With the rising popularity of timber structures and the increasing complexity of timber engineering projects, the need for numerical simulation tools specific to this building material is gaining rapidly in importance.in particular, moisture transport processes and the quasi-brittle failure behavior, both difficult to describe, present major challenges and are of great relevance in practical construction.For these reasons, this article presents numerical modeling concepts for predicting moisture gradients, estimating effective stiffness and strength, and numerically identifying potential cracking mechanisms in wooden components.These concepts are validated through experimental test programs, and the associated challenges are addressed.selected results ultimately demonstrate the capabilities and relevance of such methods for timber engineering.

Dynamic fracture is a prevalent phenomenon in engineering structures subjected to dynamic loads, and reliable and simple numerical simulations of such phenomenon has been an ongoing research topic of computational mechanics. Although the finite element method (FEM) has been widely used for fracture simulations, there are still challenges such as the crack introduction and the mesh distortion. In recent years, meshless methods have emerged as potential alternatives to overcome these issues. In this paper, an explicit updated Lagrangian Fragile Points Method (FPM) is proposed for dynamic fracture simulations. The FPM is a point-based discontinuous meshless method, thus it on one hand circumvents the mesh distortion, and on the other hand allows for a simple, explicit introduction of cracks. In this paper, the formulations of the explicit updated Lagrangian FPM are introduced. Then the method is applied to various dynamic fracture problems including the spalling fracture and the crack branching, and for each cases the FPM provides convincing results. This paper shows that the explicit updated Lagrangian FPM is an effective yet simple numerical tool for predicting dynamic fracture. Note that though only small deformation dynamic fracture examples are used in this paper, the proposed method is able to handle finite strain problems, verified by some simple examples, since it is developed in the updatedLagrangian form.

The numerical simulation of four-point bending tests on glued laminated timber (GLT) beams requires an adequate description of the material behavior and of relevant failure mechanisms. The wooden lamellas, building up the GLT element, include knots, as a result of the natural tree growth process, which significantly affect the mechanical behavior. The variability of the morphology and arrangement of these knots lead to a large fluctuation, especially of strength properties, along the wooden lamellas. This leads to complex and, in general, quite brittle structural failure mechanisms of the GLT element. Such failure mechanisms can numerically be described with discrete cracks, using the framework of the extended finite element method (XFEM) for cracks without predefined positions or cohesive surfaces for cracks with predefined positions. In this work, a modeling approach to reliably estimate the bending strength and failure mechanisms of GLT beams subjected to four-point bending tests is proposed. Herein, the approach is validated by simulating replications of experimentally tested GLT beams of two beam sizes and strength classes, where each knot group is considered as a section with reduced individual stiffness and strength in exactly the same position as in the real beam. The results show that the application of quasi-brittle material failure may still result in a brittle global failure of GLT beams. The present study exemplarily shows how valuable insight into progressive failure processes can be gained by allowing the formation of continuous crack patterns. Moreover, a refined consideration of the knot geometries with such sophisticated realizations of discrete cracks may be able to simulate the actual failure mechanisms even more precisely.

Wood exhibits an intrinsic structural hierarchy. It is composed of wood cells, which are hollow tubes oriented in the stem direction. The cell wall is built up by stiff cellulose fibrils which are embedded in a soft polymer matrix. This structural hierarchy is considered in a four-step homogenization scheme, predicting the macroscopic elastic behavior of different wood species from tissue-specific chemical composition and microporosity, based on the elastic properties of nanoscaled universal building blocks. Special attention is paid to the fact that the fibrils are helically wound in the cell wall, at an angle of 00 - 300, generally denoted as microfibril angle. Consideration of this microfibril angle in the continuum micromechanics model for wood is mandatory for appropriate prediction of macroscopic stiffness properties, in particular of the longitudinal elastic modulus and the longitudinal shear modulus. The presented developments can be readily extended to the prediction of poroelastic properties, such as Biot and Skempton coefficients.

Dieser Beitrag präsentiert computergestützte Modellierungskonzepte zur Vorhersage von Feuchteverläufen und zugehörigen Spannungsfeldern sowie zur numerischen Bestimmung potenzieller Risstiefen von Holzbauteilen. Die vorgestellten Konzepte werden anhand experimenteller Versuchsprogramme validiert und die damit einhergehenden Herausforderungen diskutiert. Ausgewählte Ergebnisse zeigen letztendlich die Möglichkeiten und auch die Relevanz solcher Methoden für den Ingenieurholzbau auf.

