Higher-gradient and micro-inertia contributions on the mechanical response of composite beam structures

In the current work, we study the role of higher-order and micro-inertia contributions on the mechanical behavior of composite structures. To that scope, we compute the complete set of the effective static and dynamic properties of composite beam structures using a higher-order dynamic homogenization method which incorporates micro-inertia effects. We consider different inner composite element designs, with material constituents that are of relevance for current engineering practice. Thereupon, we compute the effective static longitudinal higher-gradient response, quantifying the relative difference with respect to the commonly employed, Cauchy-mechanics formulation. We observe that within the static analysis range, higher-order effects require high internal length values and highly non-linear strain profile distributions for non-negligible higher-order effects to appear. We subsequently analyze the longitudinal, higher-gradient eigenfrequency properties of composite structural members, accounting for the role of micro-inertia contributions. Thereupon, we derive analytical expressions that relate the composite material's effective constitutive parameters with its macroscale vibration characteristics. We provide for the first-time evidence that micro-inertia contributions can counteract the effect of second-gradient properties on the eigenfrequencies of the structure, with their relative significance to depend on the mode of interest. What is more, we show that the internal length plays a crucial role in the significance of micro-inertia contributions, with their effect to be substantial for low, rather than for high internal length values, thus for a wide range of materials used in engineering practice.