The stability of viscoelastic composites with negative stiffness (NS) inclusions and their associated extreme mechanical properties are studied with time-domain finite element analysis and composite theory. In the finite element analysis, the stability of the plane-strain, two-phase NS composite is evaluated by monitoring the stress divergence under uniaxial straining. In addition, 2D and 3D two-phase NS composites are studied by using composite theories and the elastic-viscoelastic correspondence principle. Effective stiffness and damping anomalies are observed, and the stability of the composites is evaluated. In the low frequency regime, stability conditions for purely elastic systems are suitable to estimate the stability of the viscoelastic composites. This is verified with the finite element analysis. For the 2D problem, the finite element analysis and composite theory agree well with each other in terms of the overall properties and stability. For the 3D problem, only the results obtained from the composite theory are presented. Our analysis shows that the extreme mechanical properties for both of the 2D and 3D cases are located near the strong ellipticity boundary. When the matrix modulus is suitably chosen to satisfy all stability conditions, the effective stiffness softening anomaly (i.e., damping enhancement) may be in the stability range. The effective stiffness enhancement locates in the nonelliptic range of the negative inclusion bulk modulus parameter space.

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Composite materials containing negative‐stiffness inclusions embedded in positive‐stiffness matrix may exhibit unconventional (anomalous) effective coupled‐field properties through interactions of the two phases. Effective coupled‐field properties are calculated with the finite element methods under the quasi‐static assumption. Stability boundaries are determined by applying 10 Hz sinusoidal loading on boundary surfaces, and the system is unstable if its energy becomes divergent for a chosen inclusion Young's modulus ratio (λE) or bulk modulus ratio (λK). Effective viscoelastic properties and their stability are studied for negative λE at 10 Hz, while the Poisson's ratio of the purely elastic inclusion is kept constant. For small inclusion volume fractions, their stability boundary is at λE ∼ –0.3, and extreme large effective damping and viscoelastic modulus are in the unstable regime. Furthermore, in the viscoelastic case, inclusion shapes have no effects on stability. As for the effective coupled‐field properties, all anomalous peaks are in the unstable regime for negative λE or λK, except for an anomalous peak in effective thermal expansion coefficient with electrically insulated inclusions. Insulated inclusions may cause charge accumulation at the inclusion‐matrix interface and boundary surface effects may serve as stabilizing agents to the composite system.

The occurrence of invasive breast cancer and lymphatic infiltration (LI) is highly relevant. Even though medical screening and imaging technology has made considerable progress today, there are many patients with metastasis phenomenon of axillary lymph gland at the first inspection of breast cancer. This is because the early signs of LI are very difficult to detect. To prevent the breast cancer cells spreading to distant organs through the lymphatic system or bloodstream, physicians usually recommend breast cancer patients for lymphadenectomy (lymph node dissecting). However, it is estimated that about 70% of patients with early breast cancer undergo unnecessary lymphadenectomy. Nowadays, LI is examined through a microscope and results are obtained by the doctor's experience and expertise. It is time-consuming, labor-intensive and prone to inter-observer discrepancy. Therefore, in this paper, we present a multistage model of automated system of lymphocyte detection. Cell nuclei, including lymphocyte, from the patients' H&E images are first segmented. Then the lymph nodes are classified morphologically with support vector machine in which the corresponding feature vectors are extracted according to scale-invariant feature transform. The experimental result demonstrates the agreement between the automated lymphocyte detection and physician manual detection. In addition to helping the early breast cancer patients avoid unnecessary lymphadenectomy surgery, the system also confirmed that it would greatly reduce the burden for physicians.

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