Stability of viscoelastic continuum with negative‐stiffness inclusions in the low‐frequency range

Physica Status Solidi (b)

Shen

Liao

2017

Self Cite

Microstructured plates, consisting of various conventional and re‐entrant cells, are numerically constructed and analyzed for their effective elastic properties under in‐plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two‐dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus.

Section: Introductionmentioning

confidence: 99%

Microstructural Effects on the Poisson's Ratio of Star‐Shaped Two‐Dimensional Systems

Physica Status Solidi (b)

Shen

Liao

2017

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3D viscoelastic computational grains with spherical inclusions with or without interphases/coatings for micromechanical modeling of heterogeneous materials

Huang

Numerical Meth Engineering

Dong

et al. 2021

In this article, the 3D viscoelastic computational grains (CGs) with spherical inclusions, with and without interphases/coatings are developed to study the viscoelastic behavior of polymer-based heterogeneous materials.Papkovich-Neuber solutions and spherical harmonics are adopted to develop the independent displacement fields inside the grains, and Wachspress coordinate is used to interpolate compatible displacement fields at inter-element surfaces. The elemental stiffness matrices are developed with multi-field boundary variational principles in the Laplace domain, after which Zakian technique is adopted to invert both the homogenized and localized responses back to the time domain with good accuracy and efficiency. With different kinds of models to describe the property of the viscoelastic polymers, the generated homogenized moduli and localized stress distributions are validated against the experimental data, simulations by commercial FE software, and predictions by composite spherical assemblage models. Parametric studies are also carried out to investigate the influence of material and geometric parameters on the behavior of viscoelastic composites. Finally, the viscoelastic CG is also used to study the effect of the negative Young's modulus of particles on the stability and loss tangent of viscoelastic composites.

Uniaxial dynamic mechanical responses of ferroelastic materials under temperature cycling via phase field modeling

Physica Status Solidi (b)

Shen

2016

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Phone: þ886 6 275 7575, ext. 63140, Fax: þ886 6 235 8542The dynamic mechanical responses of the ferroelastic materials under uniaxial straining and temperature cycling are studied via the Landau-type phase field model in two dimensions. The model may exhibit a single-well (doublewell) energy profile when temperature is greater (less) than the critical temperature. Effective negative stiffness in the vicinity of the temperature-induced solid-solid phase transformation is numerically demonstrated through monotonic uniaxial straining on a single-domain ferroelastic under temperature cycling around the Curie temperature. Under sinusoidal uniaxial straining, the effective Young's modulus and damping, as indicated by the enclosed area of the stress-strain curve, may be largely increased due to the phase transition. Our calculated responses here are consistent with experimental data reported in the literature, as well as theoretical results based on the composite theory with inclusions assumed to have negative modulus. No negative stiffness values are directly assigned in our phase field model as the underlying physics of the order parameters, i.e., spontaneous strains, provides effective negative stiffness into the systems.