Holm Altenbach

Theories for laminated and sandwich plates

The growing use of sandwich and laminated plates requires a theoretically based prediction of the mechanical behavior of structural elements of such type. Starting with the pioneering studies of Reissner, a great number of theories for the engineering calculations have been developed. The review deals with the classification of the theories and discusses some of them in detail.

An alternative determination of transverse shear stiffnesses for sandwich and laminated plates

Abstract Two-dimensional shear-deformable laminated plate theories can be classified as equivalent single-layer theories and layerwise theories. Layerwise theories lead to better approximations than equivalent single-layer theories, but the large number of independent unknowns in these theories requires more computational power in comparison with calculations, based on equivalent single-layer theories. The quality of any equivalent single-layer theory based calculation is influenced by the correct determination of the effective stiffnesses. Many theories result in identical stiffnesses for bending, tension/compression, in-plane shear and torsion. The differences between the approaches are connected with the transverse shear stiffnesses. The method of determination of the transverse shear stiffnesses proposed here leads to expressions which depend on the solution of a Sturm–Liouville-problem. For special cases, the stiffnesses are calculated and compared with results from other authors. It can be shown that the present approach can be useful not only in the case of laminated plates, but also for sandwich plates.

The influence of surface tension on the effective stiffness of nanosize plates

The unique features of nanomaterials make them quite attractive for applications [1, 2]. One of the factors that is responsible for the anomalous behavior of nanomaterials is due to the surface effects. In particular, taking into account the surface tension allows us to describe the observed finite size effect, i.e., the dependence of the properties of the material, e.g., its Young modulus, on the sizes of the specimen. Experimental and theoretical studies of the influence of the surface tension on effective properties of nanomaterials (nanoporous media, nanofiners, etc.) were described in a significant number of papers (see, e.g., [3-6]). In the present work, we consider the problem of bending of a nanosize plate, taking into account the action of the surface effects. We obtain expressions for the effective stiffnesses.

Mechanics of generalized continua

State of the Art and prospects in generalized GCM.- Microstructure, homogenisation and GCM modelling.- Application of GCM to intertwined fabrics.- GCM modelling of granular materials.- Scaling effects and metamaterials.-Applications of GCM in the strength of materials.- Application of GCM in 3D periodic structures.- GCM and numerics.- Hierarchy of scales in modelling materials.-Fractals and GCM.- Nonlinear waves in Cosserat continuum.- Analytical and numerical solutions for problems of the theory of asymmetric elasticity and their applications for experimental studies.- Kinetics of chemical reactions in deformable solids with dynamic loading.- Constitutive models of mechanical behaviour of media with stress state dependent material properties.- Theory of continuously distributed disclinations and dislocations in micropolar media.- On one model of generalised continuum and its thermodynamical interpretation.- Mechanics of carbon nanostructures.- The influence of the Cosserat concept on the theory of strength of materials.-Visualization at studying hydrodynamic instability in strong .-Nonlinear dynamic processes in media with internal structure.- On the Application of Generalized Continua Models to Structural Mechanics.- An Axiomatic Framework for Gradient-Materials.- Logarithmic Deformation Measures and Tensors Applied to Generalized Continua.- Modelling and Simulation Aspects of Generalised Multiphysics Continuum Models.- A Micro-Macro-Based Investigation of Micropolar Media.- Micromechanical Interpretation of Kinematically Extended Continua.- Subgrid Interaction and Homogenisation: New Invariance Conditions in Gradient Elasticity.- Numerical Considerations of FE^2 Problems.- Dispersive Waves in Generalized Continua: Experimental and Theoretical Investigations.- Generalized Continua Applied to Nano-size Objects

On elastoplastic deformation of grey cast iron

Abstract Many engineering materials appear an independent from the kind of loading elastoplastic material behavior. With respect to the sign convention we get, for instance, the same stress-strain diagrams for tension and compression. For materials which contain voids, pores, etc., different elastoplastic stress–strain curves can be obtained in tension and compression tests. In addition to these experimental observations, such materials often show inelastic volumetric deformations. Grey cast iron is a typical example of this kind of material. Constitutive equations for this special elastoplastic behavior are derived as a particular case of generalized constitutive equations for isotropic materials based on a potential. The yield condition is established on the second invariant of the stress deviator and, additionally, on the first invariant of the stress tensor and on a hardening parameter. The plastic potential depends on the same arguments, but a nonassociated flow rule is assumed. For the hardening function, a modification of the plastic work hardening model is used. All parameters of the model are identified by tests. The verification is realized by different independent tests.

