Distribution-enhanced homogenization framework and model for heterogeneous elasto-plastic problems |
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| Institution: | 1. Department of Civil Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, United States;2. Theoretical Division, Los Alamos National Laboratory, United States;1. Department of Physics, University of Évora, Colégio Luís António Verney, Rua Romão Ramalho, 59, 7002-554 Évora, Portugal;2. Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423 Weimar, Germany;3. Mechanical Engineering Department, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal;4. ICIST, Instituto Superior Técnico, Lisboa, Portugal;1. Institute of Oceanography, National Taiwan University, Taipei, Taiwan;2. Institute of Marine Geology and Chemistry, National Sun Yat-sen University, Kaohsiung, Taiwan;3. Institute of Marine Environmental Chemistry and Ecology, National Taiwan Ocean University, Keelung, Taiwan;1. College of Information Science and Engineering, Ocean University of China, 23 Xianggang Road East, Qingdao 266100, China;2. Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S1 3JD, UK;3. Department of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK;4. Advanced Manufacturing Research Centre with Boeing, The University of Sheffield, Advanced Manufacturing Park, l Wallis Way, Catcliffe, Rotherham S60 5TZ, UK;5. The University of Sheffield, Department of Mechanical Engineering, Mappin Street, Sheffield S1 3JD, UK;1. Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou, 310014, China;2. Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800, China |
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| Abstract: | Multi-scale computational models offer tractable means to simulate sufficiently large spatial domains comprised of heterogeneous materials by resolving material behavior at different scales and communicating across these scales. Within the framework of computational multi-scale analyses, hierarchical models enable unidirectional transfer of information from lower to higher scales, usually in the form of effective material properties. Determining explicit forms for the macroscale constitutive relations for complex microstructures and nonlinear processes generally requires numerical homogenization of the microscopic response. Conventional low-order homogenization uses results of simulations of representative microstructural domains to construct appropriate expressions for effective macroscale constitutive parameters written as a function of the microstructural characterization. This paper proposes an alternative novel approach, introduced as the distribution-enhanced homogenization framework or DEHF, in which the macroscale constitutive relations are formulated in a series expansion based on the microscale constitutive relations and moments of arbitrary order of the microscale field variables. The framework does not make any a priori assumption on the macroscale constitutive behavior being represented by a homogeneous effective medium theory. Instead, the evolution of macroscale variables is governed by the moments of microscale distributions of evolving field variables. This approach demonstrates excellent accuracy in representing the microscale fields through their distributions. An approximate characterization of the microscale heterogeneity is accounted for explicitly in the macroscale constitutive behavior. Increasing the order of this approximation results in increased fidelity of the macroscale approximation of the microscale constitutive behavior. By including higher-order moments of the microscale fields in the macroscale problem, micromechanical analyses do not require boundary conditions to ensure satisfaction of the original form of Hill's lemma. A few examples are presented in this paper, in which the macroscale DEHF model is shown to capture the microscale response of the material without re-parametrization of the microscale constitutive relations. |
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