This article presents computational modeling concepts for predicting moisture gradients, the corresponding stress distributions, and addresses the numerical determination of potential crack depths of wooden components. The concepts presented are validated using experimental test programs, and the associated challenges are discussed Selected results ultimately show the possibilities as well as the relevance of such methods for timber engineering.

In recent years there has been widespread use of nanoadditives for various applications, especially for influencing the characteristics of concrete and cement [1], [2], [3], [4], [5], [6]. Herein, we consider four different Portland cement mixtures containing combinations of three additives, namely: a polycarboxylate superplasticizer, SiO2 nanoparticle, and carbon nanotubes. The four mixture types have been subjected to three test methods: Ultrasonic tests for identification of effective elastic properties, Nanoindentation for determining material phases and related mechanical properties, and EDX measurements for investigating the chemical composition. First insights based on this combined experimental approach are given and the great potential of such a combined approach will be demonstrated.

Moisture content (MC) fields in wood are in strong interplay with the surrounding climate, leading to dimensional changes in wooden elements as well as variation of their material behavior. In the European standard for the design of timber structures (EC 5) these effects are considered by assigning wood members to service classes which are solely based on environmental conditions, but independent of the cross-sectional dimensions. Moisture-induced stresses resulting from dimensional changes are not directly considered. In this paper, we compare the EC 5 assignment of service classes to an assignment based on the actual MCs, determined by simulations. Further, we present an approach to assign the service class for solid and glued laminated timber cross sections, depending on the dimensions of the cross section and based on realistic climate simulations for one location. With the proposed approach, the influence of moisture on serviceability design can be taken into account more appropriately, which is important when computing deflections and performing simulations based on 2nd order theory. In addition, a method to estimate MC distributions for larger cross sections solely based on relative humidities is proposed. With these, also moisture-induced stresses and dimensional changes can easily be considered in a static analysis.

Preliminary results for the cement specimens under study have been obtained by the nanoindentation method. It has been found that the elastic modulus increases in the specimens that contain a complex admixture with nanosize particles. Also, the effect is observed on adding an admixture containing only one type of nanoparticles (sol of nanosilica SiO 2 or the MWCNT carbon material). Parameters of the nanoindentation method have been selected that ensure obtaining final consistent results. These results are presented by the histograms of distribution of nanoindentation points by elastic moduli and hardness, and also by the distributions in these characteristics in the horizontal plane xy, which is perpendicular to the nanoindenter′s motion. The obtained results suggest that there is a change in the nanostructure of the C–S–H gel, which is compared with the increment in the strength, the Young moduli, and the shear on adding SiO 2 nanoparticles and MWCNT nanoparticles.

Timber-concrete composite (TCC) structures are an efficient way to combine the advantages of cross-laminated timber (CLT) and concrete plates. By cutting notches into the timber part and applying the concrete on top, efficient shear connections can be formed, eliminating the need for additional use of any type of fasteners. However, fresh concrete releases moisture after application, which is absorbed by the highly hygroscopic wood and can lead to a critical reduction in mechanical properties or to problematic situations due to a difference in expansion behavior. Therefore, a separating foil is usually applied between the two materials, which represents an additional time and cost effort and can also negatively influence the connection properties or make the use of notchonly connections impossible. Thus, we investigate numerically what effects the exclusion of such a foil has on the moisture distribution in the CLT plate. Further, the moisture propagation after a fictitious installation on site is analyzed by applying realistic indoor climates to the open wood surface on the bottom of the CLT plate for a period of two years. In addition, the numerical model allows us to study the effect of local sealings of the most critical wooden part, the end-grain surfaces in the notch region. We were able to confirm that, especially in the unsealed case, locally high moisture contents can occur in the critical region next to the notch, where the highest shear stresses are also to be expected. However, by fully sealing the end-grain surfaces in these regions, the moisture levels and thus the risk of failure could be reduced efficiently. The use of such detailed moisture simulations, where moisture uptake due to bleeding of fresh concrete has been calibrated based on experiments, allows the long-term moisture behavior of such critical situations to be studied and effective solutions to be developed.

