Aspects of computational homogenization in magneto-mechanics: Boundary conditions, RVE size and microstructure composition
TL;DR: In this article, the behavior of heterogeneous magnetorheological composites subjected to large deformations and external magnetic fields is studied and different types of boundary conditions based on the primary variables of the magneto-elastic enthalpy and internal energy functionals are applied to solve the problem at the micro-scale.
Abstract: In the present work, the behavior of heterogeneous magnetorheological composites subjected to large deformations and external magnetic fields is studied. Computational homogenization is used to derive the macroscopic material response from the averaged response of the underlying microstructure. The microstructure consists of two materials and is far smaller than the characteristic length of the macroscopic problem. Different types of boundary conditions based on the primary variables of the magneto-elastic enthalpy and internal energy functionals are applied to solve the problem at the micro-scale. The overall responses of the RVEs with different sizes and particle distributions are studied under different loads and magnetic fields. The results indicate that the application of each set of boundary conditions presents different macroscopic responses. However, increasing the size of the RVE, solutions from different boundary conditions get closer to each other and converge to the response obtained from periodic boundary conditions.
Citations
More filters
01 Jan 2016
TL;DR: Kindly say, the nonlinear finite elements for continua and structures is universally compatible with any devices to read.
Abstract: nonlinear finite elements for continua and structures is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the nonlinear finite elements for continua and structures is universally compatible with any devices to read.
445 citations
TL;DR: Hard-magnetic soft composites consist of magneto-active polymers (MAPs) where the fillers are composed of hardmagnetic (magnetically polarised) particles as mentioned in this paper.
Abstract: Hard-magnetic soft composites consist of magneto-active polymers (MAPs) where the fillers are composed of hard-magnetic (magnetically polarised) particles. These novel multifunctional materials are experiencing a great advance from the last few years. This rise has been motivated by the possibility of controlling ferromagnetic patterns during the manufacturing process. Thus, structures with programmable functionalities can be conceptualised and implemented, opening new routes into the design of smart components with great opportunities in the biomedical engineering and soft robotics fields. In this work, we provide an overview of the state of the art of such MAPs, providing the key fundamentals and reference works. To this end, we present the current synthesis and experimental characterisation methods, the different computational modelling approaches across scales, and a detailed presentation of their current potential applications. Finally, we provide an overall discussion on future perspectives.
70 citations
TL;DR: In this article, a fully-coupled two-scale finite element computational homogenization procedure is used to derive the material response at the macro-scale from the averaged response of the underlying micro-scale problem.
Abstract: In the current work, the response of heterogeneous magnetorheological elastomers (MREs) which are loaded by external magnetic fields in the absence and also in the presence of free space is studied. A fully-coupled two-scale finite element computational homogenization procedure is used to derive the material response at the macro-scale from the averaged response of the underlying micro-scale problem. Different combinations of boundary conditions, that satisfy the Hill-Mandel condition and are based on the primary variables of the magneto-elastic enthalpy and energy functionals are applied to solve the micro-scale boundary value problem. Furthermore, the influences of various microstructures on the macroscopic response of the MREs are investigated. The results indicate that the choice of microscopic boundary conditions and microstructure types can significantly affect the macroscopic responses of MREs.
25 citations
TL;DR: In this paper, the authors compare large-scale non-simplified and non-ergodic models with simplified, parametric, ergodic, and sometimes periodic models and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions.
Abstract: Due to high computational costs associated with stochastic computational homogenization, a highly complex random material microstructure is often replaced by simplified, parametric, ergodic, and sometimes periodic models. This replacement is often criticized in the literature due to unclear error resulting from the periodicity and ergodicity assumptions. In the current contribution we perform a validation of both assumptions through various numerical examples. To this end we compare large-scale non-simplified and non-ergodic models with simplified, ergodic, and periodic solutions. In addition we analyze the Hill–Mandel condition for stochastic homogenization problems and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions. As an example, we propose two novel stochastic periodic boundary conditions which possess a clear physical meaning. The effect of these novel periodic boundary conditions is also analyzed by comparing with non-ergodic simulation results.
16 citations
TL;DR: In this paper, an efficient finite element framework for modeling the finite deformations of slender magneto-active elastomers (MAE) under applied magnetic fields or currents is presented.
Abstract: In this paper, we present an efficient finite element framework for modeling the finite deformations of slender magneto-active elastomers (MAE) under applied magnetic fields or currents. For the co...
14 citations
Cites methods from "Aspects of computational homogeniza..."
...…extended to the homogenization scheme and are applied to model the macroscopic response of MAE with microstructures formed by microparticles of different sizes and distributions [Danas, 2017; Javili et al., 2013; Keip and Rambausek, 2015; Ponte Castañeda and Galipeau, 2011; Zabihyan et al., 2018]....
