this work to support nonlinear stress and post-buckling analyses (using a realisation of the classical arc-length method in FEniCSx) will be provided as a part of the package dolfiny (https://github.com/michalhabera/dolfiny)

The FEniCS Project on AWS Graviton3

We show initial performance results executing the FEniCS Project finite element software on Amazon Web Services (AWS) c7g instances with Graviton3 processors. Graviton3 processors are based on the ARM64 instruction set and provide Scalable Vector Extensions (SVE) for single instruction, multiple data (SIMD) operations. The c7g instances include a fast Elastic Fabric Adaptor (EFA) interconnect for low-latency high-bandwidth Message Passing Interface (MPI) based parallel communication. Comparing clang 15 and GCC 12 series compilers for compiling a high-order elasticity finite element kernel our results show that GCC emitted more vectorised loops with variable width SVE instructions than clang. The runtime performance of the GCC compiled kernel was 20% faster than the clang compiled kernel. We also tested multi-node weak scalability of a Poisson solver on the EFA interconnect up to 512 MPI processes. We find that overall performance and weak scalability of the AWS provisioned cluster is similar to a dedicated AMD EPYC x86-64 HPC installed at the University of Luxembourg.Preprint for distribution at Supercomputing' 2

Scalable computational modelling of concrete ageing and degradation

The typical lifespan of concrete structures ranges from tens to hundreds of years. During such a long period of time many external factors including weather conditions, loading history or environmental pollution. play a crucial role in concrete health and serviceability state. Prediction (via the means of computer simulation) of the long-term material properties of concrete can thus provide valuable insights and lead to better reusability of construction components. Several very complex multi-physics models were developed in the past decades for this purpose. While these models usually include a wide range of phenomena, the numerical problem which has to be solved poses major challenges and significantly increases required computational time. This makes a predictive simulation of any larger-scale structure non-feasible. On the other hand, commercial codes (ABAQUS, ANSYS, etc.) either lack the material models for a more accurate creep prediction or provide custom material routines which are not computationally optimised. In addition, a specific model and discretisation approach often requires a very specific choice of solvers and preconditioners in order to achieve good parallel scaling properties, so much required for execution on modern HPC infrastructures. In this thesis a 3-D material model for a reinforced concrete based on the micro-prestress solidification theory (MPS) of Bažant, continuum damage mechanics and the temperature and humidity model of Kunzel is efficiently implemented in the finite-element software FEniCS. A high-performance code for the assembly of residual and tangent operators is automatically derived using automatic differentiation capabilities (AD) of FEniCS. Seamless parallel integration with the linear algebra solvers suite PETSc then offers a wide range of solvers. The combination of AD, code generation techniques (e.g. FEniCS), and parallel performance of PETSc solvers for predictive modelling of concrete degradation is not present in the existing literature. It is believed that the results presented here allow the study of reusability and degradation of concrete components also for larger structures, where the conventional existing approaches cannot provide a reasonable computation time

Modeling of porous metal oxide layer growth in the anodization process

Under suitable conditions anodic metal oxidation leads to growth of complex porous structures. The initiation and growth of these structures is an interesting and challenging task for electrochemical modelling. One must identify chemical reactions in a multi-phase framework, derive a proper partial differential equations and solve them in time dependent domains. In this work, electrochemical model for the oxide growth in nano scales is presented. Physically motivated equations are formulated with precise mathematical meaning and existence of solutions is studied. Electrostatic potential fulfilling high-field conduction law and interfacial jump conditions is sought for. Numerical discretization is performed with the use of finite element method and free boundaries are tracked with characteristic level-set functions. Basic mechanism governing the growth of porous structures is given and numerical experiments are explained on it's basis. This thesis presents novel contributions to the electrochemical and mathematical picture of nanopores growth

Modelování růstu porézních vrstev oxidů kovů v procesu anodické oxidace

Pri vhodných podmienkach vedie anodická oxidácia k rastu komplexných poréznych štruktúr. Zrod a rast týchto štruktúr je zaujímavou a náročnou úlohou pre elektrochemické modelovanie. Je nutné identifikovať chemické reakcie vo viacfázovom systéme, odvodiť pre ne parciálne diferenciálne rovnice a riešiť ich v časovo závislých oblastiach. V tejto práci je prezentovaný elektrochemický model pre rast oxidu v nano škálach. Fyzikálne motivované rovnice sú formulované s presným matematickým významom a je skúmaná existencia riešenia. Je hľadaný elektrostatický potenciál splňujúci zákon vodivosti vo vysokých elektrických poliach a skokové podmienky na rozhraniach. Numerická diskretizácia je zavedená pomocou metódy konečných prvkov a voľné hranice sú sledované pomocou level- set metódy. Je podaný základný mechanizmus riadiaci rast poréznych štruktúr a numerické experimenty sú vysvetlené na jeho základe. Táto diplomová práca prináša nové poznatky do súčasného elektrochemického a matematického pohľadu na rast nanopórov.Under suitable conditions anodic metal oxidation leads to growth of complex porous structures. The initiation and growth of these structures is an interesting and challenging task for electrochemical modelling. One must identify chemical reactions in a multi-phase framework, derive a proper partial differential equations and solve them in time dependent domains. In this work, electrochemical model for the oxide growth in nano scales is presented. Physically motivated equations are formulated with precise mathematical meaning and existence of solutions is studied. Electrostatic potential fulfilling high-field conduction law and interfacial jump conditions is sought for. Numerical discretization is performed with the use of finite element method and free boundaries are tracked with characteristic level-set functions. Basic mechanism governing the growth of porous structures is given and numerical experiments are explained on it's basis. This thesis presents novel contributions to the electrochemical and mathematical picture of nanopores growth.Mathematical Institute of Charles UniversityMatematický ústav UKFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

High-performance modeling of concrete ageing

Long-term behaviour of concrete structural elements is very important for evaluation of its health and serviceability range. The phenomena that must be considered are complex and lead to coupled multiphysics formulations. Such formulations are difficult not only from physical perspective, but also from computational perspective. In this contribution attention to computational efficiency and effective implementation is payed. Presented model for concrete ageing is based on microprestress-solidification (MPS) theory of Bazant [1], Kunzel’s model for heat and moisture transport [2] and Mazars model for damage [3]. Ageing linear viscoelastic response, which is immanent to MPS theory and concrete creep, leads to ordinary differetial equation for internal variables solved for every quadrature/nodal point. Numerical structure of the finite element discretisation is examined. Few simplifications on physical model lead to a very efficient linear algebra problem for which standard preconditioned Krylov solvers are reviewed. In parallel, weak and strong scaling tests are performed. All results are produced within open-source finite element framework FEniCS [4]. These models are usually a basis for more involved thermo-hygro-chemo-mechanical (THCM) models with migrating chemical species. It is anticipated, that presented results will help practitioners or other structural engineerers with the choice of suitable and efficient methods for long-term concrete modeling

firedrakeproject/tsfc: The Two Stage Form Compiler

<p>This release is specifically created to document the version of tsfc used in a particular set of experiments using Firedrake. Please do not cite this as a general source for Firedrake or any of its dependencies. Instead, refer to https://www.firedrakeproject.org/citing.html</p&gt

firedrakeproject/fiat: The Finite Element Automated Tabulator

<p>This release is specifically created to document the version of fiat used in a particular set of experiments using Firedrake. Please do not cite this as a general source for Firedrake or any of its dependencies. Instead, refer to https://www.firedrakeproject.org/citing.html</p&gt