Josef Eberhardsteiner

Micromechanical modeling of solid-type and plate-type deformation patterns within softwood materials. A review and an improved approach

Abstract Wood exhibits a highly diverse microstructure. It appears as a solid-type composite material at a length scale of some micrometers, while it resembles an assembly of plate-like elements arranged in a honeycomb fashion at the length scale of some hundreds of micrometers. These structural features result in different load-carrying mechanisms at different observation scales and under different loading conditions. In this paper, we elucidate the main load-carrying mechanisms by means of a micromechanical model for softwood materials. Representing remarkable progress with respect to earlier models reported in the literature, this model is valid across various species. The model is based on tissue-independent stiffness properties of cellulose, lignin, hemicellulose, and water obtained from direct testing and lattice-dynamics analyses. Sample-specific characteristics are considered in terms of porosity and the contents of cellulose, lignin, hemicelluloses and water, which are obtained from mass density measurements, environmental scanning micrographs, analytical chemistry, and NMR spectroscopy. The model comprises three homogenization steps, two based on continuum micromechanics and one on the unit cell method. The latter represents plate-like bending and shear of the cell walls due to transverse shear loading and axial straining in the tangential stem direction. Accurate representation of these deformation modes results in accurate (orthotropic) stiffness estimates across a variety of softwood species. These stiffness predictions deviate, on average, by less than 10% from corresponding experimental results obtained from ultrasonic or quasi-static testing. Thus, the proposed model can reliably predict microscopic and macroscopic mechanical properties from internal structure and composition, and is therefore expected to significantly support wood production technology (such as drying techniques) and mechanical analyses of timber structures.

Extracellular bone matrix exhibits hardening elastoplasticity and more than double cortical strength: Evidence from homogeneous compression of non-tapered single micron-sized pillars welded to a rigid substrate.

We here report an improved experimental technique for the determination of Young׳s modulus and uniaxial strength of extracellular bone matrix at the single micrometer scale, giving direct access to the (homogeneous) deformation (or strain) states of the tested samples and to the corresponding mechanically recoverable energy, called potential or elastic energy. Therefore, a new protocol for Focused Ion Beam milling of prismatic non-tapered micropillars, and attaching them to a rigid substrate, was developed. Uniaxial strength turns out as at least twice that measured macroscopically, and respective ultimate stresses are preceded by hardening elastoplastic states, already at very low load levels. The unloading portion of quasi-static load-displacement curves revealed Young׳s modulus of 29GPa in bovine extracellular bone matrix. This value is impressively confirmed by the corresponding prediction of a multiscale mechanics model for bone, which has been comprehensively validated at various other observation scales, across tissues from the entire vertebrate animal kingdom.

Biaxial testing of orthotropic materials using electronic speckle pattern interferometry

Abstract In the scope of a research program material properties of wood under biaxial stress conditions have to be examined. Therefore, a new biaxial hydraulic testing machine for orthotropic materials was developed. For measuring the spatial displacement field at the surface of the cruciform wooden specimen a 3D electronic speckle pattern interferometer was adapted to the testing machine. The specimen were loaded displacement-controlled in up to 70 single steps and at each step three interferograms were taken. In order to avoid time-dependent deformations the cycle time was reduced to less than 15 seconds. The basic considerations of the testing machine and of the measurement system are described in this paper. An example of application is given.

Micromechanical Estimates for Elastic Limit States in Wood Materials, Revealing Nanostructural Failure Mechanisms

At the macroscale, wood materials show great variability and diversity. At the nanoscale, however, they exhibit common (universal) building blocks which build up universal organizational patterns over several length scales up to the macroscale. In the framework of continuum micromechanics, this building principle was recently expressed in quantitative terms, allowing for a prognosis of tissue-specific anisotropic elasticity properties of wood from tissue-specific chemical composition and porosity, and from universal elastic properties of the elementary constituents “amorphous cellulose,” “crystalline cellulose,” “hemicellulose,” “lignin,” and “water.” In this paper, we extend this investigation to tissue-specific macroscopic elastic limit states: We show that shear failure of the nanoscale building block “lignin,” which exhibits an isotropic, tissue-independent (“universal”) shear strength, is the dominant determinant of anisotropic macroscopic failure of wood under different loading conditions. In a continuum micromechanics setting, quadratic strain averages over material phases represent microstructural strain peaks, which are responsible for material phase failure. The good agreement of tissue-specific micromechanical predictions of macroscopic limit stresses with corresponding tissue-specific strength experiments underlines the role of lignin as the governing strength-determining component of wood.

A 3D finite element formulation describing the frictional behavior of rubber on ice and concrete surfaces

The frictional behavior of rubber materials on various contact surfaces is strongly affected by the contact pressure and the relative sliding velocity as well as the environmental temperature. Based on a great number of experiments of rubber blocks moving on concrete and ice surfaces, a friction law for 3D contact analyses is presented in this paper. It is characterized by the dependency on the contact pressure, sliding velocity and the environmental temperature. The identification and correction of the parameters of this friction law were done by means of a least‐square method followed by re‐analyses of the respective experiments. Several examples are given in a numerical investigation of the frictional behavior of rubber materials.

