Granular materials: Parameter identification and modelling of localisation problems

The prediction of landsliding requires an exact knowledge of the mechanical behaviour of granular materials. This kind of materials, e. g., sand, have a very complex deformation behaviour, which depend on the stress state and on the loading history. In this work, the deformation behaviour of the solid skeleton is characterised via homogeneous triaxial tests on dry sand specimens. Additionally, an appropriate elasto-plastic material law to describe the solid skeleton in the frame of Theory of Porous Media (TPM) is used, which is implemented in the FE tool PANDAS. Furthermore, a single-surface yield criterion with isotropic hardening, which limits the elastic domain, and a non-associated plastic flow are employed. The determination of the material parameters of the linear elasticity law as well as the single-surface yield criterion are based on test data of triaxial experiments. The material parameters are identified using a derivative-based optimisation method (donlp2), which is coupled with PANDAS. Finally, a simulation of a benchmark test is presented to show shear band localisation effects, where the material behaviour is described by a triphasic porous media model based on the TPM, where the constituents are a deformable solid skeleton and two pore fluids, water and air. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of deformation and failure in rubber-toughened polymers – effect of distributed crazing

A continuum mechanical model for rubber-toughened polymers undergoing inelastic deformation solely by distributed crazing is introduced. Scaling relations with regard to microstructural parameters are derived analytically from a simple unit cell model. The constitutive model is calibrated from experimental data for a commercial ABS material and well captures various aspects of its deformation and failure behaviour. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Permeability Studies on Soft Open‐Cell Foams

The behaviour of fluid‐saturated solid foams can be very well described using multiphasic continuum mechanical models [4]. Concerning permeable soft foams, like e. g. gas‐filled open‐cell polyurethane (PU) foams, the transient compressive response is strongly influenced by the outstreaming pore‐fluid. Following this, it is the objective of the present contribution to point out the macroscopic permeability properties of soft foams including non‐linear phenomena influenced by the pore space deformation at varying flow rates. In particular, based on experimental investigations, an appropriate constitutive setting is presented considering the dependency of the permeability on the deformation state and on the seepage velocity in the sense of a modified Forchheimer ansatz. The constitutive equations are embedded into the macroscopic Theory of Porous Media (TPM), where the numerical treatment of the strongly coupled problem can effciently be performed with the finite element method (FEM). Finally, a numerical example shows the applicability of the presented approach.     

Analytical modelling of the in-plane compressive behaviour of pile fibres in Spacer Fabric Composites

The mechanical behaviour of Spacer Fabric Composites (SFC) is highly influenced by their pile fibres. Within this work, the in-plane compressive behaviour of pile fibres in SFC is investigated. An analytical model is developed based on rigid hinged struts. Therefore, a representative part of the continuous fibre is chosen. The bending behaviour and the interaction of the pile fibre with facesheet fibres is modelled using rotational and extension springs respectively. The system proposed is fully defined by three generalized coordinates. The total potential energy of the system is determined and used to obtain information about the deformation behaviour. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element simulation of deformation behaviour of cellular rubber components

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using porous hyperelastic material model. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The new material model which is based on Danielsson et al [1] decouples the influence of porosity from the mechanical properties of the solid material by introducing volume fraction of the pores as an explicit scalar variable. The finite element simulations are then followed by experiments on complex model to validate the material model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A non-affine micro-sphere formulation for electroactive polymers

With the capability to convert electrical energy into mechanical energy, electroactive polymers (EAP) continuously find new and more advanced applications. Their ability to considerably change in size and shape together with low cost and weight makes them suitable for technological applications in robotics and biomimetics as actuators and sensors. A dielectric actuator, one of the most common applications of EAP, consists of a soft elastomer sandwiched between two electrodes. Common for elastomeric material is a viscous response and associated time dependence on both electric and mechanical behaviour. In this work, an electromechanically coupled micro-sphere formulation for nonlinear electroelasticity formerly proposed by the authors is further extended and includes non-affine deformation measurements as well as viscous effects. Also, a finite element simulation of a cylindrical specimen and calibration of mechanical parameters have been performed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Simulation of Food Foams

