Honeycombs or foams with reentrant microstructures exhibit effective negative Poisson's ratio. Although they are light weight due to inherently empty space, their overall stiffness and damping are somewhat limited. With judiciously chosen filler material to fill the voids in star-shaped honeycomb, it is numerically demonstrated its auxeticity may be enhanced. By combining the filler and skeleton, the hierarchical composite materials are constructed. The magnitude of the enhancement depends on inner and outer filler's modulus mismatch, as well as the types of filling. Filler's auxeticity also largely enhances overall auxeticity of the outer-and all-filled honeycomb. In addition, for outer-filled honeycomb, its effective viscoelastic modulus and damping are significantly increased, while maintaining relatively light weight, due to local stress concentration.

Mechanical behavior of negative-stiffness (NS) plates containing cracks, under sinusoidal straining, are numerically studied with the phase-field modeling techniques. Ferroelastic phase transition is triggered by thermal loading with the Landau-type energy function to generate the double-well potential. NS arises from regions of the multi-domain plates, and interacts with surrounding positive-stiffness neighboring regions to give rise to anomalous mechanical behavior and energy dissipation. It is found that the anomalies in effective elastic modulus and damping are preserved in the presence of cracks, regardless of their shape or tip radius. Cracks do not diminish the negative-stiffness effects on overall properties; they may provide more enhancement in dissipation. Crack tips concentrate stress, and cause phase transition to start earlier than other regions in the plates. As opposed to passive materials whose overall damping must be positive, we observe negative effective damping in the plates due to generation of energy from the phase transition. Phase-Field Modeling of Negative-Stiffness Effects

Elastoplastic analysis of a composite cylinder, consisting of an isotropic elastic inclusion surrounded by orthotropic matrix, is conducted via numerical parametric studies for examining its residual stress under thermal cycles. The matrix is assumed to be elastically and plastically orthotropic, and all of its material properties are temperature-dependent (TD). The Hill’s anisotropic plasticity material model is adopted. The interface between the inclusion and matrix is perfectly bonded, and the outer boundary of the cylinder is fully constrained. A quasi-static, uniform temperature field is applied to the cylinder, which is analyzed under the plane-strain assumption. The mechanical responses of the composite cylinder are strongly affected by the material symmetry and temperature-dependent material properties. When the temperature-independent material properties are assumed, larger internal stresses at the loading phase are predicted. Furthermore, considering only yield stress being temperature dependent may be insufficient since other TD material parameters may also affect the stress distributions. In addition, plastic orthotropy inducing preferential yielding along certain directions leads to complex residual stress distributions when material properties are temperature-dependent.

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