Orthotropic Damage Model Research Articles

Quantitative validation of carbon-fiber laminate low velocity impact simulations

Simulations of low velocity impact with a flat cylindrical indenter upon a carbon fiber fabric reinforced polymer laminate are rigorously validated. Comparison of the impact energy absorption between the model and experiment is used as the validation metric. Additionally, non-destructive evaluation, including ultrasonic scans and three-dimensional computed tomography, provide qualitative validation of the models. The simulations include delamination, matrix cracks and fiber breaks. An orthotropic damage and failure constitutive model, capable of predicting progressive damage and failure, is developed in conjunction and described. An ensemble of simulations incorporating model parameter uncertainties is used to predict a response distribution which is then compared to experimental output using appropriate statistical methods. Finally, the model form errors are exposed and corrected for use in an additional blind validation analysis. The result is a quantifiable confidence in material characterization and model physics when simulating low velocity impact in structures of interest.

Finite Element Analysis of Hot Melt Adhesive Joints in Carton Board

The mechanical behaviour of adhesive joints is critical for the performance of adhesively joined carton board packages. In this work, finite element analyses of hot melt adhesive (HMA) joints in carton board is conducted and compared to experimental results obtained using a Y-peel testing device. The aim of the present study is to analyse the behaviour of adhesive joints tested in the Y-peel testing device using a layered carton board model. The carton board is modelled as a layered structure where the layers are assumed to obey Hill's orthotropic elastic–plastic model, and the interfaces are modelled using a softening orthotropic damage model. The HMA is modelled as isotropic linear elastic, and the influence from a varying elastic modulus of the HMA is explored. It is found that the pre-peak behaviour of the Y-peel force-elongation curves is reasonably well captured by the FE simulations, although the initial stiffness is somewhat too high. Also, the pre-peak behaviour is practically insensitive to changes of the elastic modulus of the HMA. The deformation and delamination pattern obtained in the simulations was compared with microscope pictures taken during the corresponding Y-peel experiments, and it is shown that they conform to the observed behaviour during Y-peel testing at comparable loading levels. However, the delamination opening is somewhat underestimated by the model. Copyright © 2014 John Wiley & Sons, Ltd.

Study on Deformation and Damage of Rock Mass Subject to High <i>In Situ</i> Stress by Using a Elastoplastic Damage Model and Considering the Impact of Weak Planes

Large scale underground caverns are under construction in high in-situ stress field at Houziyan hydropower station. To investigate deformation and damage of surrounding rock mass, a elastoplastic orthotropic damage model capable of describing induced orthotropic damage and post-peak behavior of hard rock is used, together with a effective approach accounting for the presence of weak planes. Then a displacement based back analysis was conducted by using the measured deformation data from extensometers. The computed displacements are in good agreement with the measured ones at most of measurement points, which confirm the validities of constitutive model and numerical simulation model. The result of simulation shows that damage of surrounding rock mass is mainly dominated by the high in-situ stress rather than the weak planes and heavy damage occur at the cavern shoulders and side walls.

Structural analysis of a multi-span railway masonry bridge combining in situ observations, laboratory tests and damage modelling

The paper presents a structural analysis by means of an orthotropic damage model of a multi-span masonry railway bridge built in the early years of the 20th century. Its aim is to show how this type of model allows for the current bridge mechanical behaviour under service loads to be assessed and the ultimate load to be forecast. It includes a phase of research on archived documents, an in situ investigation phase, an experimental phase carried out on core samples in the laboratory, and a computation phase. Among the different calculation steps, a simulation of the bridge history is performed in order to consider the current cracked state induced by support settlement. In a following step, the traffic loads are applied to assess the mechanical behaviour of the bridge under service loads up to failure. The mechanical behaviour of masonry is described by means of an original 3D anisotropic damage model able to consider the opening and the progressive reclosing of localized cracks. The model uses homogenized parameters considering the weakness of the stone-mortar interface. It has the capability to use material pre-damage. The calculation determines the crack pattern induced in the bridge by support displacements and loads. The support displacement study consists of an inverse analysis aimed at determining the actual present state of the structure from the cracking pattern observed on the bridge. The methodology highlights the importance of considering the whole history of a masonry structure when assessing the current state.

Orthotropic damage coupled with localized crack reclosure processing: Part II: Applications

This paper is concerned with the application of the orthotropic damage model described in the accompanying paper (Part I). The part I of the paper deals with several theoretical cases illustrating model’s abilities to treat unilateral behaviour aspect, anisotropic loading and non radial loading pass. The second part illustrates the model’s capabilities to simulate traditional laboratory tests using 3D FEM which include three points bending tests of notched beams, and examples which involve curved crack propagation, strongly anisotropic loading, and multiple cracks propagation in reinforced concrete beams.

