SPH-FEM simulation of shaped-charge jet penetration into double hull: a comparison study for steel and SPS

A high-speed metal jet capable to cause severe damage to a double-hull structure can be produced after detonation of a shaped charge. A Smoothed Particle Hydrodynamics (SPH) method with a mesh-free and Lagrange formulations has natural advantages in solving extremely dynamic problems. Hence, it was used to simulate the formation process of a shaped-charge jet. A Finite Element Method (FEM) is suitable for a structural analysis and is highly efficient for simulations of a complex impact process in a relatively short time; therefore, it was applied to develop a double-hull model. In this paper, a hybrid algorithm fully utilizing advantages of both SPH and FEM is proposed to simulate a metal-jet penetration into a double hull made of different materials – steel and SPS (Sandwich Plate System). First, a SPH-FEM model of a sphere impacting a plate was developed, and its results were compared with experimental data to validate the suggested algorithm. Second, numerical models of steel/SPS double-hull subjected to a shaped-charge jet were developed and their results for jet formation, a penetration process and a damage response were analysed and compared. The obtained results show that the velocity of the metal jet tended to decrease from its tip to the tail during its formation process. The jet broke into separate fragments after the first steel shell was penetrated, causing the damage zone of the second shell that grew as a result of continuous impact by fragments. As for the SPS structure, its damage zone was smaller, and the jet trended to bend becoming thinner due to the resistance of the composite layer. It was found that the polyurethane layer could have a protective effect for the second shell

Eine gitterfreie Raum-Zeit-Kollokationsmethode für gekoppelte Probleme auf Gebieten mit komplizierten Rändern

In der vorliegenden Arbeit wird eine neuartige gitterfreie Raum-Zeit-Kollokationsmethode (engl. STMCM) zur Lösung von Systemen partieller und gewöhnlicher Differentialgleichungen durch eine konsistente Diskretisierung in Raum und Zeit als Alternative zu den etablierten netzbasierten Verfahren vorgeschlagen. Die STMCM gehört zur Klasse der tatsächlich gitterfreien Methoden, die nur mit Punktwolken ohne a priori Netzkonnektivität arbeiten und kein Diskretisierungsnetz benötigen. Das Verfahren basiert auf der Interpolating Moving Least Squares Methode, die eine vereinfachte Erfüllung der Randbedingungen durch die von den Kernfunktionen erfüllte Kronecker-Delta-Eigenschaft ermöglicht, was beim größten Teil anderer netzfreier Verfahren nicht der Fall ist. Ein Regularisierungsverfahren zur Bewältigung des beim Aufbau der Kernfunktionen auftretenden Singularitätsproblems, sowie zur Berechnung aller benötigten Ableitungen der Kernfunktionen wird dargelegt. Ziel ist es dabei, eine Methode zu entwickeln, die die Einfachheit der Verfahren zur Lösung partieller Differentialgleichungen in starker Form mit den Vorteilen der gitterfreien Verfahren, insbesondere mit Blick auf gekoppelte Probleme des Ingenieurwesens mit sich bewegenden Grenzflächen, verknüpft. Die vorgeschlagene Methode wird zunächst zur Lösung linearer und nichtlinearer partieller sowie gewöhnlicher Differentialgleichungen angewendet. Dabei werden deren Konvergenz- und Genauigkeitseigenschaften untersucht. Die implizite Rekonstruktion der Gebiete mit komplizierten Rändern als Abbildungsstrategie zur Punktwolken-Streuung wird durch die Interpolation von Punktwolkendaten in zwei und drei Raumdimensionen demonstriert. Anhand der Modelle zur Simulation von Biofilm- und Tumor-Wachstumsprozessen werden Anwendungsbeispiele aus dem Bereich der Umweltwissenschaften und der Medizintechnik dargestellt.In this thesis an innovative Space-Time Meshfree Collocation Method (STMCM) for solving systems of nonlinear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an alternative to established mesh-based methods. The STMCM belongs to the class of truly meshfree methods, i.e. the methods which do not have any underlying mesh, but work on a set of nodes only without an a priori node-to-node connectivity. The STMCM is constructed using the Interpolating Moving Least Squares technique, allowing a simplified implementation of boundary conditions due to fulfilment of the Kronecker delta property by the kernel functions, which is not the case for the major part of other meshfree methods. A regularization technique to overcome the singularity-by-construction problem and compute all necessary derivatives of the kernel functions is presented. The goal is to design a method that combines the simplicity and straightforwardness of the strong-form computational techniques with the advantages of meshfree methods over the classical ones, especially for coupled engineering problems involving moving interfaces. The proposed STMCM is applied to linear and nonlinear partial and ordinary differential equations of different types and its accuracy and convergence properties are studied. The power of the technique is demonstrated by implicit reconstruction of domains with complex boundaries via interpolation of point cloud data in two and three space dimensions as a `mapping' strategy for distribution of computational points within such domains. Applications from the fields of environmental and medical engineering are presented by means of a mathematical model for simulating a biofilm growth and a nonlinear model of tumour growth processes

