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.     

Modelling and Simulation of the Transport of Protein Foams

The behaviour of foams at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. The present article deals with protein foams as they have a great importance in food production. In the first part, the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid is considered. The aim is to calculate the foam volume and the concentration of the dissolved, volatile components as a function of the material and process parameters. In the second part, material equations for bubble suspensions with gas volume fractions ϕ ≤ 0.6 and small bubble deformations (i.e. N_Ca ≪ 1) are presented. The basics form two constitutive laws which are used for describing a steady shear flow. If the rates of work of the two models are compared, material equations for the shear viscosity and the normal stress differences can be derived. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of the deformation processes and the localization of plastic deformations in the torsion–tension of solids of revolution

Generalized two-dimensional problems of the torsion of elastoplastic solids of revolution of arbitrary shape for large deformations under non-uniform stress-strain conditions are formulated and a method for their numerical solution is proposed. The use of this method to construct strain diagrams of materials based on experiments on the torsion of axisysmmetric samples of variable thickness until fracture occurs is described. Experimental and numerical investigations of processes of elastoplastic deformation, loss of stability and supercritical behaviour of solid cylindrical steel samples of variable thickness under conditions of monotonic kinematic loading with a torque, a tension and a combined load are presented. The mutual influence of torsion and tension on the deformation process and the limit states is estimated, and the universality (the independence of the form of the stress-strain state) of the “stress intensity – Odqvist parameter” diagram for steel for large deformations is proved.     

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)     

Experimental and numerical investigation of metal foams undergoing large deformations

Open cell aluminum metal foams are a new kind of material that are used in composite structures to reduce their weight, to increase their sound or energy absorption capability or to decrease their thermal conductivity. The design and analysis of such structures requires a macroscopic constitutive model of the foam that has to be determined by various experiments under different loading conditions. We support this procedure by analyzing the microstructure of the metal foam numerically under large deformations. To this end, we employ the finite cell method that can deal with large deformations and allows for an automatic and efficient discretization of the CT-image of the foam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Updated Lagrangian Taylor-SPH method for large deformation in dynamic problems

In this paper, the updated Lagrangian Taylor-SPH meshfree method is applied to the numerical analysis of large deformation and failure problems under dynamic conditions. The Taylor-SPH method is a meshfree collocation method developed by the authors over the past years. The governing equations, a set of first-order hyperbolic partial differential equations, are written in mixed form in terms of stress and velocity. This set of equations is first discretized in time by means of a Taylor series expansion in two steps and afterwards in space using a corrected form of the SPH method. Two sets of particles are used for the computation resulting on the elimination of the classical tensile instability. In the paper presented herein the authors propose an updated Lagrangian Taylor-SPH approach to address the large deformations of the solid, and therefore the continuous re-positioning of the particles. In order to illustrate the performance and efficiency of the proposed method, some numerical examples based on elastic and viscoplastic materials involving large deformations under dynamic conditions are solved using the proposed algorithm. Results clearly show that the updated Lagrangian Taylor-SPH method is an accurate tool to model large deformation and failure problems under dynamic loadings.     

Collapse criteria of foam cells under various loading

Recently porous materials are widely used in civil and mechanical engineering. In particular, such porous materials as metal and polymer foams have applications in lightweight structures. From mechanics point of view foams can demonstrate unusual behavior such as strain localization related to foam cells buckling under certain loads. The aim of this work is the elaboration of the model of foam material taking into account the cell collapse. We consider the cell collapse initiation during the elastic instability and its further evolution under loading. The geometrical structure of foam is generated with the use of the Voronoi algorithm. Based on stochastic distributions of cells we create various geometrical models of foams. The influence of the cell volume, wall thicknesses and material properties of the foam material on critical loads is obtained. The calculations are performed with the use of Abaqus CAD/CAE system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A general modelling framework and specific mechanical approaches to simulate curing phenomena in polymers

Polymers are employed as adhesives, filling or sealing materials, among others. Within these applications, a chemical reaction (e.g. polymerization) leads the materials to cure from a liquid to a solid. In this contribution, first a general continuum mechanical modelling framework for the simulation of curing phenomena is highlighted. It takes into account the main chemical, thermal and mechanical phenomena of polymeric curing processes. Secondly, different mechanical models to capture the mechanical behaviour of polymeric curing processes are regarded. It is shown that elastic, viscoelastic and viscoplastic models at large deformations can be employed. (© 2016 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)