Session: 13-03-03: General: Mechanics of Solids, Structures and Fluids III

Paper Number: 166249

Continuum-Level Finite Element Modeling on Bi-Modulus Adaptive Metamaterial Designs 

Nature is full of adaptive materials that respond dynamically to their environment with on-demand properties. Examples include bone, which remodels based on stress, wood, which grows reaction wood for stability, and seedcoat respond to environments to switch between protection and triggering germination. Researchers also work on designing adaptive metamaterials to achieve similar on-demand properties based on external stimuli including, stress, temperature, humidity, light etc. Often, either the adaptive materials in nature or adaptive metamaterial designs possess complex microstructures. To explicitly model complex microstructures often suffer from high computational costs, particularly when simulating large-scale or dynamic systems. A continuum level model can significantly decrease the computation cost and increase simulations efficiency.  However, the numerical implementation of homogenized materials with on-demand properties is challenging.

In this investigation, to meet this challenge, a finite element (FE) modeling technique is developed to model materials with on-demand bi-moduli. A user-defined material subroutine (UMAT) is developed to capture this unique property for stress adaptive materials. To verify this modeling technique. A 2D bi-modulus adaptive metamaterial design is proposed. The new design is able to change stiffness when the effective stress/strain reaches to a certain level, indicating on-demand stiffness. FE models of the new design with detailed microstructure are developed to predict the mechanical responses of it under external loads. Then, the homogenized FE models of the same design are also developed to implement the technique by using the UMAT subroutine developed. The model results are compared to verify the prediction capability and evaluate the computational efficiency of the proposed continuum FE modeling technique.

To capture the on-demand stiffness, in the FE models, UMAT-based constitutive model enables dynamically updated stiffness tensor of individual finite elements based on real-time strain measurements. The model operates on a critical strain threshold: once the principal strain magnitude (either tensile or compressive) exceeds this threshold, the material stiffness increases instantaneously. This approach eliminates the need for explicit microstructure meshing, reducing computational complexity while preserving the mechanical fidelity of the system. Validation was performed through comparative simulations between the UMAT model and a fully resolved microstructure model in Abaqus/Standard. The results demonstrate strong agreement in stress-strain responses across multiple loading scenarios, including uniaxial tension/compression and biaxial loading. Notably, the UMAT model achieved a computational speedup compared to the explicit microstructure simulation, with negligible loss of accuracy.

Parametric studies on strain thresholds and stiffness transition rates confirm the model’s robustness in mimicking the microstructure’s nonlinear hardening behavior. The framework’s generalizability is highlighted by its ability to emulate complex microstructural responses through simple material parameter adjustments, offering a versatile tool for designing metamaterials with on-demand stiffness modulation. This work bridges the gap between high-resolution microstructure modeling and computational efficiency, enabling rapid exploration of architected materials for applications in energy absorption, adaptive structures, and soft robotics.

Presenting Author: Yunzheng Yang Northeastern University

Presenting Author Biography: Completed a bachelor's degree at Sun Yat-sen University, obtained a master's degree at Northeastern University, and currently pursuing a Ph.D. at Northeastern University.

Authors:

Yunzheng Yang Northeastern University
Yaning Li Northeastern University