The rheological behaviour of protein solutions containing bubbles at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. Protein foams have a great importance in food production because of their special sensory properties. A suspension that contains bubbles in a Newtonian liquid exhibits inherently a complex rheological behaviour, such as elastic effects, a shear- and time-dependent viscosity and normal stress differences. The deformation state of the bubbles in a suspension subjected to a steady shear is a function of the gas volume fraction ϕ and the capillary number N_Ca. In the present article, material equations for protein solutions with gas volume fractions ϕ ≤ 0.75 and small bubble deformations, i. e. N_Ca ≪ 1, are analysed and further developed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite element model for biofilm volume growth

In this work, we present a continuum-based approach for biofilm volume growth. The deformation gradient will be multiplicatively decomposed into two parts: a growth part due to bacteria formation and an elastic part due to the interaction with the environment. In order to define the growth behaviour of biofilms, we use the Monod approach that depends non-linearly on the substrate concentration. The substrate concentration in the biofilm is computed by means of a diffusion process, which includes substrate consumption, together with the mechanical behaviour as part of a coupled problem. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel model to describe the intervertebral disc mechanical response

The main objective of the present work is the development of a simplified, efficient and easy-to-implement single-phase material model, which is able to describe the essential effects characterising the behaviour of multi-phase saturated materials, such as of intervertebral discs (IVDs). The presented new model mainly focuses on extending a viscoelastic material model in order to not only take the mechanical behaviour of the solid part into account, but also the fluid-flow-dependent behaviour of the material. By applying this model, the complexity and constitutive parameters are reduced, the implementation is more convenient and the experimental investigations can be better supported in comparison to multi-phase material models of IVDs. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Porous Media Model to Describe the Behaviour of Brain Tissue

The human brain is a very sensitive organ. Even small changes in the cranium cavity can cause life–threatening effects. In case of medical intervention, biomechanics can assist the therapy decisions by simulating the physical behaviour of brain tissue, e.g., the coupled interaction of the fluid motion and the deformation of the brain tissue. In the context of the Theory of Porous Media (TPM), a convenient model of the brain is introduced, which is able to simulate essential mechanical effects in the porous structure of the brain material. The fluid–saturated brain can be treated as an immiscible binary mixture of constituents. In this macroscopic biphasic model, the mixture consists of a solid phase (brain tissue) and a fluid phase (interstitial fluid or blood plasma). Both constituents are assumed to be materially incompressible. The resulting set of coupled partial differential equations is then spatially discretised using mixed finite elements with a backward Euler time integration. Numerical examples are presented illustrating the fundamental effects on the brain tissue under heart–rate dependent pulsative pressure variations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the nonlinear matrix material behaviour on the effective properties of textile-reinforced thermoplastics

For a consistent lightweight design the consideration of the nonlinear macroscopic material behaviour of composites, which is amongst others driven by damage and strain-rate effects on the mesoscale, is required. Therefore, a modelling approach using numerical homogenization techniques is applied to predict the effective nonlinear material behaviour of the composite based on the finite element simulation of a representative volume element (RVE). In this RVE suitable constitutive relations account for the material behaviour of each constituents. While the reinforcing glass fibres are assumed to remain linear elastic, a viscoplastic constitutive law is applied to represent the strain-rate dependent, inelastic deformation of the matrix material. In order to analyse the influence of the nonlinear matrix material behaviour on the global mechanical response of the composite, effective stress-strain-curves are computed for different load cases and compared to experimental observations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Harmonic decomposition analysis of contact mechanics of bonded layered elastic solids

The paper presents an iterative method for obtaining footprint, pressure distribution, local deformation and sub-surface stress field for the contact between a rigid cylindrical indenter and an elastic flat substrate. The methodology is applicable for semi-infinite, as well as for thin or thick bonded elastic layered solids with high or low elastic moduli. All findings are in accord with the observed behaviour of hard wear resistant and soft solid lubricating coatings. It is shown that the decomposed contact pressure distribution into a series of harmonic waves induces sub-surface stress fields that decay into the depth of the solid according to their wavelengths. Consequently, conditions vis-à-vis fatigue spalling and adhesion performance may be predicted for given thickness of layered bonded elastic solids.     

