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Researchers: [Zihe Wang]
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Collaborators: Prof. Jaehyung Ju at Shanghai Jiaotong University [S-Lab link]
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Themes: Engineering applications
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Non-reciprocal mechanical responses are often associated with chirality, active driving, or dissipation. Recent passive architected media, however, demonstrate that pronounced directional and coupled non-reciprocity can also emerge under quasi-static conditions through geometric nonlinearity and internal-state switching. This work investigates a two-dimensional lattice obtained by orthogonal tessellation of an Euler–Bernoulli beam-frame unit cell, where self-contact activation/deactivation occurs under opposite loading protocols, causing different paths to sample distinct effective stiffness branches. To provide a unified continuum-level description, we formulate a 2D micropolar model with an out-of-plane microrotation and establish the work-conjugate generalized strain–stress measures. Under quasi-static small-deformation assumptions, the total potential-energy density is constructed as the sum of micropolar elastic energy and a penalty-based self-contact potential, from which a state-dependent tangent constitutive operator is derived. In the decoupled micropolar modal space, the shear strain and local rotation are decoupled, and a pair of path-opposed effective stiffness matrices, 𝑞+ and 𝑞−, is introduced to capture protocol-dependent linearized responses induced by contact switching. The proposed framework describes not only directional non-reciprocity in axial, shear, and rotational modes, but also systematically exposes multiple channels of coupled non-reciprocity, with particular emphasis on axial–bending coupling enabled by self-contact. Moreover, it clarifies how a potential-compatible tangent stiffness at a fixed contact state can coexist with an apparent breakdown of Maxwell–Betti reciprocity when different loading protocols traverse different contact-dependent stiffness branches. Overall, the theory provides a scalable constitutive construction for self-contact-triggered non-reciprocal metamaterials.
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