Orthotropic Damage Model Research Articles

A constitutive model considering creep damage of wood

AbstractThe serviceability of wooden structures involves multiphysical phenomena, notably the interactions among creep, plasticity, and damage. The influence of creep on the initialization of the damage and on its growth and spread can be adjusted by an additional alpha parameter in order to take into account the coupled effect between creep and damage more properly. We integrate an orthotropic viscoelastic model, based on the generalized Kelvin chain, with an orthotropic damage model, capturing both the immediate nonlinear elastic–plastic–damage response and the time-dependent viscous response of timber. The combination of these material models is important to obtain a realistic description of wood behavior, because the timber shows an immediate nonlinear elastic–plastic–damage response, but also the time-dependent viscous response. In this paper, we algorithmize, implement, and validate the concept of ‘creep damage’, a phenomenon observed in wooden structures. Benchmark tests reveal two distinct patterns of damage in beech wood, immediate postload damage that evolves over time and damage that occurs and spreads during the loading period.

1D higher-order theories for quasi-static progressive failure analysis of composites based on a full 3D Hashin orthotropic damage model

This work investigates the crack propagation in composites by adopting a novel full three-dimensional (3D) Hashin-based orthotropic damage model combined with higher-order one-dimensional (1D) finite elements based on the Carrera Unified Formulation (CUF). Previous literature has proven that CUF provides structural formulations with great accuracy and improved computational efficiency. Moreover, a Layer-Wise (LW) formulation can be implemented within the CUF framework, allowing an accurate description of the 3D stress state in composite laminate, representing crucial information for progressive failure analysis. A Newton–Raphson predictor–corrector algorithm is used for the numerical solution of classical case tests, i.e., compact tension and three-point bending tests. The obtained results are compared with experimental outcomes and with solutions from well-established 2D damage models and a 3D Abaqus numerical model, demonstrating the capability of the proposed method to efficiently capture both the failure load and shape of the crack pattern.

Orthotropic damage model for composite structures using the 3D Tsai-Wu failure criterion

This paper presents a novel approach concerning the development of an orthotropic damage model based on the original 3D Tsai-Wu failure criterion. In its original formulation, the Tsai-Wu criterion is only capable of identifying the existence of damage at a certain point in the material. However, it is not capable of identifying if the damage is located in the fiber, matrix or interlaminar zone. This work plans to fill this gap in knowledge by providing a simple method, based on equivalent stresses and strains, that identifies the failure modes when the Tsai-Wu failure criterion is near the on-set of damage. Using this novel method, it is possible to implement classical damage evolution laws based on the formulation of Matzenmiller. The proposed damage model is implemented in the commercial finite element software ABAQUS using user-subroutine UMAT, and the numerical results are compared with experimental data obtained earlier by other authors for different applications of glass fiber reinforced polymer (GFRP) structures. The numerical stabilization is achieved by using a new implicit to explicit material time step algorithm.

An orthotropic damage model for masonry walls with consistent damage evolution laws

This research presents a constitutive model for the macro scale simulation of masonry structures. The model is containing an orthotropic plane stress assumption, which appears as an appropriate assumption for the in-plane analysis of masonry walls. The material model is based upon damage mechanics, split into tensile and compression parts. The novelty herewith is the consistent mapping of the damage evolution laws. Aim of this research is to develop a simple but accurate constitutive law, suitable to simulate large scale structures and buildings with reasonable computational costs. The developments are presented and compared with available literature examples from laboratory testings.