An orthotropic damage model for the analysis of masonry structures

This paper presents a numerical model for nonlinear analysis of masonry structural elements based on Continuum Damage Mechanics. The material is described at the macro-level, i.e. it is modeled as a homogeneous orthotropic continuum. The orthotropic behavior is simulated by means of an original methodology, resulting from the concept of mapped tensors from the anisotropic field to an auxiliary workspace. The application of this idea to strain-based Continuum Damage Models is innovative and leads to several computational benefits. The suitability of the model for representing the behavior of different types of brickwork masonry is shown via the simulation of experimental tests.

An orthotropic mesh corrected crack model

This paper recovers the original spirit of the continuous crack approaches, where displacements jumps across the crack are smeared over the affected elements and the behaviour is established through a softening stress–(total) strain law, using standard finite element displacement interpolations and orthotropic local constitutive models. The paper focuses on the problem of shear locking observed in the discrete problem when orthotropic models are used. The solution for this drawback is found in the form of a mesh corrected crack model where the structure of the inelastic strain tensor is linked to the geometry of the cracked element. The discrete model is formulated as a non-symmetric orthotropic local damage constitutive model, in which the softening modulus is regularized according to the material fracture energy and the element size. The resulting formulation is easily implemented in standard non-linear FE codes and suitable for engineering applications. Numerical examples show that the results obtained using this crack model do not suffer from dependence on the mesh directional alignment, comparing very favourably with those obtained using related standard isotropic or orthotropic damage models.

On the mathematical and thermodynamical descriptions of strain equivalence based anisotropic damage model

Despite the substantial research efforts and the noteworthy contributions, the modeling of damage induced anisotropy remains an unsolved and challenging issue. A mathematically rigorous and thermodynamically consistent framework for strain equivalence based anisotropic damage model is developed in this paper. The mathematical description rests on an improved representation theorem on stiffness. More specifically, to determine the stiffness that is expressed in the form of an irreducible decomposition, two decoupled orientation distribution functions for the shear and bulk moduli are introduced and then represented in terms of the Fourier series expansions. Upon such observations, two independent damage variables are then naturally selected to characterize the distinct damage mechanisms in the deviatoric and volumetric spaces. Based on the principle of strain equivalence and the concept of effective stress, the equivalent thermodynamical description is established, which constitutes the necessary supplement to its mathematical counterpart and facilitates the postulation of consistent damage evolution laws. For those initially isotropic materials, the isotropic, orthotropic and anisotropic (microplane-type) damages as well as the shear–bulk coupling effects, are rigorously modeled within the mathematical and thermodynamical descriptions, respectively, while the thermodynamical consideration of the microcrack closure–reopening effects is also presented. Together with the appropriately postulated damage loading function and the consistently derived evolution laws for the internal variables, a new orthotropic damage model characterized by product-type symmetrized effective stress and secant stiffness, is developed with application to concrete modeling under mode-I failure. The numerical predictions under uniaxial tension are also presented, preliminarily illustrating the capability of the model. To gain further insight, the overall theoretical aspect of the improved representation theorem and the secant stiffness of the developed orthotropic damage model, are comparatively discussed, from which the advantages of the proposed framework are identified.

An orthotropic damage model for crash simulation of composites

In this paper, a practical orthotropic damage model is developed and tested for composite materials during crash. The model uses the Hashin's failure criteria in which the fibre and matrix failures are described explicitly, both in tension and compression. A linear softening degradation is proposed and a close-form solution of the corresponding damage parameter is provided. To reduce the mesh dependency, an embedded discontinuous element is proposed. It is a virtual embedded element in the sense that an actual element is divided into two zones, one elastic (undamaged) zone and one localization (damaged) zone. Their equivalence is preserved by constraining the kinematics and equilibrium equations. Since the damage zone is introduced into the element, the corresponding dissipated energy due to damage is fixed, independent of the element size. The numerical simulations using the developed damage model show a mesh objective result and correlate well with the energy dissipation in dynamic 3-point bending experiments. It is concluded that an accurate material calibration is crucial for the success of failure simulations. The traditional strain mapping cannot be applied to failure problems in which the strain distribution is highly non-uniform. Material parameter calibration should take into account the ratio of the failure zone and the gauge length. A practical approximation formula is provided.

