Material data identification in generalized continua

TL;DR

This paper presents a novel data-driven framework for identifying material behavior in generalized continua using full-field measurements, enabling accurate extraction of complex stress states without relying on traditional assumptions.

Contribution

The method uniquely infers generalized stress--strain data directly from boundary value problems, bypassing classical homogenization and constitutive assumptions.

Findings

Successfully extracts non-symmetric and higher-order stress states

Provides reliable material datasets for model calibration or data-driven simulations

Validated with synthetic data and applied to mechanical metamaterials

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.