Implicit to Explicit Algorithm for ABAQUS Standard User-Subroutine UMAT for a 3D Hashin-Based Orthotropic Damage Model

This study examines a new approach to facilitate the convergence of upcoming user-subroutines UMAT when the secant material matrix is applied rather than the conventional tangent (also known as Jacobian) material matrix. This algorithm makes use of the viscous regularization technique to stabilize the numerical solution of softening material models. The Newton–Raphson algorithm predictor-corrector of ABAQUS then applies this type of viscous regularization to a UMAT using only the secant matrix. When the time step is smaller than the viscosity parameter, this type of regularization may be unsuitable for a predictor-corrector with the secant matrix because its implicit convergence is incorrect, transforming the algorithm into an undesirable explicit version that may cause convergence problems. A novel 3D orthotropic damage model with residual stresses is proposed for this study, and it is analyzed using a new algorithm. The method’s convergence is tested using the proposed implicit-to-explicit secant matrix as well as the traditional implicit and explicit secant matrices. Furthermore, all numerical models are compared to experimental data. It was concluded that both the new 3D orthotropic damage model and the new proposed time step algorithm were stable and robust.

Describing the Material Behavior of Steel and Carbon Fiber Reinforced Composites Using a Combined Damage-Plasticity Approach

Metal fiber hybrids (MFH) exhibit outstanding mechanical properties. They combine the advantages of ductile metallic materials with the well-known advantages of classical glass or carbon fibers in polymer matrices. Previous research has shown that these hybrid material concepts can improve structural integrity and energy absorption while maintaining their excellent weight-specific mechanical properties as well as allowing a wider range of multifunctional applications. In today’s component design process, simulation is a powerful tool for engineers to exploit the full mechanical potential of the material used. However, describing the material behavior including its multifunctional usability in numerically aided design processes of components is currently one of the major challenges for MFH. Against this background, this work focuses on the development and evaluation of a description method for MFH in the finite element analysis (FEA). A steel and carbon fiber reinforced epoxy resin (SCFRP) with hybridization at the laminate level is chosen as the reference material. To describe the behavior of unidirectional steel fiber reinforced plastic (SFRP) layers, a material model combining an orthotropic damage model and a 1D-plasticity model is proposed and implemented as a user-defined subroutine for LS-Dyna. In addition, SCFRP laminates are manufactured, tested under tensile loading, and used to parameterize the material models and to validate the description method for SCFRP. In this study, it is shown that the description method in combination with the newly developed material model is able to describe the complex failure mechanism of SCFRP. In particular, with respect to the material behavior up to the failure of the carbon fibers, a very good mapping accuracy can be achieved. Strain localization effects occur in both numerically predicted and experimentally measured post-failure behavior. Therefore, it could be concluded that the accuracy of the numerical predictions strongly depends on the geometric resolution of the discretization.

An orthotropic damage model with internal sliding and friction for masonry-like material

Quasi-brittle materials like masonry exhibit mechanical properties and develop nonlinearities that are mainly driven by their joints. In the present work, a Continuum Damage Mechanics point of view is considered to describe the macroscopic behavior of masonry. Based on damage models developed for ceramic matrix composite materials, a fixed directional damage approach is proposed. From this formulation, unilateral effect, as well as internal sliding and friction coupled with damage, are introduced. Numerical examples of the response of the model for different loading cases involving cyclic and non-proportional loadings are carried out and compared to experimental results.

Effective elastic and fracture properties of regular and irregular masonry from nonlinear homogenization

Prediction of effective elastic and strength parameters of both regular and irregular masonry walls from homogenization is presented. To that end, the widely accepted first order homogenization method is adopted to provide the homogenized elastic stiffnesses or compliances as well as macroscopic parameters of the selected nonlinear constitutive models. These include the tensile and compressive strength and fracture energies of a generally orthotropic material extracted from the computationally derived macroscopic stress strain curves. In this regard, two types of boundary/loading conditions resulting from the strain-based and mix type formulation of the homogenization problem are examined. The response provided by an orthotropic damage model, expected to describe the behavior of the homogenized structure on macroscale, is compared to that derived via a classical isotropic scalar damage model. It reveals that strong constraints of the orthotropic damage model offer results inapplicable for estimating the macroscopic fracture properties thus promoting the application of a simple isotropic damage model when solving the homogenization problem. The results also show that the mixed boundary conditions, allowing us to represent a pure tension/compression loading mode while being capable of tracking the softening branch of the stress–strain curve, deliver the response comparable to that of a purely strain-based formulation.