The preliminary results of the studied cement samples were obtained by the nanoindentation method. It was revealed that the elastic modulus M increases in samples that contain a complex additive containing nanosized particles. The effect is also observed with the introduction of an additive containing only one type of nanoparticles (nanosilica sol SiO2 or carbon nanomaterial MCNT). The selection of the parameters of the nanoindentation method, which ensured the obtaining of the final consistent results, was performed. These results are presented by histograms of the distribution of nanoindentation points in modulus of elasticity M and hardness H and distributions in M and H in the horizontal XY plane perpendicular to the motion of the nanoindentor. The results obtained indicate that there is a change in the nanostructure of the C – S – H gel, which is compared with an increase in strength, Young’s moduli and shear, upon the introduction of SiO2 nanoparticles and MCNT nanoparticles.

This work is a further development of its predecessor, the topic of which was verification of serviceability limit states of reinforced concrete hinges. Herein, the same conceptual approach is used to derive analytical formulae, supporting verification of ultimate limit states. These formulae limit tolerable relative rotations as a function of the compressie normal force transmitted across the neck. The mechanical model is based on the Bernoulli-Euler hypothesis and on linear-elastic and ideally-plastic stress-strain relationships for both concrete in compression and steel in tension. The usefulness of the derived formulae and the corresponding dimensionless design diagrams is assessed by means of experimental data from structural testing of reinforced concrete hinges, taken from the literature. This way, it is shown that the proposed mechanical model is suitable for describing ultimate limit states. Corresponding design recommendations are elaborated and exemplarily applied to verification of ultimate limit states of the reinforced concrete hinges of a recently built integral bridge. Since the reinforcement is explicitly accounted for, the tolerable relative rotations are larger than those according to existing guidelines. It is included that bending-induced tensile macrocracking beyond one half of the smallest cross-section of the neck is acceptable, because the tensile forces carried by the reinforcement ensure the required position stability of the hinges.

Concrete hinges are monolithic necks in reinforced concrete structures. The serviceability limit states addressed herein refer to the open question how to limit tolerable relative rotations as a function of the compressive normal force transmitted across the neck. Analytical formulae are derived in the framework of the Bernoulli-Euler hypothesis and of Hooke's law. The usefulness of corresponding dimensionless design diagrams is assessed based on experimental data taken from the literature and on new results from structural testing of reinforced concrete hinges. This way, it is shown that the proposed mechanical model is suitable for describing serviceability limit states. Corresponding design recommendations are elaborated and exemplarily applied to verification of serviceability limit states of the reinforced concrete hinges of a recently built integral bridge. Because the reinforcement is explicitly accounted for, the tolerable relative rotations are larger than those according to the guidelines of Leonhardt and Reimann. Bending-induced tensile macrocracking beyond one half of the smallest cross-section of the neck is acceptable, because the tensile forces carried by the reinforcement ensure the required position stability of the hinges.

2D materials < such > as planar fibrous networks exhibit several mechanical peculiarities, which we here decipher through a 3D-to-2D transition in the framework of continuum micromechanics or random mean-field homogenization theory. Network-to-fiber concentration (or “downscaling”) tensors are derived from Eshelby–Laws matrix-inclusion problems, specified for infinitely long, infinitely flat fibers, and for infinitely flat spheroidal pores of vanishing stiffness. Overall material failure is associated with microscopic shear failure orthogonal to the fiber direction. Corresponding structure–property relations between porosity on the one hand, and in-plane stiffness as well as strength on the other hand, appear as linear. This is in good agreement with mechanical experiments carried out on pulp fibers, on pulp fiber-to-pulp fiber bonds, and on corresponding paper sheets.

Cross-laminated timber (CLT) is an innovative wood product with increasing utilisations. It is well known that the orthotropic and inhomogeneous strength properties of wooden boards have a strong influence on the load bearing capacity of CLT plates, especially when the complex wood fibre distribution due to randomly occurring knots is considered. Thus, high safety factors are used in current standards and a generally accepted numerical tool for the strength prediction of CLT plates is still not available. In this paper, we combine recent advances in 3D numerical limit analysis and a knot reconstruction algorithm, where not only the bending strength of CLT plates under concentrated loading is estimated using the numerical approach, but also the scatter of strength properties resulting from the material’s inhomogeneities is investigated using a stochastic approach. For the latter, data collected during the grading process of wooden boards are condensed into so-called strength profiles for single wooden boards. The limit analysis approach then allows a time-efficient simulation of a large number of randomly assembled CLT plates. The comparison of the resulting strength predictions to experiments shows good agreement with respect to both the mean load bearing capacity and the statistical scatter of strength.

