Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 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)     

Modeling of Anisotropic Damage in Arterial Walls

In a certain range of overexpansion arterial walls are characterized by an orthotropic elastic material behavior. Due to different stabilities of the helically arranged fibers, i.e. breakage of collagen crosslinks between the fibers, damage effects are observed in experiments. Because of the fibrous composition it is assumed that damage mainly occurs in the fiber direction. The proposed damage model is extended to arterial wall applications by introducing a referential damage state. The damage approach is applied to a polyconvex model for the hyperelastic behavior of arteries in order to obtain a materially stable model, which guarantees the existence of solutions of the underlying boundary value problem. The performance of the proposed model is presented in a numerical example, where the overexpansion of an atherosclerotic artery is simulated. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A three-dimensional progressive damage model for fiber reinforced composites with an implicit-explicit integration scheme

This contribution proposes a fully three dimensional “continuum damage model” (CDM) to describe the interlaminar and intralaminar failure mechanisms of transversely isotropic elastic-brittle materials under static loading. The constitutive model is derived from an energy function with independent damage variables for each damage mode. The evolution law is based on energy dissipation within the damage process, taking into account the critical energy release rate to weaken the effect of mesh dependent outcome. The onset of damage can be predicted with Cuntze's failure mode concept [1] as well as with Hashin's failure criteria. In this model linear stress decreasing is assumed. In addition, an implicit-explicit integration scheme, first proposed by Oliver [3] for isotropic damage models, is adapted to increase the stability and robustness of numerical simulations and to decrease the computational cost of material failure analyses. By comparing the results from implicit-explicit integration schemes and standard implicit integration schemes, a high level of agreement is found. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage modelling and lifetime prediction of adhesively bonded joints under sustained loading with constant and variable amplitudes

The lifetime of adhesively bonded joints under service loading is predicted by a linear viscoelastic traction–separation model, which is enhanced by an isotropic damage approach. Therefore, a scalar damage variable is defined according to the concept of effective stresses based on the hypothesis of strain equivalence in the framework of continuum damage mechanics. The damage evolution is driven by a specific equivalent stress, adapted for ductile adhesives. Experimental data acknowledge the validity of the proposed model for the lifetime prediction of adhesive joints. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of an elastoplastic material model coupled to nonlocal damage in an implicit-gradient framework

In this work, an elastoplastic material model coupled to nonlocal damage is discussed which is based on an implicit gradient-enhanced approach. Combined nonlinear isotropic and kinematic hardening as well as continuum damage of Lemaitre-type are considered. The model is a direct nonlocal extension of a corresponding local model which was presented earlier (see e. g. [1], [2], [3]). Conclusions drawn from a numerical benchmark test performed in this study demonstrate that the nonlocal damage model is suitable to provide mesh-independent solutions in finite element simulations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On nonlinear damage accumulation and creep-fatigue interaction of a damage model for the lifetime prediction of adhesively bonded joints

Damage accumulation and creep-fatigue interaction are investigated and depicted for a continuum damage model proposed for the lifetime prediction of bonded steel joints with the structural adhesive BETAMATE 1496V™. The nonlinearity of damage accumulation is caused by the nonlinearity of damage interaction as a result of the identified parameters. In consequence of the nonlinear accumulation, the model allows for the loading sequence effect, which is the influence of the chronological order of the load values on the lifetime. Although the nonlinearity of the damage accumulation is not very pronounced, the model prediction is in good agreement with lifetimes from tests with service loading of the adhesive at hand. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of interfacial damage and delamination of sprayed coatings with cohesive elements

Delamination of thermally sprayed corrosion protection coatings as a consequence of thermo-mechanical fatigue is investigated. This study focusses on the modelling of interfacial damage initiation and evolution under cyclic loading with the help of a cohesive zone model. The presented model features a slight non-linearity at unloading from the exponential “damage locus” as well as cyclic damage accumulation restricted to (re)loading conditions. Additionally, an endurance limit is introduced indicating the maximum sustainable traction for an infinite number of load cycles. The capability of the model is demonstrated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Causes of the damage created by laser pulses in transparent polymers

The characteristics of the damage created in PMM, PS, and PC specimens by multiple irradiation are discussed. It is shown that, in addition to the growth of the damage zone, the processes of crack development that determine this zone are also important. The damage created in PMM when the laser beam is interrupted by a cylindrical cavity is considered. In this case, the cavity acts as a diverging lens and the damage beyond it is determined by the scattered flux. The damage produced in specimens of different shapes is investigated. A model is proposed for crack development in a polymer irradiated by a powerful flux. The model is consistent with most of the known experimental facts.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1035–1042, 1967     

Micro-mechanical studies on the effect of various stress-states on ductile damage and failure

