This contribution investigates the extension of the microplane formulation to the description of transversely isotropic materials such as shale rock, foams, unidirectional composites, and ceramics. Two possible approaches are considered: (1) the spectral decomposition of the stiffness tensor to define the microplane constitutive laws in terms of energetically orthogonal eigenstrains and eigenstresses and (2) the definition of orientation-dependent microplane elastic moduli. The first approach, as demonstrated previously, provides a rigorous way to tackle anisotropy within the microplane framework, which is reviewed and presented herein in a clearer manner; whereas the second approach represents an approximation which, however, makes the formulation of nonlinear constitutive equations much simpler. The efficacy of the second approach in modeling the macroscopic elastic behavior is compared to the thermodynamic restrictions of the anisotropic parameters showing that a significant range of elastic properties can be modeled with excellent accuracy. Further, it is shown that it provides a very good approximation of the microplane stresses provided by the first approach, with the advantage of a simpler formulation. It is concluded that the spectral stiffness decomposition represents the best approach in such cases as for modeling composites, in which accurately capturing the elastic behavior is important. The introduction of orientation-dependent microplane elastic moduli provides a simpler framework for the modeling of transversely isotropic materials with remarked inelastic behavior, as in the case, for example, of shale rock.
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January 2017
Research-Article
Elastic Microplane Formulation for Transversely Isotropic Materials
Congrui Jin,
Congrui Jin
Department of Mechanical Engineering,
State University of New York at Binghamton,
Binghamton, NY 13902
e-mail: cjin@binghamton.edu
State University of New York at Binghamton,
Binghamton, NY 13902
e-mail: cjin@binghamton.edu
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Marco Salviato,
Marco Salviato
William E. Boeing Department of Aeronautics
and Astronautics,
University of Washington,
Seattle, WA 98195
e-mail: salviato@aa.washington.edu
and Astronautics,
University of Washington,
Seattle, WA 98195
e-mail: salviato@aa.washington.edu
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Weixin Li,
Weixin Li
Department of Civil
and Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: w.li@u.northwestern.edu
and Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: w.li@u.northwestern.edu
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Gianluca Cusatis
Gianluca Cusatis
Department of Civil and
Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: g-cusatis@northwestern.edu
Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: g-cusatis@northwestern.edu
Search for other works by this author on:
Congrui Jin
Department of Mechanical Engineering,
State University of New York at Binghamton,
Binghamton, NY 13902
e-mail: cjin@binghamton.edu
State University of New York at Binghamton,
Binghamton, NY 13902
e-mail: cjin@binghamton.edu
Marco Salviato
William E. Boeing Department of Aeronautics
and Astronautics,
University of Washington,
Seattle, WA 98195
e-mail: salviato@aa.washington.edu
and Astronautics,
University of Washington,
Seattle, WA 98195
e-mail: salviato@aa.washington.edu
Weixin Li
Department of Civil
and Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: w.li@u.northwestern.edu
and Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: w.li@u.northwestern.edu
Gianluca Cusatis
Department of Civil and
Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: g-cusatis@northwestern.edu
Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: g-cusatis@northwestern.edu
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 11, 2016; final manuscript received September 1, 2016; published online October 5, 2016. Editor: Yonggang Huang.
J. Appl. Mech. Jan 2017, 84(1): 011001 (14 pages)
Published Online: October 5, 2016
Article history
Received:
August 11, 2016
Revised:
September 1, 2016
Citation
Jin, C., Salviato, M., Li, W., and Cusatis, G. (October 5, 2016). "Elastic Microplane Formulation for Transversely Isotropic Materials." ASME. J. Appl. Mech. January 2017; 84(1): 011001. https://doi.org/10.1115/1.4034658
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