TY - JOUR
T1 - Fractional topology optimization of periodic multi-material viscoelastic microstructures with tailored energy dissipation
AU - Giraldo-Londoño, Oliver
AU - Paulino, Glaucio H.
N1 - Funding Information:
We acknowledge the endowment provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology. We thank Prof. Americo Cunha, from State University of Rio de Janeiro (UERJ), Brazil, for his insightful comments to the manuscript. The information provided in this paper as well as the interpretation of the results is solely that by the authors, and it does not necessarily reflect the views of the sponsors or sponsoring agencies.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - The microstructural configuration of a material affects its macroscopic viscoelastic behavior, which suggests that materials can be engineered to achieve a desired viscoelastic behavior over a range of frequencies. To this end, we leverage topology optimization to find the optimized topology of a multi-phase viscoelastic composite to tailor its energy dissipation behavior as a function of frequency. To characterize the behavior of each material phase, we use a fractional viscoelastic constitutive model. This type of material model uses differential operators of non-integer order, which are appropriate to represent hereditary phenomena with long- and short-term memory. The topology optimization formulation aims to find the lightest microstructure that minimizes the sum of squared loss modulus residuals for a given set of target frequencies. This leads to the design of materials with either maximized loss modulus for a given target frequency or tailored loss modulus for a predefined set of frequencies. We present several numerical examples, both in 2D and 3D, which demonstrate that the microstructural configuration of multi-phase materials affects its macroscopic viscoelastic behavior. Thus, if properly designed, the material behavior can be tailored to dissipate energy for a desired frequency (maximized loss modulus) or for a range of frequencies (tailored energy dissipation behavior).
AB - The microstructural configuration of a material affects its macroscopic viscoelastic behavior, which suggests that materials can be engineered to achieve a desired viscoelastic behavior over a range of frequencies. To this end, we leverage topology optimization to find the optimized topology of a multi-phase viscoelastic composite to tailor its energy dissipation behavior as a function of frequency. To characterize the behavior of each material phase, we use a fractional viscoelastic constitutive model. This type of material model uses differential operators of non-integer order, which are appropriate to represent hereditary phenomena with long- and short-term memory. The topology optimization formulation aims to find the lightest microstructure that minimizes the sum of squared loss modulus residuals for a given set of target frequencies. This leads to the design of materials with either maximized loss modulus for a given target frequency or tailored loss modulus for a predefined set of frequencies. We present several numerical examples, both in 2D and 3D, which demonstrate that the microstructural configuration of multi-phase materials affects its macroscopic viscoelastic behavior. Thus, if properly designed, the material behavior can be tailored to dissipate energy for a desired frequency (maximized loss modulus) or for a range of frequencies (tailored energy dissipation behavior).
KW - Fractional calculus
KW - Fractional viscoelasticity
KW - Material design
KW - Multi-phase composite
KW - Topology optimization
KW - ZPR update scheme
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U2 - 10.1016/j.cma.2020.113307
DO - 10.1016/j.cma.2020.113307
M3 - Article
AN - SCOPUS:85090326712
SN - 0045-7825
VL - 372
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 113307
ER -