Numerical simulation based on FEM/MLS coupling for solid mechanics

This paper presents the development of Meshless Methods based on the weighted least squares approximation (MLS) [1,3,14] to solve 2D mechanical problems. A particular construction support of weight functions involved in the construction of the MLS shape functions is elaborated. We propose a numerical simulation based on the coupling between the FEM and the MLS method. A Huerta et al. formulation is used to build the MLS shape function in the transition area FEM/MLS

Three-dimensional and Two-dimensional Modelling of Springback in the Single-pass Conventional Metal Spinning of Cones

Parts for industrial and domestic use have been formed by means of the metal spinning process as far back as the ancient Egyptians. Research into the field was initially concentrated on experimental and theoretical studies. The development of numerical methods alongside the increasing capabilities of modern computing brought about numerical investigations into the process. This thesis presents a three-dimensional numerical model developed using the finite element method. In addition, a formability parameter is proposed and a formability surface linking the round off radius, rotational speed and half cone angle of the mandrel is presented. This thesis also presents the first numerical parametric study into springback using a three-dimensional finite element model

Interfaces in crystalline materials

Interfaces such as grain boundaries in polycrystalline as well as heterointerfaces in multiphase solids are ubiquitous in materials science and engineering. Far from being featureless dividing surfaces between neighboring crystals, elucidating features of solid-solid interfaces is challenging and requires theoretical and numerical strategies to describe the physical and mechanical characteristics of these internal interfaces. The first part of this manuscript is concerned with interface-dominated microstructures emerging from polymorphic structural (diffusionless) phase transformations. Under high hydrostatic compression and shock-wave conditions, the pressure-driven phase transitions and the formation of internal diffuse interfaces in iron are captured by a thermodynamically consistent framework for combining nonlinear elastoplasticity and multivariant phase-field approach at large strains. The calculations investigate the crucial role played by the plastic deformation in the morphological and microstructure evolution processes under high hydrostatic compression and shock-wave conditions. The second section is intended to describe such imperfect interfaces at a finer scale, for which the semicoherent interfaces are described by misfit dislocation networks that produce a lattice-invariant deformation which disrupts the uniformity of the lattice correspondence across the interfaces and thereby reduces coherency. For the past ten years, the constant effort has been devoted to combining the closely related Frank-Bilby and O-lattice techniques with the Stroh sextic formalism for the anisotropic elasticity theory of interfacial dislocation patterns. The structures and energetics are quantified and used for rapid computational design of interfaces with tailored misfit dislocation patterns, including the interface sink strength for radiation-induced point defects and semicoherent interfaces.Comment: 138 pages, 70 figure

Physics-informed neural networks for data-free surrogate modelling and engineering optimization – An example from composite manufacturing

Engineering components require an optimization of design and manufacturing parameters to achieve maximum performance – usually involving numerous physics-based simulations. Optimizing these parameters is a resource-intensive endeavor, though, especially in high-dimensional scenarios or for complex materials like fiber reinforced plastics. Surrogate models are able to reduce the computational effort, however, data generation still proves to be resource-intensive. Additionally, their data-driven nature may lead to physically implausible results in limit cases. As a remedy, physics-informed neural networks (PINNs) include known physics into the training for enhanced surrogate reliability. This allows to cast a physically consistent, data- and mesh-free manufacturing surrogate for variable process conditions and material parameters. The paper demonstrates how PINNs can be embedded in a design-framework to enhance process understanding, to devise engineering-interpretable processing windows and to support time-efficient process optimization at the example of a thermochemical manufacturing process with fiber-reinforced composite materials. In this work, an over 500-fold speed up of the process optimization is achieved compared to conventional approaches

A neural network-based data-driven local modeling of spotwelded plates under impact

Solving large structural problems with multiple complex localized behaviors is extremely challenging. To address this difficulty, both intrusive and non-intrusive Domain Decomposition Methods (DDM) have been developed in the past, where the refined model (local) is solved separately in its own space and time scales. In this work, the Finite Element Method (FEM) at the local scale is replaced with a data-driven Reduced Order Model (ROM) to further decrease computational time. The reduced model aims to create a low-cost, accurate and efficient mapping from interface velocities to interface forces and enable the prediction of their time evolution. The present work proposes a modeling technique based on the Physics-Guided Architecture of Neural Networks (PGANNs), which incorporates physical variables other than input/output variables into the neural network architecture. We develop this approach on a 2D plate with a hole as well as a 3D case with spot-welded plates undergoing fast deformation, representing nonlinear elastoplasticity problems. Neural networks are trained using simulation data generated by explicit dynamic FEM solvers. The PGANN results are in good agreement with the FEM solutions for both test cases, including those in the training dataset as well as the unseen dataset, given the loading type is present in the training set

Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations

Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov type formulation brings the mathematical rigor (the well-posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization)

Multi-field modeling and simulation of fiber-reinforced polymers

This work proposes a new numerical approach for analyzing the behavior of fiber-reinforced materials, which have gained popularity in various applications. The approach combines theories and methods to model the fracture behavior of the polymeric matrix and the embedded fibers separately, and includes a modified plasticity model that considers the temperature-dependent growth of voids. Tests are conducted to explore different types and sequences of failure in long fiber-reinforced polymers

Numerical modelling for flexible pavement materials applying advanced finite element approach to develop Mechanistic-Empirical design procedure

The mechanistic-empirical design method of flexible pavement is studied. Series of numerical simulation on different combination of pavement layers is conducted. Two different loading combinations are examined and different materials properties are included. Finite element method is employed to consider especially developed constitutive model to reflect shakedown behaviour of granular materials used in base layers. In final step of simulation effects of soil-asphalt interaction is studied. Results are compared and concluded