Accurately modelling damage propagation in composites with 3D explicit finite element methods requires high-dimensional models, making simulations computationally prohibitive. Conventional reduced-order models (ROMs) trained offline are ineffective for fracture problems, since stress redistribution and crack growth cannot be anticipated a priori. In this work, a hybrid offline–online ROM that couples elastic-only offline training with adaptive online enrichment of the reduced basis during damage evolution is introduced. Proper Orthogonal Decomposition (POD) is combined with Energy-Conserving Mesh Sampling and Weighting (ECSW) and Gappy data reconstruction to achieve efficient time integration with 3D solid and cohesive elements. Unlike existing domain decomposition approaches, the proposed framework does not require prior knowledge of crack paths and can refine the basis anywhere in the domain as damage develops. The method is demonstrated on open-hole tensile tests at two distinct length scales, capturing delamination, fibre failure and failure stress with good accuracy when compared to full-order simulations and experiments. Improved computational savings are achieved, with efficiency gains increasing with model size. These results establish the hybrid ROM as a scalable and general approach for modelling distributed, path-dependent fracture in composite materials. • Introduces a hybrid offline–online reduced-order modelling framework for distributed damage in composites. • Elastic-only offline training enables inexpensive basis construction without prior crack path knowledge. • Adaptive online enrichment refines the basis in situ to capture stress redistribution and path-dependent damage. • Simultaneously models weak and strong discontinuities (with CDM and CZM) using the same reduced order setting. • Demonstrated on open-hole tensile specimens at multiple length scales, with improved computational efficiency.

We present a novel body-fitted iso geometric topology optimization framework for maximizing phononic band gaps, featuring an accurate boundary representation of evolving geometries. Analytical design sensitivities are derived, with particular focus on a narrow band of control points near the interface, shown to be critical due to the underlying physical mechanisms of Bragg scattering. Benchmark comparisons against density-based finite element approaches confirm the superior convergence behavior and predictive accuracy of our method. These highlight the main contributions of this work, namely: high reliability and engineering credibility, achieved by generating computational results that are directly manufacturable without post-processing and with no performance degradation; and substantially faster convergence rates in the numerical evaluation of band gap simulations compared to conventional FEM-based methods. Numerical examples demonstrate the advantages of the proposed framework, positioning it as a reliable computational tool for band gap engineering in phononic materials.

This work investigates the progressive damage analysis of pultruded composite structures using the higher-order beam models with Node-Dependent Kinematics (NDK) based on Carrera Unified Formulation (CUF). A three-dimensional (3D) Tsai-Wu orthotropic damage model is implemented, in which the fracture energy and viscous regularization techniques are coupled. Subsequently, three experimental benchmarks involving compact tension, three-point bending, and four-point bending tests on pultruded composite structures are selected to validate the proposed numerical framework. The comparison between numerical and experimental results shows that the numerical framework is able to provide accurate and objective structural responses. Furthermore, the use of NDK enhances the computational efficiency of the progressive damage analysis without affecting accuracy.