[...]
References
More filters
TL;DR: In this paper, an elementary account of several theoretical methods of attack is given, among them the derivation of inequalities between various moduli, and the approach is completely general and exact.
Abstract: The title problem concerns two isotropic phases firmly bonded together to form a mixture with any concentrations. An elementary account of several theoretical methods of attack is given, among them the derivation of inequalities between various moduli. The approach is completely general and exact. Additionally, the problem is fully solved when the phases have equal rigidities but different compressibilities, the geometry being entirely arbitrary.
4,141 citations
"Aspects of computational homogeniza..." refers methods in this paper
...One of the most widely used multi-scale tools to predict the beavior of inhomogeneous materials is computational homogenizaion which is based on Hill (1963) and Hill and Rice (1972) and llows to study the effective behavior of composite materials Kouznetsova et al., 20 01; Miehe and Koch, 20 02;…...
[...]
Book•
12 Sep 2000
TL;DR: In this paper, the authors present a list of boxes for Lagrangian and Eulerian Finite Elements in One Dimension (LDF) in one dimension, including Beams and Shells.
Abstract: Preface. List of Boxes. Introduction. Lagrangian and Eulerian Finite Elements in One Dimension. Continuum Mechanics. Lagrangian Meshes. Constitutive Models Solution Methods and Stability. Arbitrary Lagrangian Eulerian Formulations. Element Technology. Beams and Shells. Contact--Impact. Appendix 1: Voigt Notation. Appendix 2: Norms. Appendix 3: Element Shape Functions. Glossary. References. Index.
3,928 citations
TL;DR: Magnetorheological (MR) fluids, foams and elastomers comprise a class of smart materials whose rheological properties may be controlled by the application of an external magnetic field.
Abstract: Magnetorheological (MR) fluids, foams and elastomers comprise a class of smart materials whose rheological properties may be controlled by the application of an external magnetic field. MR fluids are liquids whose flow or shear properties are easily controlled to enable a variety of unique torque transfer or vibration control devices. MR foams, in which the controllable fluid is contained in an absorptive matrix, provide a convenient way of realizing the benefits of MR fluids in highly cost sensitive applications. MR elastomers are solid, rubber-like materials whose stiffness may be controlled to provide tunable or adjustable mounts and suspension devices.
1,104 citations
TL;DR: In this paper, a general time-independent constitutive framework for crystals capable of crystallographic shearing is presented, where no restrictions are placed on their elasticity or on the amounts of slip.
Abstract: A general time-independent constitutive framework is constructed for crystals capable of crystallographic shearing. No restrictions are placed on their elasticity or on the amounts of slip. In deriving properly-objective relations due account is taken of the separate motions of the material and lattice. A precise specification of the structure of the flow rule leads to conditions for the existence of plastic potentials, as well as to an exact statement of the slip criterion required for normality of the plastic strain-increment in conjugate variables. Objective hardening laws are also examined and sufficiency conditions obtained for uniqueness of the slip magnitudes.
935 citations
"Aspects of computational homogeniza..." refers methods in this paper
...…widely used multi-scale tools to predict the beavior of inhomogeneous materials is computational homogenizaion which is based on Hill (1963) and Hill and Rice (1972) and llows to study the effective behavior of composite materials Kouznetsova et al., 20 01; Miehe and Koch, 20 02; Zohdi and…...
[...]
TL;DR: A micro-macro strategy suitable for modeling the mechanical response of heterogeneous materials at large deformations and non-linear history dependent material behaviour is presented and its performance is illustrated by the simulation of pure bending of porous aluminum.
Abstract: A micro-macro strategy suitable for modeling the mechanical response of heterogeneous materials at large deformations and non-linear history dependent material behaviour is presented. When using this micro-macro approach within the context of finite element implementation there is no need to specify the homogenized constitutive behaviour at the macroscopic integration points. Instead, this behaviour is determined through the detailed modeling of the microstructure. The performance of the method is illustrated by the simulation of pure bending of porous aluminum. The influence of the spatial distribution of heterogeneities on the overall macroscopic behaviour is discussed by comparing the results of micro-macro modeling for regular and random structures.
848 citations
"Aspects of computational homogeniza..." refers background in this paper
...…strain setting has been studied exensively ( Terada and Kikuchi, 1995; Ponte Castañeda, 1996; Terda and Kikuchi, 2001; Yvonnet et al., 2009; Miehe et al., 1999; ouznetsova et al., 2002; Costanzo et al., 2005; Hirschberger t al., 2008; Temizer and Wriggers, 2008; Javili et al., 2013b ), mong others....
[...]