FAST PHYSICS-BASED SIMULATION OF VASCULAR SURGERY

Ph.DDOCTOR OF PHILOSOPH

Approximation of phase-field models with meshfree methods: exploring biomembrane dynamics

Las biomembranas constituyen la estructura de separación fundamental en las celulas animales, y son importantes en el diseño de sistemas bioinspirados. Su simulación presenta desafíos, especialmente cuando ésta implica dinámica y grandes cambios de forma o se estudian sistemas micrométricos, impidiendo el uso de modelos atomísticos y de grano grueso. El objetivo principal de esta tesis es el desarrollo de un marco computacional para entender la dinámica de biomembranas inmersas en fluido viscoso usando modelos de campo de fase. Los modelos de campo de fase introducen un campo escalar contínuo que define una interfase difusa, cuya física está codificada en las ecuaciones en derivadas parciales que la gobiernan. Estos modelos son capaces de soportar cambios dramáticos de forma y topología, y facilitan el acoplamiento de distintos fenómenos físicos. No obstante, presentan desafíos numéricos significativos, como el alto orden de las ecuaciones, la resolución de frentes móviles y abruptos, o una eficiente integración en el tiempo. En esta disertación abordamos estos puntos mediante la combinación de una discretización espacial con métodos sin malla usando las funciones base locales de máxima entropía, y una formulación variacional Lagrangiana para acoplamiento elástico-hidrodinámico. La suavidad del método sin malla genera una aproximación precisa del campo de fase y puede lidiar fácilmente con adaptatividad local, la aproximación Lagrangiana extiende de manera natural esta adaptividad a la dinámica, y la formulación variacional permite una integración variacional temporal no linealmente estable y robusta. La implementación numérica de estos métodos en un entorno de computación de alto rendimiento ha motivado el desarrollo de un nuevo código computacional. Este código integra el estado del arte de las librerías en paralelo e incorpora importantes contribuciones técnicas para solventar cuellos de botella que aparecen con el uso de métodos sin malla en computación a gran escala. El código resultante es flexible y ha sido aplicado a otros problemas científicos en varias colaboraciones que incluyen flexoelectricidad, conformado metálico, fluidos viscosos o fractura en materiales con energía de superficie altamente anisotrópica.Biomembranes are the fundamental separation structure in animal cells, and are also used in engineered bioinspired systems. Their simulation is challenging, particularly when large shape changes and dynamics are involved, or micrometer systems are considered, ruling out atomistic or coarse-grained molecular modeling. The main goal of this thesis is to develop a computational framework to understand the dynamics of biomembranes embedded in a viscous fluid using phase-field models. Phase-field models introduce a scalar continuous field to define a diffuse moving interface, whose physics is encoded in partial differential equations governing it. These models can deal with dramatic shape and topological transformations and are amenable to multiphysics coupling. However, they present significant numerical challenges, such as the high-order character of the equations, the resolution of sharp and moving fronts, or the efficient time-integration. We address all these issues through a combination of meshfree spacial discretization using local maximum-entropy basis functions, and a Lagrangian variational formulation of the coupled elasticity-hydrodynamics. The smooth meshfree approach provides accurate approximations of the phase-field and can easily deal with local adaptivity, the Lagrangian approach naturally extend adaptivity to dynamics, and the variational formulation enables nonlinearly-stable robust variational time integration. The numerical implementation of these methods in a high-performance computing framework has motivated the development of a new computer code, which integrates state-of-the-art parallel libraries and incorporates important technical contributions to overcome bottlenecks that arise in meshfree methods for large-scale problems. The resulting code is flexible and has been applied to other scientific problems in a number of collaborations dealing with flexoelectricity, metal forming, creeping flows, or fracture in materials with strongly anisotropic surface energy

