Microstructural Statistics Informed
Boundary Conditions for Statistically
Equivalent Representative Volume
Elements (SERVEs) of Polydispersed
Elastic Composites
Somnath Ghosh, Dhirendra V. Kubair, and Craig Przybyla
1 Introduction
The representative volume element or RVE of a heterogeneous material is an
optimally representative microstructural subdomain, with morphological characteristics and effective response similar to that of the entire microstructure [1–5].
Direct numerical simulations of the RVE are essential for determining higher
length-scale homogenized constitutive models without having to solve the larger
microstructural domains. Homogenization involves averaging principles like the
Hill-Mandel condition [6] with assumptions of scale separation, along with energy
equivalence of the microstructural RVE and the homogenized medium under equivalent loading conditions. Computational homogenization from micromechanical
analysis of complex microstructures is now quite common [7–10]. Most of the
analyses assume periodic repetition of the RVE to uncouple governing equations
at different scales. Furthermore, the uncoupling process requires specific boundary
conditions like uniform displacement, traction, or periodicity on the RVE boundaries. Asymptotic expansion-based computational homogenization methods with
assumptions of macroscopic homogeneity and microscopic periodicity have found
extensive applications in [9, 11–16]. Analogously, the FE 2 multi-scale methods [17]
S. Ghosh ()
Departments of Civil, Mechanical Engineering and Materials Science & Engineering, Johns
Hopkins University, Baltimore, MD, USA
e-mail: sghosh20@jhu.edu
D. V. Kubair
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA
e-mail: dkubair1@jhu.edu
C. Przybyla
Air Force Research Laboratory/RX, Wright-Patterson Air Force Base, Dayton, OH, USA
e-mail: craig.przybyla@wpafb.af.mil
© Springer Nature Switzerland AG 2020
S. Ghosh et al. (eds.), Integrated Computational Materials Engineering (ICME),
https://doi.org/10.1007/978-3-030-40562-5_11
297
Boundary Conditions for Statistically
Equivalent Representative Volume
Elements (SERVEs) of Polydispersed
Elastic Composites
Somnath Ghosh, Dhirendra V. Kubair, and Craig Przybyla
1 Introduction
The representative volume element or RVE of a heterogeneous material is an
optimally representative microstructural subdomain, with morphological characteristics and effective response similar to that of the entire microstructure [1–5].
Direct numerical simulations of the RVE are essential for determining higher
length-scale homogenized constitutive models without having to solve the larger
microstructural domains. Homogenization involves averaging principles like the
Hill-Mandel condition [6] with assumptions of scale separation, along with energy
equivalence of the microstructural RVE and the homogenized medium under equivalent loading conditions. Computational homogenization from micromechanical
analysis of complex microstructures is now quite common [7–10]. Most of the
analyses assume periodic repetition of the RVE to uncouple governing equations
at different scales. Furthermore, the uncoupling process requires specific boundary
conditions like uniform displacement, traction, or periodicity on the RVE boundaries. Asymptotic expansion-based computational homogenization methods with
assumptions of macroscopic homogeneity and microscopic periodicity have found
extensive applications in [9, 11–16]. Analogously, the FE 2 multi-scale methods [17]
S. Ghosh ()
Departments of Civil, Mechanical Engineering and Materials Science & Engineering, Johns
Hopkins University, Baltimore, MD, USA
e-mail: sghosh20@jhu.edu
D. V. Kubair
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA
e-mail: dkubair1@jhu.edu
C. Przybyla
Air Force Research Laboratory/RX, Wright-Patterson Air Force Base, Dayton, OH, USA
e-mail: craig.przybyla@wpafb.af.mil
© Springer Nature Switzerland AG 2020
S. Ghosh et al. (eds.), Integrated Computational Materials Engineering (ICME),
https://doi.org/10.1007/978-3-030-40562-5_11
297