Bayesian Inversion with Open-Source Codes for Various One-Dimensional Model Problems in Computational Mechanics

The complexity of many problems in computational mechanics calls for reliable programming codes and accurate simulation systems. Typically, simulation responses strongly depend on material and model parameters, where one distinguishes between backward and forward models. Providing reliable information for the material/model parameters, enables us to calibrate the forward model (e.g., a system of PDEs). Markov chain Monte Carlo methods are efficient computational techniques to estimate the posterior density of the parameters. In the present study, we employ Bayesian inversion for several mechanical problems and study its applicability to enhance the model accuracy. Seven different boundary value problems in coupled multi-field (and multi-physics) systems are presented. To provide a comprehensive study, both rate-dependent and rate-independent equations are considered. Moreover, open source codes (https://doi.org/10.5281/zenodo.6451942) are provided, constituting a convenient platform for future developments for, e.g., multi-field coupled problems. The developed package is written in MATLAB and provides useful information about mechanical model problems and the backward Bayesian inversion setting

Influence of Moisture Content and Wet Environment on the Fatigue Behaviour of High-Strength Concrete

The influence of a wet environment on the fatigue behaviour of high-strength concrete has become more important in recent years with the expansion of offshore wind energy systems. According to the few investigations documented in the literature, the fatigue resistance of specimens submerged in water is significantly lower compared to that of specimens in dry conditions. However, it is still not clear how the wet environment and the moisture content in concrete influence its fatigue behaviour and which damage mechanisms are involved in the deterioration process. Here the results of a joint project are reported, in which the impact of moisture content in concrete on fatigue deterioration are investigated experimentally and numerically. Aside from the number of cycles to failure, the development of stiffness and acoustic emission (AE) hits are analysed as damage inductors and discussed along with results of microstructural investigations to provide insights into the degradation mechanisms. Subsequently, an efficient numeric modelling approach to water-induced fatigue damage is presented. The results of the fatigue tests show an accelerated degradation behaviour with increasing moisture content of the concrete. Further, it was found that the AE hits of specimens submerged in water occur exclusively close to the minimum stress level in contrast to specimens subjected to dry conditions, which means that additional damage mechanisms are acting with increasing moisture content in the concrete

A virtual element formulation for general element shapes

The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries. © 2020, The Author(s)

Phase field cohesive zone modeling for fatigue crack propagation in quasi-brittle materials

The phase field method has gathered significant attention in the past decade due to its versatile applications in engineering contexts, including fatigue crack propagation modeling. Particularly, the phase field cohesive zone method (PF-CZM) has emerged as a promising approach for modeling fracture behavior in quasi-brittle materials, such as concrete. The present contribution expands the applicability of the PF-CZM to include the modeling of fatigue-induced crack propagation. This study critically examines the validity of the extended PF-CZM approach by evaluating its performance across various fatigue behaviors, encompassing hysteretic behavior, S-N curves, fatigue creep curves, and the Paris law. The experimental investigations and validation span a diverse spectrum of loading scenarios, encompassing pre- and post-peak cyclic loading, as well as low- and high-cyclic fatigue loading. The validation process incorporates 2D and 3D boundary value problems, considering mode I and mixed-modes fatigue crack propagation. The results obtained from this study show a wide range of validity, underscoring the remarkable potential of the proposed PF-CZM approach to accurately capture the propagation of fatigue cracks in concrete-like materials. Furthermore, the paper outlines recommendations to improve the predictive capabilities of the model concerning key fatigue characteristics

Numerical recipes of virtual element method for phase field modeling of brittle fracture

In this work, a new and efficient virtual element formulation for non-standard phase field model of brittle fracture is presented. A multi-pass alternative minimization solution scheme based on algorithm operator splitting is utilized, which decouples the whole problem into two parts, namely, mechanical and damage sub-problems. The former is treated as elasto-static problem, while the latter one is treated as Poisson-type of reaction-diffusion equation subjected to bounded and irreversibility constraint. To demonstrate the performance of proposed formulation, several benchmark problems are studied and results are in good agreement with corresponding finite element calculations and experimental studies

Phase field cohesive zone modeling for fatigue crack propagation in quasi-brittle materials