SPH-FEM simulation of shaped-charge jet penetration into double hull: A comparison study for steel and SPS

This paper was accepted for publication in the journal Composite Structures and the definitive published version is available at http://dx.doi.org/10.1016/j.compstruct.2016.08.002A high-speed metal jet capable to cause severe damage to a double-hull structure can be produced after detonation of a shaped charge. A Smoothed Particle Hydrodynamics (SPH) method with a mesh-free and Lagrange formulations has natural advantages in solving extremely dynamic problems. Hence, it was used to simulate the formation process of a shaped-charge jet. A Finite Element Method (FEM) is suitable for a structural analysis and is highly efficient for simulations of a complex impact process in a relatively short time; therefore, it was applied to develop a double-hull model. In this paper, a hybrid algorithm fully utilizing advantages of both SPH and FEM is proposed to simulate a metal-jet penetration into a double hull made of different materials – steel and SPS (Sandwich Plate System). First, a SPH-FEM model of a sphere impacting a plate was developed, and its results were compared with experimental data to validate the suggested algorithm. Second, numerical models of steel/SPS double-hull subjected to a shaped-charge jet were developed and their results for jet formation, a penetration process and a damage response were analysed and compared. The obtained results show that the velocity of the metal jet tended to decrease from its tip to the tail during its formation process. The jet broke into separate fragments after the first steel shell was penetrated, causing the damage zone of the second shell that grew as a result of continuous impact by fragments. As for the SPS structure, its damage zone was smaller, and the jet trended to bend becoming thinner due to the resistance of the composite layer. It was found that the polyurethane layer could have a protective effect for the second shell

Nonlinear solid mechanics analysis using the parallel selective element-free Galerkin method

A variety of meshless methods have been developed in the last fifteen years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The main objective of this thesis is the development of an efficient and accurate algorithm based on meshless methods for the solution of problems involving both material and geometrical nonlinearities, which are of practical importance in many engineering applications, including geomechanics, metal forming and biomechanics. One of the most commonly used meshless methods, the element-free Galerkin method (EFGM) is used in this research, in which maximum entropy shape functions (max-ent) are used instead of the standard moving least squares shape functions, which provides direct imposition of the essential boundary conditions. Initially, theoretical background and corresponding computer implementations of the EFGM are described for linear and nonlinear problems. The Prandtl-Reuss constitutive model is used to model elasto-plasticity, both updated and total Lagrangian formulations are used to model finite deformation and consistent or algorithmic tangent is used to allow the quadratic rate of asymptotic convergence of the global Newton-Raphson algorithm. An adaptive strategy is developed for the EFGM for two- and three-dimensional nonlinear problems based on the Chung & Belytschko error estimation procedure, which was originally proposed for linear elastic problems. A new FE-EFGM coupling procedure based on max-ent shape functions is proposed for linear and geometrically nonlinear problems, in which there is no need of interface elements between the FE and EFG regions or any other special treatment, as required in the most previous research. The proposed coupling procedure is extended to become adaptive FE-EFGM coupling for two- and three-dimensional linear and nonlinear problems, in which the Zienkiewicz & Zhu error estimation procedure with the superconvergent patch recovery method for strains and stresses recovery are used in the FE region of the problem domain, while the Chung & Belytschko error estimation procedure is used in the EFG region of the problem domain. Parallel computer algorithms based on distributed memory parallel computer architecture are also developed for different numerical techniques proposed in this thesis. In the parallel program, the message passing interface library is used for inter-processor communication and open-source software packages, METIS and MUMPS are used for the automatic domain decomposition and solution of the final system of linear equations respectively. Separate numerical examples are presented for each algorithm to demonstrate its correct implementation and performance, and results are compared with the corresponding analytical or reference results