Data-Driven Constitutive Modeling of Graded Metamaterial with Microstructural Contact
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Mechanical metamaterials derive their effective macroscopic properties primarily from their engineered microstructure, rather than being determined solely by the properties of their constituent materials. These properties are governed by the geometry and interactions of their unit cells, the repeating microstructural building blocks of the material. Controlling such microstructural features opens new possibilities for applications in adaptive structures, impact absorption, and programmable stiffness materials. This talk explores the design of unit cells incorporating self-contact mechanisms to achieve mechanical metamaterials with programmable, progressive stiffness properties. Particular emphasis is placed on graded architectured materials, where spatially varying geometric properties on the micro-scale—such as internal contact surfaces—enable location-dependent mechanical responses. Using nonlinear finite element models from computational contact mechanics, we demonstrate how spatial variation in microstructural parameters enables the tuning of macroscopic stiffness fields. To address the computational cost associated with modeling such systems, we consider data-driven constitutive models as alternatives to sequential multiscale schemes such as FE². These approaches become prohibitively expensive for complex metamaterial unit cells or for simulations at practically relevant scales. In this context, we assess data-driven surrogate constitutive laws trained on the homogenized stress response and the tangent stiffness tensor obtained from nonlinear finite element simulations of representative volumes elements with contact interactions. The constitutive response is expressed in terms of macroscopic deformation measures and microstructural geometric parameters characterizing contact-related geometric features.
