2026 Theses Doctoral

Gradient-Enhanced Damage Modeling of Anisotropic Materials: Formulation and Computational Efficiency

Shala, Shqipron

This dissertation presents a comprehensive computational framework for modeling damage initiation and evolution in anisotropic materials, with a particular emphasis on timber. Due to its hierarchical microstructure, timber exhibits pronounced anisotropic behavior and complex failure mechanisms that depend strongly on the loading conditions. While quasi-brittle fracture dominates under tensile and shear loading, compressive loading activates ductile deformation mechanisms associated with irreversible structural collapse. Accurately capturing these distinct yet interacting mechanisms within a unified numerical framework remains a significant challenge. All formulations are developed within the framework of infinitesimal strain theory, while allowing for finite inelastic (plastic) strains.

To address this, the present work is developed within the localized gradient framework of continuum damage mechanics, which introduces an intrinsic length scale to regularize strain localization and ensure mesh-objective finite element solutions. The first part of the dissertation introduces a three-dimensional anisotropic gradient damage model for transversely isotropic materials. The formulation employs nonlocal damage variables based on physically motivated failure criteria, enabling the differentiation between damage mechanisms parallel and perpendicular to the grain direction and accurately capturing quasi-brittle fracture under tensile and shear loading.

Building upon this foundation, the framework is extended to fully orthotropic materials through an enhanced failure formulation. This extension introduces multiple directional damage variables associated with the principal material axes, allowing for the representation of anisotropic damage evolution and the influence of material orientation on failure behavior.

To address the computational challenges inherent to gradient-enhanced damage models, a novel acceleration scheme is proposed. The method introduces an adaptive criterion that selectively switches between local and nonlocal formulations based on the predicted evolution of damage, thereby reducing the number of active degrees of freedom. The proposed approach significantly improves computational efficiency while maintaining the accuracy and robustness of the numerical solution.

Finally, a unified constitutive framework is developed that combines quasi-brittle damage with compression-induced plasticity and ductile damage mechanisms. This formulation enables the simulation of the full spectrum of timber failure behavior under complex loading conditions, capturing both brittle fracture processes and ductile degradation associated with compressive loading.

The proposed models are implemented within a consistent finite element framework and validated against representative numerical and experimental benchmark problems. The results demonstrate the capability of the developed formulations to accurately predict damage initiation, propagation, and failure in anisotropic timber structures, while ensuring computational efficiency and numerical robustness.