334 押出しアルミニウム部材の圧潰解析への直交異方性損傷モデルの適用(GS1(5) 変形,破壊挙動,疲労,クリープ,衝撃)

334 押出しアルミニウム部材の圧潰解析への直交異方性損傷モデルの適用(GS1(5) 変形,破壊挙動,疲労,クリープ,衝撃)

An orthotropic damage model for masonry structures

AbstractAn orthotropic damage model specifically developed for the analysis of brittle masonry subjected to in‐plane loading is described. Four independent internal damage parameters, one in compression and one in tension for each of the two natural axes of the masonry, are defined allowing the stiffness recovery at crack closure as well as the different inelastic behaviour along each natural axis to be considered. The damage field of the material is defined in terms of four equivalent stresses and results, in the space of the in‐plane effective stresses, in a double pyramid with a rectangular base where the slopes of the faces correspond to the internal friction angle of the material. The equivalent stresses also control the growth of the damage parameters. The returning path from the effective to the damaged stresses is given by multiplication by a fourth‐rank damage effect tensor, which is a function of the damage parameters and of the effective stress state. Mesh size regularization is achieved by means of an enhanced local method taking into account the finite element size. Good agreement has been found in the comparison between numerical results and experimental data both for masonry shear panels and for a large‐scale masonry holed wall. Copyright © 2002 John Wiley & Sons, Ltd.

A micro-mechanics damage approach for fatigue of composite materials

A new model for fatigue damage evolution of polymer matrix composites (PMC) is presented. The model is based on a combination of an orthotropic damage model and an isotropic fatigue evolution model. The orthotropic damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. This approach facilitates the determination of model parameters since the orthotropic damage model parameters can be determined from available data from quasi-static-loading tests. Then, limited amount of fatigue data is needed to adjust the fatigue evolution model. The combination of these two models provides a compromise between efficiency and accuracy. Decomposition of the state variables down to the constituent scale is accomplished by micro-mechanics. Phenomenological damage evolution models are then postulated for each constituent and for the micro-structural interaction among them. Model parameters are determined from available experimental data. Comparison between model predictions and additional experimental data is presented.

Validation of two-dimensional calculations of free edge delamination in laminated composites

In this paper the use of two-dimensional calculations, which are often applied for the analysis of free edge delamination in a T-bone specimen, is validated by comparing the results with complete three-dimensional calculations. The specimen that is discussed shows mode-I delamination in the midplane of the specimen which is modelled in the analysis by means of an orthotropic damage model for interface elements. Although symmetry does not exist because of the material lay-up, use is made of assumed symmetry conditions, which are validated by analyses without symmetry conditions. It is shown that a two-dimensional analysis suffices for the determination of the ultimate load bearing capacity of the strip, but that a three-dimensional analysis is necessary to obtain a reliable view of the evolution of the delamination zone.

A Unified Damage Approach for Predicting Forming Limit Diagrams

Plastic deformation in sheet metal consists of four distinct phases, namely, uniform deformation, diffuse necking, localized necking, and final rupture. The last three phases are commonly known as nonuniform deformation. A proper forming limit diagram (FLD) should include all three phases of the nonuniform deformation. This paper presents the development of a unified approach to the prediction of FLD to include all three phases of nonuniform deformation. The conventional method for predicting FLD is based on localized necking and adopts two fundamentally different approaches. Under biaxial loading, the Hill’s plasticity method is often chosen when α(=ε2/ε1) <0. On the other hand, the M-K method is typically used for the prediction of localized necking when α > 0 or when the biaxial stretching of sheet metal is significant. The M-K method, however, suffers from the arbitrary selection of the imperfection size, thus resulting in inconsistent predictions. The unified approach takes into account the effects of micro-cracks/voids on the FLD. All real-life materials contain varying sizes and degrees of micro-cracks/voids which can be characterized by the theory of damage mechanics. The theory is extended to include orthotropic damage, which is often observed in extensive plastic deformation during sheet metal forming. The orthotropic FLD model is based on an anisotropic damage model proposed recently by Chow and Wang (1993). Coupling the incremental theory of plasticity with damage, the new model can be used to predict not only the forming limit diagram but also the fracture limit diagram under proportional or nonproportional loading. In view of the two distinct physical phenomena governing the cases when α(=ε2/ε1) < or α > 0, a set of instability criteria is proposed to characterize all three phases of nonuniform deformation. The orthotropic damage model has been employed to predict the FLD of VDIF steel (Chow et al, 1996) and excellent agreement between the predicted and measured results has been achieved as shown in Fig. 1. The damage model is extended in this paper to examine its applicability and validity for another important engineering material, namely aluminum alloy 6111-T4.

An orthotropic damage model for concrete at different temperatures

An orthotropic damage model for concrete at different temperatures is presented in this paper. It also considers the unilateral effect of concrete in a three-dimensional problem. An uniaxial compression experiment at different temperatures is made successfully. This model corresponds well to the experimental results. As an example, this model is well verified by the three-points bending experiment and the measurements of a railway prestressed reinforced concrete arch bridge across the Maoling River in China.