Dramatically stiffer elastic composite materials due to a negative stiffness phase?
This paper is devoted to the discussion of effects of constituents with negative stiffness in composite materials. It is shown that, if one phase has the appropriate negative stiffness, the overall stiffness of the composite can be made dramatically large. In the presence of a small nonlinearity, extremely high stiffness can be achieved without singularity of elastic fields. First, based on a spherically symmetric problem, for a spherical isotropic matrix containing a spherical inclusion of another material, under spherically symmetric boundary conditions, it is illustrated what happens to a full exact elasticity solution when one phase of composite has a sufficiently negative stiffness. The problem is analyzed first within linearized elasticity theory, and to verify that the conclusions obtained are not artifacts of the infinitesimal-displacement-gradient formulation, the problem is analyzed again within a fully nonlinear finite deformation formulation. Then the authors consider the effect of phases of negative stiffness in several three-dimensional composites, for which elasticity solutions are known. An existing variational principle, that provides estimates for the overall elastic modulus for random composite materials, remains valid when one of the composite's phases has negative stiffnesses, and it is shown that the estimates from this variational principle exibit an extremally large composite stiffnesses by suitable choice of the moduli of negative stiffness phase. Taking into account that a negative stiffness constituent alone is unstable, the authors argue that composite made with a small volume fraction of negative stiffness inclusions can be stable. In particular, the objects with negative stiffness can be stabilized if they are constrained rigidly or by an elastic composite matrix. Negative shear modulus in a continuum can give rise to a banding (domain) instability associated with loss of ellipticity, but the violation of strong ellipticity does not guarantee the loss of stability of inclusions. Finally, the authors discuss experimental results which show extreme composite behavior in selected viscoelastic systems under sub-resonant sinusoidal load.
infinitesimal-displacement-gradient formulation
scientific article; zbMATH DE number 1788078
scientific article