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)

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

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

Virtual Element Method for Cross-Wedge Rolling during Tailored Forming Processes

In this work we present an application of the virtual element method (VEM) to a forming process of hybrid metallic structures by cross-wedge rolling. The modeling of that process is embedded in a thermomechanical framework undergoing large deformations, as outlined in [1, 2]. Since forming processes include mostly huge displacements within a plastic regime, the difficulty of an accurate numerical treatment arises. As shown in [3], VEM illustrates a stable, robust and quadratic convergence rate under extreme loading conditions in many fields of numerical mechanics. Numerically, the forming process is achieved by assigning time-dependent boundary conditions instead of modeling the contact mechanics yielding to a simplified formulation. Based on the two metallic combinations of steel and aluminum, different material properties are considered in the simulations. The purpose of this contribution is to illustrate the effectiveness of such a non-contact macroscopic framework by employing suitable boundary conditions within a virtual element scheme. A comparison with the classical finite element method (FEM) is performed to demonstrate the efficiency of the chosen approach. The numerical examples proposed in this work stem out from the DFG Collaborative Research Centre (CRC) 1153 “Process chain for the production of hybrid high-performance components through tailored forming”

Multilevel Global-Local techniques for adaptive ductile phase-field fracture

This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global-Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic-plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic-plastic fracturing response. (ii) The main objective of the second model is to introduce an adoption of the Global-Local approach toward the multilevel local setting. To this end, an elastic-plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic-plastic material and the next local domain is modeled due to the fracture state. To further reduce the computational cost, predictor-corrector adaptivity within Global-Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic-plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting with two-way adaptivity procedure. The overall response of the Global-Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples.Comment: 50 pages, 24 Figures, 4 Table