The phase field method has gathered significant attention in the past decade due to its versatile applications in engineering contexts, including fatigue crack propagation modeling. Particularly, the phase field cohesive zone method (PF-CZM) has emerged as a promising approach for modeling fracture behavior in quasi-brittle materials, such as concrete. The present contribution expands the applicability of the PF-CZM to include the modeling of fatigue-induced crack propagation. This study critically examines the validity of the extended PF-CZM approach by evaluating its performance across various fatigue behaviors, encompassing hysteretic behavior, S-N curves, fatigue creep curves, and the Paris law. The experimental investigations and validation span a diverse spectrum of loading scenarios, encompassing pre- and post-peak cyclic loading, as well as low- and high-cyclic fatigue loading. The validation process incorporates 2D and 3D boundary value problems, considering mode I and mixed-modes fatigue crack propagation. The results obtained from this study show a wide range of validity, underscoring the remarkable potential of the proposed PF-CZM approach to accurately capture the propagation of fatigue cracks in concrete-like materials. Furthermore, the paper outlines recommendations to improve the predictive capabilities of the model concerning key fatigue characteristics

3D Virtual Elements for Elastodynamic Problems

A virtual element framework for nonlinear elastodynamics is outlined within this work. The virtual element method (VEM) can be considered as an extension of the classical finite element method. While the finite element method (FEM) is restricted to the usage of regular shaped elements, VEM allows to use non-convex shaped elements for the spatial discretization [1]. It has been applied to various engineering problems in elasticity and other areas, such as plasticity or fracture mechanics as outlined in [3, 4]. This work deals with the extension of VEM to dynamic problems. Low-order ansatz functions in two and three dimensions, with elements being arbitrary shaped, are used in this contribution. The formulations considered in this framework are based on minimization of energy, where a pseudo potential is used for the dynamic behavior. While the stiffness-matrix needs a suitable stabilization, the mass-matrix can be calculated fully through the projection part. For the implicit time integration, Newmark-Method is used. To show the performance of the method, various numerical examples in 2D and 3D are presented

Računalna mehanika u znanosti i inženjerstvu – Quo vadis

Computational Mechanics has many applications in science and engineering. Its range of application has been enlarged widely in the recent decades. Hence, nowadays areas such as biomechanics and additive manufacturing are among the new research topics, in which computational mechanics helps solve complex problems and processes. In this contribution, these emerging areas will be discussed together with new discretization schemes, e. g. virtual element method and particle methods, whereby the latter need high performance computing facilities in order to solve problems such as mixing in an accurate way. Failure analysis of structures and components is another topic that is developing fast. Here, modern computational approaches rely on the phase field method that simplifies discretizations schemes. All these approaches and methods are discussed and evaluated by means of examples.Računalna mehanika ima široku primjenu u znanosti i inženjerstvu. Njeno područje primjene se znatno povećalo u zadnjim desetljećima. Danas polja kao biomehanika i aditivna proizvodnja nova su područja istraživanja u kojima računalna mehanika pomaže rješavati složene probleme i procese. U radu se razmatraju ova granična područja zajedno s novim diskretizacijskim postupcima kao što su metoda virtualnih elemenata i metoda čestica, gdje potonja zahtijeva moćnu računalnu opremu da bi se mogli točno riješiti problemi kao što je miješanje. Analiza oštećenja konstrukcija i njenih komponenata je drugo područje koje se brzo razvija, pa se ovdje moderni računalni postupci odnose na metodu faznih polja koja pojednostavljuje diskretizacijske sheme. Svi navedeni postupci i metode su razmatrani i vrednovani u numeričkim primjerima

3D mixed virtual element formulation for dynamic elasto-plastic analysis

The virtual element method (VEM) for dynamic analyses of nonlinear elasto-plastic problems undergoing large deformations is outlined within this work. VEM has been applied to various problems in engineering, considering elasto-plasticity, multiphysics, damage, elastodynamics, contact- and fracture mechanics. This work focuses on the extension of VEM formulations towards dynamic elasto-plastic applications. Hereby low-order ansatz functions are employed in three dimensions with elements having arbitrary convex or concave polygonal shapes. The formulations presented in this study are based on minimization of potential function for both the static as well as the dynamic behavior. Additionally, to overcome the volumetric locking phenomena due to elastic and plastic incompressibility conditions, a mixed formulation based on a Hu-Washizu functional is adopted. For the implicit time integration scheme, Newmark method is used. To show the model performance, various numerical examples in 3D are presented