A multiscale finite element framework for additive manufacturing process modeling

This thesis describes a finite element framework for solving partial differential equations with highly varying spatial coefficients. The goal is to model the heat transfer in a heterogeneous powder medium of the selective laser melting process. An operator based framework is developed and the implementation details are discussed. The main idea of the work is based on the two level domain decomposition and construction of special operators to transfer the system between the coarse and fine levels. The system of equations is solved on a coarse level and the solution is transferred to the fine level. The operators are computed using Localized Orthogonal Decomposition (LOD) method. The method is applied to several numerical experiments and an optimal convergence rates in the H1 and L2 norms are observed. The computational efficiency of LOD is studied and its limitations are discussed

Bringing PDEs to JAX with forward and reverse modes automatic differentiation

Partial differential equations (PDEs) are used to describe a variety of physical phenomena. Often these equations do not have analytical solutions and numerical approximations are used instead. One of the common methods to solve PDEs is the finite element method. Computing derivative information of the solution with respect to the input parameters is important in many tasks in scientific computing. We extend JAX automatic differentiation library with an interface to Firedrake finite element library. High-level symbolic representation of PDEs allows bypassing differentiating through low-level possibly many iterations of the underlying nonlinear solvers. Differentiating through Firedrake solvers is done using tangent-linear and adjoint equations. This enables the efficient composition of finite element solvers with arbitrary differentiable programs. The code is available at github.com/IvanYashchuk/jax-firedrake.Comment: Published as a workshop paper at ICLR 2020 DeepDiffEq worksho

Educational Dialogue in the Conditions of Edification of Primary Education: Axiological Aspect

The article presents an empirical research of the problem of educational edification in the axiological plane, analyzes scientific literature, history, and strategies of edificatory changes in response to contemporary challenges in primary education, substantiates the features of cultural and historical and pedagogical processes related to the changes in pedagogical mentality in the context of edification and the new paradigm of education. The essence of edifying changes in the sphere of human culture and educational activity as a part of this culture are analyzed, including systematized general historical and pedagogical and general pedagogical foundations of edification in elementary education through educational dialogue as the means of active formation of a personality of the younger student. It is established that valuable and epistemological anthropocentrism determine the specifics of social philosophical analysis of the role of human-centric education, that sociocentrism of the sociological approach promotes the integration of modern theories into a unified methodological educational strategy, and that in the world a hermeneutical-dialogical tradition has been created, according to which a person develops through action and dialogue that which connects him with culture and the world. The credibility of the research results was confirmed by means of a Mann-Whitney U-test and the accuracy criterion for the differences of averages of the student's t-test for independent selections. On the basis of the research conducted the problems and directions are defined, and strategic, general pedagogical means of changes bringing edification through educational dialogue in primary education are outlined as an effective direction of its reformation

3D microstructure modelling of coating layers including grain boundaries

Nowadays, coatings have a significant role in increasing the lifetime of manufactured products. A coating layer applied to the surface of a product increases its corrosion and wear resistance. As with any other materials, coatings are subjected to damage phenomena. The damage of the coating layer usually happens because of delamination and crack propagation inside the coating layer. In order to know how to improve the coating resistance the fracture behavior is studied using finite element analysis. The system under analysis consists of two parts: the coating layer and the substrate. The Cohesive Zone Modelling technique is used to predict and describe the damage initialization and propagation. The delamination behavior is described with the cohesive elements between the coating and the substrate. Inside the coating layer, the crack usually propagates between the grains of the material. Therefore, to capture an intergranular fracture behavior first a microstructure model of the coating layer is generated, then cohesive elements are placed between the grains of the coating. For this purpose, a mathematical tool called the Voronoi diagram, which mimics the grain structure of materials, is implemented in the MATLAB script. Tensile tests and nanoindentation tests were performed in this project to validate the coating-substrate model with cohesive zone elements. The results showed that it is possible to vary the morphology of the microstructure and to change the damage behavior in the coating. The developed scripts could be used to obtain quantitatively accurate results of the coating microstructure response under loads

The MFrontGenericInterfaceSupport project

Peer reviewe

Process-Structure-Properties-Performance Modeling for Selective Laser Melting

Selective laser melting (SLM) is a promising manufacturing technique where the part design, from performance and properties process control and alloying, can be accelerated with integrated computational materials engineering (ICME). This paper demonstrates a process-structure-properties-performance modeling framework for SLM. For powder-bed scale melt pool modeling, we present a diffuse-interface multiphase computational fluid dynamics model which couples Navier–Stokes, Cahn–Hilliard, and heat-transfer equations. A computationally efficient large-scale heat-transfer model is used to describe the temperature evolution in larger volumes. Phase field modeling is used to demonstrate how epitaxial growth of Ti-6-4 can be interrupted with inoculants to obtain an equiaxed polycrystalline structure. These structures are enriched with a synthetic lath martensite substructure, and their micromechanical response are investigated with a crystal plasticity model. The fatigue performance of these structures are analyzed, with spherical porelike defects and high-aspect-ratio cracklike defects incorporated, and a cycle-amplitude fatigue graph is produced to quantify the fatigue behavior of the structures. The simulated fatigue life presents trends consistent with the literature in terms of high cycle and low cycle fatigue, and the role of defects in dominating the respective performance of the produced SLM structures. The proposed ICME workflow emphasizes the possibilities arising from the vast design space exploitable with respect to manufacturing systems, powders, respective alloy chemistries, and microstructures. By digitalizing the whole workflow and enabling a thorough and detailed virtual evaluation of the causal relationships, the promise of product-targeted materials and solutions for metal additive manufacturing becomes closer to practical engineering application.Peer reviewe