Surrogate-Based Shape Optimization of a Cruciform Specimen for Biaxial Testing of Microparticle Reinforced Epoxy Adhesives

Reliable determination of the in-plane biaxial mechanical behavior of particle-reinforced composite adhesives under multiaxial stress conditions requires cruciform specimen geometries that achieve high stress uniformity in the measurement zone. In this study, the elastic response obtained from uniaxial tensile tests was verified through representative volume element (RVE)-based micromechanical analyses by systematically examining mesh sensitivity and RVE edge size convergence across multiple random microparticle distributions under periodic boundary conditions. The probability density characterization of the effective elastic constants indicated that the remaining scatter is mainly governed by microstructural randomness and decreases as the RVE edge size increases, supporting a nearly direction-independent effective stiffness associated with the random microparticle distribution. The RVE-predicted mean tensile modulus remained in close agreement with experiments, with relative deviations of approximately −2% to +2% across the investigated reinforcement levels. The validated material parameters were based on a dynamic XGBoost (eXtreme Gradient Boosting) surrogate model driven by the geometric design variables, fillet radius and center thickness, combined with an adapted version of the LIPOTR (Lipschitz Optimization with Trust Region) algorithm. The initial and optimized geometries were then compared using both experimentally determined elastic properties and selected RVE-predicted engineering constants for the 2, 6, and 10 wt% materials. The significant reductions in the equivalent Seqv, normal S11 and S22, and shear S12 stress variations within the gauge zone of the optimized candidate geometry resulted in improved stress homogeneity.