On the elastic symmetries of growing mixed-mode cracks

Many continuum damage mechanics models for quasi-brittle materials are based on the reduction of stiffness due to elliptical crack or penny-shaped microcracks in the material. Because of this a numerical study of growing elliptical cracks in a unit cube is undertaken with the help of an FEM simulation.The propagation of the crack is governed by the principle of maximum driving force [1]. For each propagation step the tensor of elasticity is calculated and its symmetries are analyzed. It will be shown that the elastic symmetry in each step is close to orthotropy and can be approximated by an elliptical crack. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale damage analyis for steel structures

An approach to model the deterioration of steel structures is presented by transferring the results of a continuum damage mechanics analysis to an extended beam model which can account for the loss of structural integrity. Damage starts at the microscopic level by the initiation, growth and coalescence of voids with decreasing material resistance followed by the formation of microcracks at the mesoscale. Nevertheless, the material behavior can be sufficiently modelled on a phenomenological basis taking into account viscoplasticity, hardening effects and damage evolution. The associated model parameters are identified with the help of an evolutionary algorithm adapting numerical to experimental results. Using the finite element method a nonlocal formulation of the damage variable is required to obtain mesh-independent results by structural analysis. The maximum element size is limited by the small magnitude of the internal length. Therefore, numerical analyses of large scale 3D steel structures are computationally expensive. To reduce the effort a beam element is proposed to account for the plastic hinges and the loss of resistance in the course of damage evolution. The corresponding relationship of bending moment and curvature bases on the continuum damage mechanics model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New damage evolution model of rock material

As a kind of natural engineering material with original defects, there are distinctly nonlinear and anisotropic mechanical behaviors for rock materials. Nevertheless, the rock damage mechanics can solve this problem well. However, for the complexity of mechanical property of rock material, the mature and applicable model to describe the rock failure process and the method to determine the maximum damage value have not been established very well. To solve this problem, one new damage evolution model for rock material has been proposed. In this model, the least energy consumption principle proposed to describe the fracture process of materials is used. Using the experimental data of granite sample under uniaxial compression and the results of numerical tests under uniaxial tension and uniaxial compression, this model is verified. Moreover, the results of the new model have been compared with the results of the tests (numerical test and real test) and the traditional damage model. The comparison shows that the new model has the higher accuracy and better reflects for the fracture process of the granite sample. Moreover, the released damage energies of the new model and Mazars model are different, and the released damage energy of the new model is slightly less than that of the Mazars model.     

3D Simulation of Point Defect Migration in Ferroelectrics

Electric fatigue in functional materials involves a set of phenomena which lead to the degradation of materials with an increasing number of electrical cycles. Ionic and electronic charge carriers, later 0 as point defects, interact with each other and with microstructural elements in the bulk and with interfaces, which can lead to degradation, or finally to mechanical damage and dissociation reactions, see e.g. [1]. With this in mind, efforts are made to calculate the fields caused by point defects to simulate their interaction as well as to verify the used material parameters. Here, a material with linear electro mechanical coupling is used. The applied methods are integral transforms (Radon Transform) and a combination of Difference Methods and a Fast Fourier Transform to obtain solutions in an infinite domain and under periodic boundary conditions, respectively. The point defect interaction is studied within the framework of material or configurational forces. These forces are used in combination with reasonable kinetic laws to simulate defect migration, cf. [2]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical strength analysis of fiber reinforced plastics

Strength of an unidirectional lamina is computed with a representative volume element. An approximative “voxel” meshing method is used in conjunction with continuum damage mechanics to simulate crack growth in the RVE. Two material models for the nonlinear material behaviour of the epoxy resin are compared. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Life Prediction of FRP Composites by a Direct Method

