Defence of doctoral thesis: Vedad Tojaga – On fiber network fracture mechanics and kink band formation in biocomposites

This thesis summarizes seven appended papers dealing with: (1) The fracture of fibrous materials, e.g., paper and paperboard, toward understanding the upper limits of paper products and eventually optimizing packaging performance in its endeavor to replace plastics with recyclable packaging; (2) The compressive failure of flax fiber composites, a promising eco-friendly alternative to synthetic composite materials, toward understanding the low compressive-compared-to-tensile strength of biocomposites, a design-limiting feature, and ultimately engineer better performing natural fiber composites for sustainable structures. 

(1) In Paper I, we consider an elastoplastic Timoshenko beam finite element formulation with embedded strong discontinuities in the description of multi-fracturing fibers in fiber networks, a deficiency in previous studies. Seeing that the coupled (monolithic) problem is non-convex, materializing through poor robustness and undesirable material instabilities, we present an alternating minimization (staggered) algorithm for this class of problems and thus retain a positive definite stiffness matrix. In Paper II, we propose a hybrid of monolithic and staggered solution methods for robust and computationally efficient fracture simulations, with an up to 30-fold performance gain compared to the staggered approach in the benchmark exercises. The hybrid method represents a matrix regularization technique that retains a positive definite stiffness matrix while approaching the tangent stiffness matrix of the monolithic problem. In Paper III, we develop a geometrically nonlinear Simo-Reissner beam theory with embedded strong discontinuities based on the method of incompatible modes, capturing the activation of additional fibers during loading. We show that accounting for geometrical nonlinearity in the beam formulation is necessary for direct numerical simulations of fiber networks regardless of the density. 

(2) In Paper IV, we formulate a multi-scale homogenization framework for layered composite materials, where we model the instantaneous constitutive behavior of the matrix and the fiber separately utilizing a combined Voigt and Reuss approximation, followed by an upscaling to the composite. Advantages include the independence of fiber rotations because it is fully defined in the known initial configuration of the composite. In Paper V, we back-calculate the compressive stress-strain response of the flax fiber from the Impregnated Fiber Bundle Test (IFBT) in compression using the rule of mixtures, necessary input data in the micromechanical description of flax fiber composites. In Paper VI, we formulate hyperelastic models for deformation plasticity into the finite strain range. One application includes mimicking the stress-strain response of the fiber and the matrix in the homogenization of layered composite materials, which we numerically verify against a micromechanical model. In Paper VII, we extend the hyperelastic model to account for fiber damage. We show numerically and experimentally through X-ray Computed Tomography (XCT) and Scanning Electron Microscopy (SEM) that fiber damage plays the utmost role in the compressive failure of flax fiber composites – it is a major determinant of the material’s compressive stress-strain response. The micromechanisms include elementary fiber crushing and intra-technical fiber splitting.

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