Material data identification in generalized continua

TL;DR

The paper introduces a model-free data-driven framework to identify generalized micromorphic material data directly from full-field kinematics and boundary forces by enforcing non-classical balance laws. It formulates the problem in a micromorphic phase space, uses clustering to build representative stress–strain datasets, and solves an equilibrium-focused data-identification task that yields non-symmetric and higher-order stresses. Validation on synthetic micromorphic data and a mechanical metamaterial (honeycomb) demonstrates accurate recovery of generalized stresses and successful data-driven predictions for unseen configurations. This approach provides a practical route to characterize microstructured solids without prescriptive constitutive models, enabling calibration and model-free simulations in generalized continua.

Abstract

We introduce a data-driven framework for identifying material behavior from full-field kinematics and force measurements in generalized (micromorphic) continua. Unlike traditional approaches that rely on constitutive assumptions or homogenization schemes, our method extracts generalized stress--strain data by enforcing non-classical balance laws and compatibility relations on full-field boundary value problems. Specifically, the approach infers the associated generalized stresses and constructs representative material datasets via clustering in a non-classical phase space. We show that the proposed method reliably extracts non-symmetric and higher-order local stress states, providing material data suitable for either model calibration or model-free data-driven simulations of generalized continua. These capabilities are demonstrated in validation simulations with synthetic data and in an application to mechanical metamaterials, suggesting a practical route for material characterization of microstructured solids.

Figures (12)

• Figure 1: Schematic representation of a BVP in a micromorphic continuum (left) with a generic microstructure (right). The dashed blue arrows on the left represent second-order tensors. The first-order theory adopted in this work assumes that the micro-deformation ${{\raisebox{\depth}{$\chi$}}}_{ij}$ is homogeneous in $\Omega^\mathrm{m}$ but varies in $\Omega$.
• Figure 2: Boundary value problem for the perforated plate with a micromorphic material under plane strain conditions. The holes with radii $R_1=0.045H$, $R_2=0.12H$, and $R_3=0.075H$ are located at coordinates $(0.28, 0.25)H$, $(0.72, 0.42)H$, and $(0.22, 0.75)H$, respectively, measured from the bottom-left corner. We assume $H=10$ mm in the simulations.
• Figure 3: Kinematic data: displacements $u_i$ [mm] and non-symmetric microdeformations ${\raisebox{\depth}{$\chi$}}_{ij}$ at $\bar{u}_2 = 1$ mm.
• Figure 4: Comparison of second-order generalized stress fields $\sigma_{ij}+\tau_{ij}$ [GPa], showing (a) the ground-truth reference simulation and (b) the identified mechanical stress fields.
• Figure 5: Comparison of third-order generalized stress fields $\mu_{ijk}$ [GPa$\,\cdot\,$mm], showing (a) the ground-truth reference simulation and (b) the identified mechanical stress fields.