Increased use of wood has led to complex timber constructions and new types of wood-based products. In simulations, however, mainly simplified models are used to describe this material with strongly varying properties. Thus, to exploit the full mechanical potential of wood, a more accurate prediction of the mechanical behavior, especially when it comes to failure, is needed. Therefore, we developed a multi-surface failure criterion, which is able to describe brittle and ductile failure mechanisms of wood, based on simulations on several length scales [1-3]. Combined with a geometric reconstruction algorithm for knots [4], such a tool can be used to determine effective strength properties of knot sections. Due to the highly orthotropic failure behavior of wood and the strong variations of material directions close to knots, this task is very challenging. Widely used methods in fracture mechanics all have drawbacks when applied to such a material. For example, XFEM is limited by frequently occurring geometric incompatibilities, or the use of plasticity models easily encounters numerical problems due to the quasi-brittle nature of wood failure. Here, the emergence of the phase field method in recent years seems to be a promising solution for these problems [5-6]. Subsequently, such strength properties of wooden boards are condensed into so-called strength profiles [7]. By applying this approach to a large set of wooden boards, probabilistic material models can be developed and used in simulations of wood-based products. Such a framework for sensitivity analysis and robust design optimization should help engineers to design efficient timber structures.

The test machine shown in Fig. 1 shall be used for biaxial creep tests of building materials in compression. Thus, the target is to achieve spatially uniform stress and strain states inside the test specimens. This is a challenging task, because it requires highest precision standards regarding the test samples, the load application system, and the measurement equipment used to quantify the deformation of the specimens.

This work aims at a new approach for understanding failure mechanisms and predicting wood strengths, which are strongly influenced by the complex hierarchical material system of wood. Thus, a mechanical concept, where different microstructural characteristics are incorporated, appears to be necessary, based on the division of wood into meaningful scales of observation. At each scale, effective strength properties are to be determined and a multiscale approach needs to be applied, for which conventional numerical methods appear to be inefficient. In this work, numerical limit analysis approaches are further developed and applied for the first time to wood, complementing conventional methods successfully at certain scales of observation in a multiscale ‘damage’ approach. Limit analysis belongs to the group of direct plastic analysis methods, focusing exclusively on the time instant of structural collapse, and delivering the ultimate strength. Compared with conventional numerical approaches that have previously been applied to wood, limit analysis approaches are much more stable and efficient. In this work, orthotropic failure criteria and periodic boundary conditions are implemented into both lower bound and upper bound numerical limit analysis formulations. As numerical results, effective failure surfaces are obtained at both annual ring scale and clear wood scale. A validation at clear wood scale indicates that this new approach is very promising.

Deflection modes relevant for plates with rigidly supported edges are commonly used as kind of “approximation” for the deformation behavior of plates which are freely swimming on an elastic foundation. However, this approach entails systematic errors at the boundaries. As a remedy to this problem, we here rigorously derive a theory for elastically supported thin plates with arbitrary boundary conditions, based on the Principle of Virtual Power. Somewhat surprisingly, it appears that the well-known Laplace-type differential equation for the deflections needs to be extended by additional boundary integrals entailing moments and shear forces, so as to actually “release” the boundaries from “spuriously” acting external moments and shear forces. When approximating the deflections through 2D Fourier series, the Principle of Virtual Power yields an algebraic system of equations, the solution of which provides the Fourier coefficients of the aforementioned series representation. The latter converges, with increasing number of series members, to the true solution for the plate deflections. The new method is applied to relevant problems in pavement engineering, and it is validated through comparison of the numerical results it provides, with predictions obtained from Finite Element analysis. With respect to the latter, the new series-based method reduces the required computer time by a factor ranging from one and a half to almost forty.

Given the eminent role of structure-property relations in paper production, it is not surprising that various mathematical models for the mechanical interaction of pulp fibers within the overall material “paper” have been proposed. However, all these approaches did not explicitly account for the scale difference between the loads applied to the overall material and those acting on the level of the individual fiber. We here fill this essential conceptual gap by the development of a new micromechanics model: We first recall the fundamental micromechanical concept of the representative volume element (RVE) and the corresponding stress and strain average rules, before we specify these rules for planar networks such as paper material. Then we introduce elastic material behavior at the fiber level, and derive so-called concentration relations for upscaling this behavior to the planar network level. Combination of these relations with matrix-inclusion problems of the Eshelby-Laws type yields closed-form semianalytical expressions for the paper stiffness tensor, as function of fiber stiffness and porosity. The model, which is confirmed by various experimental data and which highlights the importance of the fiber's anisotropy for the overall elastic behavior, is deemed as a new support tool in the design of paper production processes.