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

Scientific Conference (2022, August)

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 ... [more ▼]

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). [less ▲]

Scalable computational modelling of concrete ageing and degradation

Doctoral thesis (2021)

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 ... [more ▼]

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. [less ▲]

High-performance modeling of concrete ageing

in Proceedings in Applied Mathematics and Mechanics (2019), 19(1),

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 ... [more ▼]

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. [less ▲]