A new formulation for air-blast fluid–structure interaction using an immersed approach: part II—coupling of IGA and meshfree discretizations

Abstract

In this two-part paper we begin the development of a new class of methods for modeling fluid-structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numeri-B Y. Bazilevs

A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves

“…The demonstrated effectiveness of our formulation for shell-against-shell contact looks promising in the context of studying damage resulting from impacts against thin composite structures, which some of us have recently become interested in [58]. The formulation’s compatibility with point cloud geometry descriptions also leads us to consider applying it to meshfree discretizations of structures fragmenting after blast loading [59, 60], but the use of an unbounded potential function in explicit computations may lead to difficulties, warranting modifications to the present framework, such as reverting to a non-singular force–separation law.…”

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“…Researchers in engineering fields have been developing more general meshfree methods that can be used to solve a wide range of PDE systems. The Reproducing Kernel Particle Method (RKPM) developed by Liu et al [1995] is a successful meshfree method, which has been widely tested in engineering problems for modeling various mechanical processes of practical materials, including non-linear deforming solids [Chen et al 1996], fragment-impact problems [Guan et al 2009], air-blast-structure interaction [Bazilevs et al 2017;Moutsanidis et al 2018]. The RKPM can be viewed as a variation of the MLS approach, whose idea has been used in graphics Müller et al [2004] for estimating deformation gradient of elastoplastic and melting solids.…”

An immersogeometric formulation for free-surface flows with application to marine engineering problems

“…Since that, the research on immersed methods has been growing significantly. Some recent developments using immersed approach can be found in [28][29][30][31][32][33][34].…”