A direct computational approach for lifetime prediction of fibre-reinforced polymer (FRP) composites is presented. The approach is based on a direct method which allows predicting the fatigue life from the stabilised damage state. The classical direct method is generalised to the case of coupled plasticity with damage mechanics of the UD-FRP composite materials [1]. The constitutive model is based on a continuous damage meso-scale approach [2]. By analysing damage variables and thermodynamical forces associated with damage at the stabilised state, fatigue life prediction law is proposed as a power law function of stabilised thermodynamic forces. The obtained numerical results have been validated by experimental test results on standard glass-fibre/epoxy angle-ply and cross-ply laminate plates. The proposed approach could serve as a useful tool for the design of FRP composites. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage and delamination processes in thermo-viscoelastic materials

This contribution addresses several models for rate-independent damage and delamination processes in thermo-viscoelastic materials. In the spirit of continuum damage mechanics, both degradation phenomena are modeled by means of internal variables, governed by a rate-independent flow rule. The latter is coupled in a highly nonlinear way with the heat equation and the momentum balance for the displacements. We present a suitable weak formulation for this class of models, and discuss existence and approximation results in the framework of variational convergence. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct FEM Simulation and Replacement Crack Approach for Mixed Mode Crack Growth in a Unit Cell

A whole class of continuum damage models uses microcracks as the main source of reduction of stiffness. For the growth of these cracks mostly only mode I is considered. We want to present a method to describe mixed mode crack growth inside a unit cell with a crack, without the need of a direct FEM simulation of crack growth per integration point. We replace the infinitesimal grown and kinked crack with the help of a replacement crack model. This replacement method is mainly based on the equivalence of the dissipation of the original kinking and the replacement crack. The resulting evolution of the stiffness of the unit cell is compared to a direct FEM simulation of mixed mode crack growth. The crack growth criterion used is the principle of maximum energy release rate, which has shown to be a direct consequence of a variational principle of a body with a crack [1]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relaxed Incremental Variational Formulation for Damage in Fiber-Reinforced Materials

An incremental variational formulation for damage at finite strains is proposed based on the classical continuum damage mechanics. Since loss of convexity is obtained at some critical deformations a relaxed incremental stress potential is constructed which convexifies the original non-convex problem. The resulting model can be interpreted as the homogenization of a micro-heterogeneous material bifurcated into a strongly and weakly damaged phase at the microscale. A one-dimensional relaxed formulation is derived and based thereon, a model for fiber-reinforced materials is given. Finally, some numerical examples illustrate the performance of the model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fatigue life investigation using non-destructive testing methods

Experimental investigations of the fatigue life prediction of two different specimen forms made from steel 42CrMo4 are described. The fatigue load is defined as a cyclic loading with constant and non constant amplitudes in tension range and with different stress ratios. This loading range leads to a high cyclic fatigue behaviour of both specimens. During the test, the growth of the fatigue crack is monitored using two different non-destructive methods, namely acoustic emission and the electric resistance. The acoustic emission is used for detecting sound waves as a result of dissipation of elastic energy during microcracks and cracks growth, as well as for the detection of the place of crack initiation. The electric resistance is used for the monitoring and quantitative investigation of the crack growth. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unit-cell simulations of damage and failure in PRMMCs

The purpose of this work is damage and failure modeling in multiphase metallic materials via unit-cell simulations and homogenization methods. To this end, we investigate such behaviour in particle-reinforced metal matrix composites (PRMMCs). Taking into account the processes of void nucleation (due, e.g., to particle debonding and/or cracking) and growth, we examine the effect of phase composition, particle sizes and distributions, as well as the nature of the particle/matrix interface, on damage and failure in the unit cell. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Anisotropic Damage Theories based on 2nd Order Damage Tensors

Isotropic and anisotropic damage theories are shortly reviewed concerning different aspects like thermodynamical consistency, effective undamaged configurations, crack-closure effects and the interpretation of the damage variable. A recently proposed damage growth criterion for second order damage tensors is discussed in integral as well as incremental form. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contact interaction inside knot connections of cables