Tsai–Wu based orthotropic damage model

This paper presents a novel approach concerning the development of an orthotropic damage model for composite materials, based on the original plane stress Tsai–Wu failure criterion. In its original formulation, the Tsai–Wu is a mode-independent criterion only capable of acknowledging the existence of damage in a certain point of a composite material. It is not capable of identifying if the damage is located in the fibre, matrix or interlaminar zone. This study aims at filling this gap in knowledge by providing a simple method, based on equivalent stresses and strains, that identifies the relevant failure modes when the Tsai–Wu failure criterion is at the onset of damage. Using this novel methodology, it is possible to implement classical damage evolution constitutive laws based on the fracture energy regularization. At present, the proposed damage formulation is based on the consideration of a plane stress space and Mode I fracture, but its generalization to a full 3D damage model is expected to be defined in the near future. The damage model is implemented in the commercial finite element software ABAQUS through a user-defined material (UMAT) subroutine, and all numerical models are compared with experimental results available in the literature.

Assessment of mesh dependency in the numerical simulation of compact tension tests for orthotropic materials

This paper presents a numerical study on the mesh dependency of the Hashin Damage Model for 2D finite element simulations of orthotropic materials. The main objective is to study and assess the efficiency of energy regularization in preventing mesh dependency in orthotropic damage models. Initially, the thermodynamic laws used to validate a damage model are presented and applied to the specific Hashin damage model. An extensive parametric study is performed using various types of finite elements: with structured and squared-structured meshes; with linear and quadratic approximations; and with full and reduced integration schemes. To verify the mesh dependency, the results of a compact tension experimental test of glass fibre reinforced plastic (GFRP) material are compared to the numerical results; some conclusions are drawn regarding the force vs. displacement behaviour, with and without regular meshes.

HOMOGENIZATION OF UNREINFORCED OLD MASONRY WALL COMPARISON OF SCALAR ISOTROPIC AND ORTHOTROPIC DAMAGE MODELS

Masonry is a heterogeneous composite material made of bricks bonded by a mortar matrix. Modeling such a material on macroscale typically calls for homogenization adopting a suitable constitutive model capable of capturing its quasi-brittle behavior. The present contribution concentrates on comparison and potential application of classical isotropic and orthotropic damage models in the framework of strain based first order numerical homogenization. As an illustrative example, a representative volume element in terms of a periodic unit cell is constructed to address the response of an unreinforced masonry (URM) structure typical of “Placa” buildings (mixed masonry-reinforced concrete buildings) built in Portugal. The performance of the two models is examined on the basis of macroscopic stress-strain curves constructed for both tensile and compressive loading. The selected geometrical constraints clearly identify the differences in the predictive capabilities of the two models.

Macroscopic response of regular masonry from homogenization: comparison of isotropic and orthotropic damage models

This paper outlines prediction of macroscopic effective properties of a regular masonry from homogenization. It focuses on the derivation of nonlinear macroscopic stress strain curves adopting either classical isotropic or more advanced orthotropic damage model. The response resulting from both tensile and compressive uniaxial loading is examined in the light of strain and stress loading regimes. A masonry structure typical of ”Placa” buildings (mixed masonry- reinforced concrete buildings) built in Portugal is selected as one particular example to illustrate the differences in the predictive capabilities of the two constitute models on the one hand and the formulation of the homogenization problem on the other hand. It is suggested that the mixed loading conditions are essentially required when estimating all macroscopic material parameters needed in the corresponding macroscopic constitutive model

Simulating Fiber-Reinforced Concrete Mechanical Performance Using CT-Based Fiber Orientation Data.