Discussion of common and new indicating properties for the strength grading of wooden boards

The naturally grown material wood exhibits, in addition to its orthotropic material structure, several types of inhomogeneities, where most of them can be allocated to knots and the resulting local fiber deviations. Since they generally lead to a reduction in strength properties, wooden boards must be subjected to a grading process before they can be used as load-bearing elements. Within this process so-called indicating properties are recorded and used to assess the wooden board strength. Common indicating properties are almost exclusively based on surface information of wooden boards while the 3D position and orientation of knots within a board is hardly considered. Thus, algorithms for the 3D reconstruction of wooden boards based on already available surface scans, laser scanning, X-ray or computer tomography data are assessed first within this work. This new knot information allows then the development of novel indicating properties, which consider the knots, the resulting fiber deviation regions and, for bending conditions, the knot location information using height-dependent weighting functions. The statistical evaluation of combinations of the new indicating properties, separately for tensile and bending load conditions, shows that the correlations to experimentally obtained strength properties could be improved significantly with such an approach.

Effective stiffness prediction of GLT beams based on stiffness distributions of individual lamellas

Abstract The mechanical properties of structural timber—particularly in terms of stiffness and strength—are subject to high variability, which also affects the properties of timber products made from structural timber, e.g., glued laminated timber (GLT). In this paper, the influence of the longitudinal stiffness variability of wooden lamellas on the effective stiffness of GLT is investigated. In a first step, the local fiber orientation on the surfaces of 350 lamellas of Norway spruce was determined by an optical scanning device. This fiber angle information in combination with a micromechanical model for wood was used for the generation of a longitudinal stiffness profile of each lamella. Recording the position and orientation of each lamella, a total number of 50 GLT beams were assembled (with 4, 7, and 10 laminations) and tested under four-point bending. Knowing the stiffness profile of each board and its location within the GLT beam allowed for an accurate numerical finite element model, which is able to predict the effective GLT stiffness with high accuracy. Interesting insights into the relation between the stiffness of lamellas and the resulting GLT beams could be gained, and finally, a numerical simulation tool which is able to reproduce the experimental results appropriately was obtained.

Micromechanics of bioresorbable porous CEL2 glass-ceramic scaffolds for bone tissue engineering

Abstract Owing to their stimulating effects on bone cells, ceramics are identified as expressly promising materials for fabrication of tissue engineering (TE) scaffolds. To ensure the mechanical competence of TE scaffolds, it is of central importance to understand the impact of pore shape and volume on the mechanical behaviour of the scaffolds, also under complex loading states. Therefore, the theory of continuum micromechanics is used as basis for a material model predicting relationships between porosity and elastic/strength properties. The model, which mathematically expresses the mechanical behaviour of a ceramic matrix (based on a glass system of the type SiO2–P2O5–CaO–MgO–Na2O–K2O; called CEL2) in which interconnected pores are embedded, is carefully validated through a wealth of independent experimental data. The remarkably good agreement between porosity based model predictions for the elastic and strength properties of CEL2-based porous scaffolds and corresponding experimentally determined mechanical properties underlines the great potential of micromechanical modelling for speeding up the biomaterial and tissue engineering scaffold development process—by delivering reasonable estimates for thematerial behaviour, also beyond experimentally observed situations.

Rate-independent mechanical behavior of biaxially stressed wood: Experimental observations and constitutive modeling as an orthotropic two-surface elasto-plastic material

Abstract Recent biaxial experiments on spruce wood show that consideration of an elliptic failure surface according to Tsai and Wu and an elastic model for stress states within this envelope lead to an insufficient description of the mechanical behavior. As compression perpendicular to the grain occurs, a non-linear stress path results from a proportional biaxial strain path. Investigation of characteristic samples with respect to loading-unloading-reloading cycles for states of stress below failure reveals behavior similar to what is known as hardening type plasticity. The experimentally observed mechanical behavior is described by means of a two-surface plasticity model addressing both failure and non-linear stress response below failure as separate mechanisms. Prediction of failure is achieved by means of a second-order failure envelope according to Tsai and Wu. The non-linear stress response has to be covered by a novel orthotropic hardening type plasticity model. Since available experimental data covers only plane stress in the LR-plane, both orthotropic failure and yield surfaces, respectively, are restricted to this case.

Development of high-performance strand boards: multiscale modeling of anisotropic elasticity

The interrelationships between microstructural characteristics and anisotropic elastic properties of strand-based engineered wood products are highly relevant in order to produce custom-designed strand products with tailored properties. A model providing a link between these characteristics and the resulting elastic behavior of the strand products is a very valuable tool to study these relationships. Here, the development, the experimental validation, and several applications of a multiscale model for strand products are presented. In a first homogenization step, the elastic properties of homogeneous strand boards are estimated by means of continuum micromechanics from strand shape, strand orientation, elastic properties of the used raw material, and mean board density. In a second homogenization step, the effective stiffness of multi-layer strand boards is determined by means of lamination theory, where the vertical density profile and different layer assemblies are taken into account. On the whole, this model enables to predict the macroscopic mechanical performance of strand-based panels from microscopic mechanical and morphological characteristics and, thus, constitutes a valuable tool for product development and optimization.