Knots as a method for the fastening of ropes and other linear materials are widely appearing in practical applications ­ in sailing, in surgery, in textile and rope structures etc. The mechanics of knots, however, appears to be not sufficiently covered neither by analytical methods, nor by computational methods. From a computational mechanics point of view a knot is a perfect example requiring both a robust smooth cable element and a robust curve-to-curve contact algorithm. The current contribution is aimed on the development this combination ­ the isogeometric approach for curvilinear beams and the robust curve-to-curve contact algorithm for curvilinear cables. The developed model is applied studying the mechanics of various knots. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of stochastic point processes in mechanics

Stochastic point processes are the mathematical tools relevant to all problems where the phenomena have the nature of a random train of events. Applications may be found in structural dynamics where some stochastic excitations may be adequately idealized as random trains of impulses or general pulses. An example of application in mechanics of materials is the stochastic model of the grain growth processes in polycrystalline nanomaterials. Based on the stochastic differential equations formulation, analysis methods such as the moment equations method or the method of equation for the response probability density are dealt with. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical modelling of cellular hybrid refractories

Refractory materials are subjected to both quasi-static and dynamic thermal loading (thermal shock) causing damage up to mechanical failure. Typical refractories are magnesia carbon bricks consisting of periclase (MgO) and carbon inclusions. Recently, a significant improvement of the thermo-mechanical behaviour could be achieved by cellular hybrid composites made of periclase-filled carbon foams. The present contribution focuses on MgO-filled carbon foams and the investigation and optimisation of the structure-property relationship with respect to a reduction of thermally induced stresses and damage. It is a transient as well as static, fully coupled thermo-mechanical problem. According to the fact that, in general, refractories are brittle materials a linear elastic model, with a damage criterion was used. To optimise the structural morphology of the cellular refractories, the effect of micro structural changes has been determined. For the investigation of the thermal shock! behaviour, the results correlate very well with the experimentally motivated Hasselman relation. There is a significant size effect depending on the pore size. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental study of fracture toughness and energy in composite materials

The paper presents an experimental investigation of fracture characteristics of composite materials. The post-peak response of the load-crack opening displacement of notched specimens is used to evaluate the fracture energy associated with progressive matrix damage and crack growth. Effects of fiber orientation and other geometric characteristics on fracture parameters are studied. The load versus crack opening displacement as well as crack length, fracture toughness, and energy versus the number of loading cycles are obtained for different specimens. Based on the experimental results of this study, concepts of the fracture mechanics are applied to evaluate the evolution of fracture toughness and energy.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Department of Mechanical & Industrial Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 323–332, May–June, 1998.     

Modeling Dislocation-Stacking Fault Interaction Using Molecular Dynamics

In a number of fcc materials such as copper or aluminum, as well as more complex materials such as twinning induced plasticity (TWIP) steels, the interaction between dislocations and other defects such as stacking faults or twins plays an important role in the hardening behavior of such materials. Interactions of dislocation and twin or stacking fault layers have been studied in this work using molecular dynamics. Depending on the material and the loading conditions, possible interaction modes include (i) penetration of the dislocation into the faulted layer, (ii) reduction of the faulted layer after interaction, (iii) growth of the faulted layer after interaction. Such studies up to this point have been performed without temperature control near zero K (0 to 2 K). In this work, we extend the previous studies to higher temperature with the help of two methods, both based on molecular dynamics (MD) modeling. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropic elasto-plastic damage formulation for finite strains using a damage structural tensor and the effective stress concept

Using the strain equivalence principle and the effective stress concept an anisotropic finite strain damage model is proposed as a direct extension of the classical isotropic LEMAITRE damage model to the anisotropic finite strain case. The damage tensor is included as a structural tensor in the complementary energy potential. This approach allows to consider a wide range of anisotropic damage phenomena on the level of continuum mechanics. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Construction of a bipotential for a multivalued constitutive law

Bipotentials are non smooth mechanics tools, which allows modelling various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). We answer the following question: given a graph M representing a material behaviour, is there a bipotential b for which M is the set of (x, y) such that b (x, y) = 〈x, y 〉? We state a simple necessary and sufficient condition for the existence of b. If it is fulfilled, we construct the bipotential. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)