The main hindrance to realistic models of fiber-reinforced concrete (FRC) is the local materials property variation, which does not yet reliably allow simulations at the structural level. The idea presented in this paper makes use of an existing constitutive model, but resolves the problem of localized material variation through X-ray computed tomography (CT)-based pre-processing. First, a three-point bending test of a notched beam is considered, where pre-test fiber orientations are measured using CT. A numerical model is then built with the zone subjected to progressive damage, modeled using an orthotropic damage model. To each of the finite elements within this zone, a local coordinate system is assigned, with its longitudinal direction defined by local fiber orientations. Second, the parameters of the constitutive damage model are determined through inverse analysis using load-displacement data obtained from the test. These parameters are considered to clearly explain the material behavior for any arbitrary external action and fiber orientation, for the same geometrical properties and volumetric ratio of fibers. Third, the effectiveness of the resulting model is demonstrated using a second, “control” experiment. The results of the “control” experiment analyzed in this research compare well with the model results. The ultimate strength was predicted with an error of about 6%, while the work-of-load was predicted within 4%. It demonstrates the potential of this method for accurately predicting the mechanical performance of FRC components.

Appraisement of planar, bending and twisting cracks in 3D with isotropic and orthotropic damage models

This paper discusses the modeling of cracking in quasi-brittle materials using isotropic and orthotropic damage constitutive laws. A mixed strain/displacement finite element formulation is used, taking advantage of its enhanced precision and its enforced interelemental strain continuity. On the one hand, this formulation avoids the spurious mesh dependency of the computed solution associated to standard elements and does not require the use of tracking techniques. On the other hand, it greatly alleviates the spurious stress locking associated to the use of orthotropic models on standard finite elements. The performance of several isotropic and orthotropic damage constitutive laws is assessed through an extensive comparison with analytical solutions, numerical tests and experimental evidence reported in the literature. The behavior of the different damage models in terms of crack surface, collapse mechanism and force displacement curves is investigated performing 3D analyses in several conditions including Mode I, Mixed Mode and Mode III fracture. When performing the appraisement of planar, bending and twisting cracks, the enhanced accuracy of the mixed formulation allows for a distinct assessment of the several damage models considered. Aspects related to the behavior of damage models, such as the influence of Poisson’s ratio, the shape of the damage surface and the adoption of isotropic and orthotropic models are investigated and noteworthy conclusions are drawn.

Tracking multi-directional intersecting cracks in numerical modelling of masonry shear walls under cyclic loading

In-plane cyclic loading of masonry walls induces a complex failure pattern composed of multiple diagonal shear cracks, as well as flexural cracks. The realistic modelling of such induced localized cracking necessitates the use of costly direct numerical simulations with detailed information on both the properties and geometry of masonry components. On the contrary, computationally efficient macro-models using standard smeared-crack approaches often result in a poor representation of fracture in the simulated material, not properly localized and biased by the finite element mesh orientation. This work proposes a possible remedy to these drawbacks of macro-models through the use of a crack-tracking algorithm. The macro-modelling approach results in an affordable computational cost, while the tracking algorithm aids the mesh-bias independent and localized representation of cracking. A novel methodology is presented that allows the simulation of intersecting and multi-directional cracks using tracking algorithms. This development extends the use of localized crack approaches using tracking algorithms to a wider field of applications exhibiting multiple, arbitrary and interacting cracking. The paper presents also a novel formulation including into an orthotropic damage model the description of irreversible deformations under shear loading. The proposed approach is calibrated through the comparison with an experimental test on a masonry shear wall against in-plane cyclic loading.

An Energy-Equivalent d⁺/d- Damage Model with Enhanced Microcrack Closure-Reopening Capabilities for Cohesive-Frictional Materials.

In this paper, an energy-equivalent orthotropic d+/d− damage model for cohesive-frictional materials is formulated. Two essential mechanical features are addressed, the damage-induced anisotropy and the microcrack closure-reopening (MCR) effects, in order to provide an enhancement of the original d+/d− model proposed by Faria et al. 1998, while keeping its high algorithmic efficiency unaltered. First, in order to ensure the symmetry and positive definiteness of the secant operator, the new formulation is developed in an energy-equivalence framework. This proves thermodynamic consistency and allows one to describe a fundamental feature of the orthotropic damage models, i.e., the reduction of the Poisson’s ratio throughout the damage process. Secondly, a “multidirectional” damage procedure is presented to extend the MCR capabilities of the original model. The fundamental aspects of this approach, devised for generic cyclic conditions, lie in maintaining only two scalar damage variables in the constitutive law, while preserving memory of the degradation directionality. The enhanced unilateral capabilities are explored with reference to the problem of a panel subjected to in-plane cyclic shear, with or without vertical pre-compression; depending on the ratio between shear and pre-compression, an absent, a partial or a complete stiffness recovery is simulated with the new multidirectional procedure.

