Reliable finite element simulation of orthotropic-dependent failure mechanisms is crucial for understanding the mechanical behavior and optimizing engineered composites and fiber-based materials. Such materials behave brittle under tension and strongly depend on the orthotropic material orientation. Existing non-local models can reproduce brittle fracture for isotropic materials but, in most cases, they are based on the equivalent strain concept for damage initiation, which is unsuitable for orthotropic materials. This contribution introduces a stress-based non-local damage model enhanced with an implicit gradient formulation of the failure criteria. A localizing non-local length is assumed to avoid any pathological broadening of the damage band. The methodology introduces direction-dependent damage variables driven by non-local stress-based damage criteria and can thus distinguish different failure modes. The verification and validation are shown on numerical and experimental benchmark examples. The implicit gradient-based non-local damage approach allows mesh-independent results. Furthermore, it does not require a priori known crack paths and makes it possible to simulate complex failure modes. Perspectively, its effective implementation in the commercial software Abaqus and combination with other constitutive laws, e.g. to account for plasticity or moisture, make it an attractive tool for describing the mechanical material behavior of orthotropic materials, such as wood and fiber-composites.

This contribution aims to increase the understanding of the complex mechanical behavior of wood through a framework for simulating mixed-mode failure. Based on physical properties assessment, appropriate constitutive laws, and experimental validation, a generally applicable numerical strength prediction tool for wood from different species and with various natural imperfections is introduced. The 3D orthotropic elastic plastic non-local CDM model considers the local fiber orientation and is implemented as material subroutines in the commercial software Abaqus. Herein, orthotropic Hill-plasticity with exponential hardening represents the plastic behavior in compression. Separated stress-based gradient-enhanced transient non-local damage represents the brittle material behavior in tension and shear. The methodology is validated with experimental data on tensile veneer tests, shear- and compression tests. Moreover, the methodology is applied to four-point bending tests of boards with heterogeneities. The numerical results demonstrate that the proposed model is able to reproduce different crack patterns observed in the four-point bending tests. Detailed investigations of the impact on the strength of the boards can be performed with this method to optimize species-independent strength prediction and engineered wood products. Further combination with other material laws e.g. moisture is possible.

Humidity fluctuations are a leading cause of damage in wooden constructions. In the case of glulam products, the multitude of possible layups concerning pith locations, diverse material properties across wood species, and the high computational cost associated with multi-field analysis have constrained many research efforts to focus on one specific glulam layup, consequently limiting the generalizability of the findings. To address this challenge, Monte Carlo simulations were employed to assess the significance of various factors. Based on which, two levels of simplification are proposed. The first level reduces the multi-layer problem to a single-layer one by applying appropriate boundary conditions. It substantially reduces the simulation costs and consequently facilitates sophisticated damage analysis, revealing the varying damage pattern across different board types. The second level of simplification further reduces the problem to a single-element model, enabling an analytical estimation of moisture stress. This level of simplification elucidates how factors such as moisture difference, material rotational angle, and other material properties influence the moisture-induced stress. Most importantly, it facilitates a rapid estimation of the critical moisture fluctuation range and the preferred sawing location of boards for different wood species, which can provide guidance to the production of higher moisture resistant glulam.

This contribution aims for an enhanced numerical representation for strength prediction of timber. This implies a validated elasto-plastic continuum damage model which considers orthotropy and heterogeneity of the material, and represents the ductile behavior under compression and the brittle material behavior under tension dependent on the three-dimensional orthogonal fiber directions. The behavior under compression is captured by Hill (1948) plasticity and an exponential hardening law enhanced by the loading direction dependency. The same model covers also the brittle damaging behavior by means of continuum damage mechanics (CDM). In this study, a separated damage mode (SDM) criterion with simultaneously evolving damage variables is investigated. After the experimental validation of the model for axially loaded clear wood samples, the developed numerical model is implemented to a sawn timber with fiber deviation, where homogenization of the material and simplification to transverse isotropy is not anymore possible. The 3D orthotropic material behavior is experimentally validated for this application example with bi-axial loading and aims for further numerical investigation of wood with heterogeneities as occurring in sawn (hard)wood for its efficient use in engineered wood products such as glued laminated timber.

When curved glulam beams are subjected to bending, tension perpendicular to grain is introduced. In this work, Monte-Carlo analysis is conducted to study the influence of the annual-ring orientation of individual board on stress concentration in the radial direction. A virtual cutting program is developed which simulates the sawing processes of boards and yields a database of sawn boards, each with a characterized material direction with respect to the pith location. Lamellas are randomly selected from the database to construct curved glulam beams in FE models for Monte-Carlo simulation. Parameters including lumber diameter distribution, taper function, orthotropic elastic properties are considered for four common wood genera in Europe: spruce, pine, larch, and beech. Statistical analysis shows that when the annual-ring effect is considered, the average radial stress in the middle height area of the glulam beams can reach up 1.56 times (even higher on the middle width and height area) compared to the common practice, where wood is usually simplified as transverse isotropic material. Such stress concentration, which can trigger early damage of the structure, indicates an underestimation of stress perpendicular to grain in common practice. Moreover, parameter studies show that the stress redistribution depends not only on the mechanical properties of wood species but also on the width of the board layer.