The paper deals with the effect of different stress states on damage and failure behavior of ductile materials. To be able to model these effects a continuum damage model has been proposed taking into account the dependence of the stress intensity, the stress triaxiality and the Lode parameter on the constitutive equations. The model is based on the introduction of damaged and fictitious undamaged configurations. Only experiments are not adequate enough to determine all constitutive parameters. Therefore, additional three-dimensional micro-mechanical simulations of representative volume elements have been performed to get more insight in the complex damage mechanisms. These simulations cover a wide range of different void sizes, void shapes and void distributions. After all, the results from the micro-mechanical simulations are used to propose the damage equations and to identify corresponding parameters. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A regularized damage-plasticity model: micromorphic formulation and numerical aspects

A gradient-extended damage-plasticity model is discussed which is based on a micromorphic approach according to Forest [1]. Damage and plasticity are treated as independent but strongly coupled dissipative phenomena by considering separate yield and damage loading functions to describe the onset of plastic flow and / or damage evolution. A numerical benchmark test conducted in the study reveals that the model is able to essentially cure the well-known mesh-dependence issue which is known from finite element simulations involving conventional (i. e. ‘local’) damage material models. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of structural hypotheses on the elastic-viscoplastic response of shock wave-loaded plates

If circular metal plates are subjected repeatedly to impulsive loadings, damage and failure of the structures can occur. In order to predict the damage evolution in finite element simulations, a structural theory combined with viscoplastic constitutive equations acounting for damage is used. However, different structural hypotheses, used in the theoretical model, can lead to variations in the numerical result. Therefore, first- and third-order shear deformations theories are applied in a finite element code. Moreover, local and non-local damage approaches are used. The aim is to determine the numerical model, which leads to the most accurate results compared to experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparative Study of the Influence of Statistically Distributed Microscopic Quantities on the Damage in Collagenous Tissues

In this contribution we investigate the influence of dispersed microscopic quantities on the damage behavior in collagenous tissues. Therefore, we derive a damage model, that may take into account statistical distributions of collagen fiber properties. In detail, we regard distributions of the orientation of fibril-interconnecting proteoglycan (PG) bridges and of an internal fibril length parameter. The damage model is embedded into the constitutive framework from [1] and a numerical example in a finite element framework is given. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional cell model analysis of ductile damage under dynamic loading condition

The paper deals with the damage and fracture behavior of ductile metals under dynamic loading conditions. The in [1–3] presented phenomenological continuum damage and fracture model, which takes into account the rate- and temperature-dependence of the material, provides reasonable results of experiments with high strain rates while the identification of the corresponding material parameters results difficult from the available experimental data. This lack of information can be resolved by micro-mechanical numerical simulations of void containing unit-cells. In this context results of dynamic micro-mechanical simulations are presented which can be used to study the damage effects on the micro-scale and to validate the rate-dependent continuum damage model. (© 2014 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)     

Certain characterizations with linearity of regression in additive damage models

This paper investigates the characterizations of certain discrete distributions within the framework of a multivariate additive damage model. The univariate case for such a model appeared in an article by [2]. In this model a p-dimensional observation is subjected to damage according to a specified probability law represented by a joint survival distribution. Here, it is shown that the linearity of regression of the damaged part on the undamaged ones leads to the characterizations of the multivariate binomial, and multiple inverse hypergeometric distribution as survival distributions.     

Thermodynamics of diffuse damage in solids

A thermodynamic model of the accumulation of diffuse damage in deformed solids is proposed. A closed system of dynamic equations of thermo-fractomechanics is constructed. A solution of the non-linear equation of the “diffusion” of damage in the form of a plane stationary kink-shaped damage wave is obtained. It is shown that the velocity of the wave front is proportional to the invariants of the strain (stress) tensor and the “diffusion” coefficient, and inversely proportional to the force of resistance to damage accumulation.     

Micro-mechanical analyses of the effect of stress triaxiality and the Lode parameter on ductile damage and failure

The paper deals with the effect of different stress states on plastic deformations, damage and fracture of ductile materials. To be able to model these effects a continuum damage model has been introduced taking into account the dependence of stress-state on the constitutive equations. The model is based on the introduction of damaged and fictitious undamaged configurations. All parameters appearing in the constitutive equations are stress-state-dependent which can be characterized by the stress intensity, the stress triaxiality and the Lode parameter. Only experiments are not adequate enough to determine all constitutive parameters. Thus, additional series of three-dimensional micro-mechanical simulations of representative volume elements have been performed to get more insight in the complex damage mechanisms. These simulations cover a wide range of stress triaxialities and Lode parameters in tension, shear and compression domains. After all, the results from the micro-mechanical simulations are used to suggest the damage equations and to identify corresponding parameters. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)