Two-scale constitutive modelling and static response of the lattice core sandwich beams according to micropolar Timoshenko beam theory

Abstract

This paper deals with the development and assessment of 1D micropolar beam models of different lattice core structures according to micropolar continuum theory. The deformation kinematics of the lattice beams are based on the equivalent single-layer Timoshenko beam theory. The discrete-to-continuum transformation, through strain energy equivalence of discrete unit cells and corresponding micropolar continuum, is applied to deduce the constitutive law. The strain energy of the discrete unit cell is written by treating each element as Euler–Bernoulli beam element. The four different types of lattice cores are considered in the present study. The principle of minimum potential energy is used to derive the equilibrium equation for the webcore 1D micropolar Timoshenko beam model. Furthermore, the successive approximations are employed in the micropolar continuum model to deduce the governing equations for the couple stress Timoshenko beam model and classical Timoshenko and Euler–Bernoulli beam models. The couple stress Timoshenko beam models are obtained by assuming the internal antisymmetric shear force (S<inf>a</inf>) equal to zero and microrotation (ψ) equal to macrorotation (Ω) for all lattice cores. Fourier series-based analytical solutions are obtained for the static behaviour of the different beams under uniformly distributed, sinusoidal and point loads. The present analytical solutions are compared with those obtained through the finite element method (ABAQUS) using plane frame element and it has been found that the accuracy of the different beam models is highly sensitive to the geometric properties of lattice. Among different theories, the micropolar continuum Timoshenko beam theory yields promising results. © 2025 Elsevier B.V., All rights reserved.