Solid-Shell Finite Elements for Tesselated Geometries

Sandwich structures made of sheets of composite materials are in widespread use, particularly in the transportation industry. Finite Element simulation of the thin, tesselated structures with complex, three-dimensional material behaviour is a challenging task for the underlying element technology. In particular, frequently used linear isoparametric approaches exhibit unphysical stiffening phenomena. Recent developments in solid-shell finite element technology aim to overcome these undesirable effects. Here, they are applied to an example of a corrugated sandwich core under transversal compression. A study of convergence is conducted with respect to commercially available shell and solid finite elements, and their ability to reproduce the bending dominated deformation state. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic Deformation of Dispersely Failing Unidirectionally Reinforced Composites

A phenomenological model is proposed for describing the elastic deformation of a unidirectionally reinforced composite capable of accumulating scattered microdamages during its loading. The composite is considered as a homogeneous transversely isotropic solid. Its damaged state at every point is characterized by a centrally symmetric scalar function on the unit sphere (the damage function), which is used to account for variations in the elastic properties of the material during its deformation. The damage itself depends on the history of some equivalent strain, for which four simplified variants are suggested. The relation between strains and stresses is defined in a differential form. Dependences are presented for determining all unknown constants from simple mechanical experiments. As an example, an actual unidirectionally reinforced GFRP is considered, for which the main two-dimensional sections of corresponding failure surfaces are also constructed.     

Analysis of the coupling effects of the longitudinal and transverse displacements on the deformation and internal forces of functionally graded beams

Functionally graded beams (FGBs) with an arbitrary gradation of the material properties along the thickness of the beams are analyzed. Such FGBs are of special interest in civil and mechanical engineering to improve both the thermal and the mechanical behaviour of the beams. In [1] and [3] free vibrations of functionally graded Timoshenko and Euler-Bernoulli beams have been considered. The obtained analytical solutions are based on the work of Li [2], where closed-form solutions of stress distributions, eigenfrequencies and eigenfunctions have been derived by means of a single differential equation of motion for the deflection. However, these previous works did not take into account the coupling between the longitudinal and the transverse displacements and its effects on the deformation and internal forces of the FGBs. This approach is appropriate only for a symmetrical material gradation but it may not be valid for general cases with an arbitrary material gradation. In this paper, the coupling effects of the longitudinal and transverse displacements on the deformation and internal forces of FGBs are investigated for different beam support conditions. Analytical solutions of the corresponding boundary value problem are derived. A comparison is also made with the numerical results obtained by the finite element method (FEM). (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A solid shell finite element formulation to simulate the behaviour of thin dielectric elastomer structures

To analyse the behaviour of thin structures of dielectric elastomer (DE) material a solid shell finite element is presented. The main characteristics of DEs are a non-linear hyper elastic behaviour, the quasi-incompressibility, and the ability to transform electric energy into mechanical work. Applying a voltage to thin DE structures may produce large elongation strains of 120-380%. These large strains, the efficient electro-mechanical coupling, and the light weight make DEs very attractive for the usage in actuators. Thus, there is a need for detailed research. With respect to the electro-mechanical coupling a constitutive model is presented. An electric stress tensor and a total stress tensor are introduced by considering the electrical body force and couple in the balance of linear momentum and angular momentum, respectively. The governing equations are derived and embedded in the solid shell formulation. The element formulation is based on a Hu-Washizu mixed variational principle using six independent fields: displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements. It allows large deformations and accounts for physical nonlinearities to capture two of the main characteristics of DEs. The shell element could be applied for the modelling of arbitrary curved thin structures. The ability of the present element formulation is demonstrated in several examples. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupled multiscale finite element analysis of shell structures

In this paper, a coupled two-scale shell model is presented. A variational formulation and associated linearisation for the coupled global-local boundary value problem is derived. The discretisation of the shell is performed with quadrilaterals, whereas the local boundary value problems at the integration points of the shell are discretised using 8-noded or 27-noded brick elements, or solid shell elements. The coupled boundary value problem is simultaneously solved within a Newton iteration scheme. Solutions for small strain problems are computed within the so-called FE² method. In an important test, the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified. Examples show that the developed two-scale model is able to analyse the global and local mechanical behaviour of heterogeneous shell structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constitutive modelling of thermo-viscoelastic-plastic behaviour of adhesively bonded joints

For ductile structural adhesives under thermal and mechanical loading, a thermo-viscoelastic-plastic interfacial constitutive model is introduced using a generalised MAXWELL solid in series with a thermal strain element and a ST.-VENANT body with isotropic hardening for plasticity. The temperature dependency of the viscosity is taken into account on assuming thermorheologically simple material behaviour, while the yield threshold and the hardening parameters depend on empirical functions of temperature. Numerical examples for the model verification and validation are discussed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)