A Combined Model for Hardening, Softening, and Damage Processes in Advanced Heat Resistant Steels at Elevated Temperature

Phenomenological constitutive equations that describe inelastic behavior of advanced steels at elevated temperature are developed. To characterize hardening, recovery, and softening processes, a composite model with creep-hard and creep-soft constituents is applied. The volume fraction of the creep-hard constituent is assumed to decrease toward a saturation value. This approach reproduces well the primary creep as a result of stress redistribution between constituents and tertiary creep as a result of softening. To describe the whole tertiary creep stage, a damage variable in the sense of continuum damage mechanics is introduced. The material parameters and the response functions in the model are calibrated against experimental creep curves for X20CrMoV12-1 steel. For the verification, simulations of the inelastic response are performed and the results compared with experimental data including creep under stress change conditions and stress-strain response under constant strain rate. Furthermore, the lifetime predictions are analyzed and compared with the published creep rupture strength data. The results show that the consideration of both softening and damage processes is necessary to characterize the long-term strength in a wide stress range. Finally, the model is generalized to the multi-axial stress state.

The Theory of Simple Elastic Shells

At present the shell theory find out new branches of applications. Biological membranes, thin polymeric films and thin structures made from shape memory materials may be pointed out as examples . In addition, the manufacturing technology of shells leads to significant changes of the material properties. As a result the conventional variants of the shell theory, based on the derivation of the basic equations from the 3D-theory of elasticity, cannot be used. The effective elastic moduli of the shell must be found directly for the shell structure. That means that we have to use the direct method for the formulation of the shell theory. The main idea of the direct approach is the introduction of a 2D-continuum with some physical properties. The basic laws of mechanics and thermodynamics are applied directly to this 2D-continuum. The main advantage of the direct approach is the possibility to obtain quite strict equations.

Creep and damage in materials and structures

General Constitutive Equations for Simple and Non-Simple Materials (P. R. Gummert).- Classical and Non-Classical Creep Models (H. Altenbach).- Material Damage Models for Creep Failure Analysis and Design of Structures (J. J. Skrzypek).- Materials Data Bases and Mechanisms-Based Constitutive Equations for Use in Design (D. R. Hayhurst).- Thermodynamically Founded CDM Models for Creep and other Conditions (J.-L. Chaboche).- Creep Plasticity Interaction (E. Krempl).- The Standard Linear Solid as a Basis for VBO.- Modeling of Rate-Independence and of Negative Rate Sensitivity.

A New Static Failure Criterion for Isotropic Polymers

A new static failure criterion for isotropic polymers with different strengths in tension and compression based on exponential dependence between the mean stress and the von Mises equivalent stress is proposed. The two material parameters introduced can be determined by two simple tests - the uniaxial tension and compression. The locus of the criterion is nearly conical for low hydrostatic pressures and tends to a cylindrical form if an increased hydrostatic pressure is applied. The validity of the criterion is demonstrated by experimental strength data taken from the literature for several polymers in the case of superimposed hydrostatic pressure.

Phenomenological Yield and Failure Criteria

Models for isotropic materials based on the equivalent stress concept are discussed. At first, so-called classical models which are useful in the case of absolutely brittle or ideal ductile materials are presented. Tests for basic stress states are suggested. At second, standard models describing the intermediate range between the absolutely brittle and ideal-ductile behavior are introduced. Any criterion is expressed by various mathematical equations formulated, for example, in terms of invariants. At the same time the criteria can be visualized which simplifies the application. At third, in the main part pressure-insensitive, pressure-sensitive and combined models are separated. Fitting methods based on mathematical, physical and geometrical criteria are necessary. Finally, three examples (gray cast iron, poly(oxymethylene) (POM) and poly(vinyl chloride) (PVC) hard foam) demonstrates the application of different approaches in modeling certain limit behavior. Two appendices are necessary for a better understanding of this chapter: in Chap. 2 applied invariants are briefly introduced and a table of discussed in this chapter criteria with references is given.