Ch. Hellmich

Estimation of Influence Tensors for Eigenstressed Multiphase Elastic Media with Nonaligned Inclusion Phases of Arbitrary Ellipsoidal Shape

The analysis of microheterogeneous materials exhibiting eigenstressed and/or eigenstrained phases requires an estimation of eigenstrain influence tensors. Within the framework of continuum micromechanics, we here derive these tensors from extended Eshelby-Laws matrix-inclusion problems, considering, as a new feature, an auxiliary matrix eigenstress. The auxiliary matrix eigenstress is a function of all phase eigenstresses and, hence, accounts for eigenstress interaction. If all material phases are associated with one and the same Hill tensor, the proposed method degenerates to the well-accepted transformation field analysis. Hence, the proposed concept can be interpreted as an extension of the transformation field analysis toward consideration of arbitrarily many Hill tensors, i.e., as an extension toward heterogeneous elastic media comprising inclusion phases with an arbitrary ellipsoidal shape and with arbitrary spatial orientation. This is of particular interest when studying heterogeneous media consisting of constituents with nonspherical phase shapes, e.g., cement-based materials including concrete, or bone. As for polycrystals studied by means of the self-consistent scheme, the auxiliary matrix eigenstress turns out to be equal to the eigenstresses homogenized over the representative volume element (RVE), which is analogous to the self-consistent assumption that the auxiliary stiffness is the average stiffness of the RVE. The proposed method opens the door for micromechanics-based modeling of a great variety of composite phase behaviors characterized by eigenstresses or eigenstrains, e.g., thermoelasticity, poroelasticity, drying-shrinkage, as well as general forms of inelastic behavior, damage, fatigue, and fracture.

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.

Creep in Shotcrete Tunnel Shells

Creep of shotcrete is modelled within the framework of thermodynamics of chemically reactive porous media. The process of creep is divided into a short-term and a long-term part. Short-term creep stems from stress-induced water movement within the capillary pores of shotcrete, located between the already formed hydrates which are the reaction products between cement and water. Thus, short-term creep is related to the accumulation of initially (micro)stress-free hydrates. Hence, it depends on increments of (macro)stress. Long-term creep results from dislocation-like processes within the (micro)stressed hydrates. Therefore, this process depends on the total (macro)stress. Microcracking of shotcrete is modelled by means of multisurface chemoplasticity. Moreover, the model accounts for chemical shrinkage and hydration heat. Finally, the significance of creep of shotcrete for real-life structures is shown by means of 3D hybrid analyses of a railway tunnel. The term ‘hybrid’ reflects the combination of advanced material modelling with in-situ displacement measurements in the framework of nonlinear Finite Element analyses.

Short-term creep of shotcrete - thermochemoplastic material modelling and nonlinear analysis of a laboratory test and of a NATM excavation by the Finite Element Method

Embedded in a thermochemoplastic material law set up in the framework of thermodynamics, the focus of the work is on the creep characteristics of shotcrete. Short-term creep, with a characteristic duration of several days, turns out to be a fundamental feature for realistic modelling of the structural behaviour of tunnels driven according to the New Austrian Tunnelling Method (NATM). Its origin is a stressinduced water movement within the capillary pores of concrete. This process is related to the accumulation of hydrates, which are initially free of micro-stress. Hence, an incremental formulation for aging viscoelasticity turns out to be a proper tool for modelling this kind of creep. The usefulness of this formulation is tested by re-analyzing a relaxation test with non-constant prescribed strains, showing quantitatively correct results for concrete and qualitatively correct results for shotcrete. The latter results indicate the necessity of classical creep tests for shotcrete.

Minutes-Long Creep Tests on Young Cement Pastes Provide Access to Creep Properties Relevant for Ageing Creep with a Duration of 2 Days

Cementitious materials are particularly creep active at early ages. The authors here perform an ageing creep test on a cement paste sample exhibiting an initial water-to-cement (w/c) mass ratio amounting to w/c = 0.50. The sample is conditioned to 20°C. The creep test is started 24 hours after production and runs for 48 hours. The loading amounts to 15% of the uniaxial compressive strength of the material at the time instant of loading. Inspired by a recently developed new testing protocol consisting of hourly-repeated three-minutes long creep tests, the authors exploit force and deformation readings recorded during the first three minutes of the authors 2-days creep test, i.e. the authors identify Young’s modulus and power-law creep properties. Given that the chemical hydration process does not progress significantly during the analyzed three minutes, the identified creep properties refer to non-ageing creep. The identified properties are combined with measurements of autogenous shrinkage, in order to predict the strain evolution over the entire 2-days runtime of the authors ageing creep test. When fitting of the creep function targets, through an appropriately chosen weight functions, the end of three minutes creep interval, in terms of both absolute creep strain and creep strain rate, then the resulting creep function remarkably well predicts creep up to a time period of 2 days.

Assessment of Protection Systems for Gravel-Buried Pipelines Considering Impact and Recurrent Shear Loading Caused by Thermal Deformations of the Pipe

Two safety topics in pipeline engineering are considered: (1) rockfall onto gravel-buried steel pipes and (2) protection of the outer anti-corrosion coating of soil-covered steel pipelines. For both cases, effective protection systems are identified, based on the results of non-linear elasto-plastic Finite Element analyses.

ANISOTROPIC FAILURE OF THE BIOLOGICAL MULTI-COMPOSITE WOOD: A MICROMECHANICAL APPROACH

Biological materials are characterized by an astonishing variability and diversity. Their hierarchical organizations are often well suited and seemingly optimized to fulfill specific mechanical functions. Still, once a (hierarchical) composite material has been adopted within a class of living organisms, its fundamental building principles, morphologies, or universal patterns of architectural organization) remain largely unchanged during biological evolution. Hence, entire material classes of biological materials exhibit common (universal) principles of (micro)mechanical design. In the theoretical framework of continuum micromechanics, such a building principle was recently expressed in quantitative terms, allowing for a prognosis of tissuespecific (inhomogeneous and anisotropic) elasticity properties of wood from tissue-specific volume fractions of (amorphous and crystalline) cellulose, hemicellulose, lignin, and water, as well as of lumen and vessel pores, based hemicellulose, lignin, and water. We here extend these investigations to tissuespecific anisotropic strength properties. Macroscopic material strength is governed by strain peaks in the material microstructure, which can be suitably characterized by quadratic strain averages over material phases, being effective for material phase failure. Macroscopic stress states estimated from local shear failure of lignin agree very well with corresponding strength experiments. This expresses the paramount role of lignin as strengthdetermining component in wood.

Protection of Infrastructure Subjected to Rockfall

Layers of gravel represent an energy-absorbing system for structures subjected to rockfall. To support the design of such structures, relations between the penetration depth and the impact force as functions of the rock boulder mass, the height of fall, and the indentation resistance of the gravel are presented. In these relations knowledge of projectiles impacting onto concrete and soil is incorporated. The indentation resistance of gravel is back-analyzed from real-scale experiments and evaluated statistically. This permits estimation of penetration depths caused by rockfall events which are beyond the experimental means of the current study. Finally, a model of the impact kinematics is deduced from experimental acceleration measurements. It yields design diagrams for impact forces, supporting probability-based engineering design of rockfall protection-systems with gravel as an energy-absorbing component.