A consistent and efficient localized damage model for concrete

Damage induced localized failure is of vital importance to evaluate residual safety and to prevent catastrophic collapse of concrete structures. Aiming for the efficient and robust modeling of localized failure in quasi-brittle solids and structures, this paper addresses a thermodynamically consistent and numerically efficient localized damage model for concrete. The thermodynamic framework is presented in such a way that not only the continuum model for the bulk material, but also the localized model for the discontinuity, can be established in a consistent approach. For the latter, a localized Helmholtz free energy potential is postulated, mimicking the classical continuum damage model. Specifically, a localized damage variable is introduced to characterize degradation of the initially-rigid discontinuity with a well-defined reference stiffness. Consistent evolution law for the localized damage variable is derived from an appropriate traction-based failure criterion and its equivalent separation-based counterpart, e.g. the novel hyperbolic damage criterion introduced in this work. The proposed model can be regularized and in particular, upon the assumption of continuous stress field, an orthotropic damage model in the context of smeared crack methods is recovered. This coincidence not only justifies the proposed model, but also sheds new lights on other classical methods. Numerically, the proposed localized damage model is incorporated into the improved stable eXtended FEM. Compared to those plasticity-based localized models, an explicit numerical algorithm can be used to update the cohesive tractions transferred across the discontinuity with no iteration on the constitutive level. This feature, together with the well-conditioned system matrix ensured by the improved stable eXtended FEM, guarantees noticeable efficiency and robustness of the overall numerical performances. The proposed model is verified against several classical benchmark tests of concrete in both mode-I and mixed-mode failure. The numerical predictions agree well with experimental test data and those reported in the literature. Remarkably, all the numerical results are mesh-size and mesh-alignment independent, and no spurious stress locking is observed, showing validity of the proposed model in the modeling of localized failure in concrete.

Mechanical characterization of 3D angle-interlock Kevlar/basalt reinforced polypropylene composites

The present work reported the mechanical characterization of novel polypropylene (PP) composites reinforced with three-dimensional angle-interlock (3D-A) Kevlar/basalt fabrics. Two homogeneous fabrics with Kevlar (K3D) and basalt yarns (B3D), and a hybrid fabric (H3D) with a combination of both Kevlar and basalt yarns were produced. Three types of two layer 3D-A composites were manufactured using vacuum-assisted compression molding method. Static tensile and in-plane compression tests were carried out on the manufactured composites. The mechanical behavior of the three 3D-A composites was compared in terms of stress-strain response, elastic modulus, strength and failure strain. Influence of hybridization on the mechanical behavior of the 3D-A composites was also studied. Significant improvement in the tensile behavior of 3D-A homogeneous composites was observed due to hybridization. Meanwhile, there was no considerable improvement in in-plane compression behavior. The damage patterns for in-plane compression loading were examined through scanning electron microscopy (SEM) to explore the possible damage patterns such as matrix cracking, fiber failure, delamination and deformation. Numerical simulations were carried out using ABAQUS/Standard, by implementing a user-defined material subroutine (VUMAT) based on the Chang-Chang linear orthotropic damage model. Good agreement between experimental and numerical simulations was achieved in terms of damage patterns.

Simplified approach to model steel rebar-concrete interface in reinforced concrete

For correct description of cracking process in reinforced concrete structural elements, the simulation of the behaviour of steel rebarconcrete interface is always of primary importance. This paper proposes a simplified method to model the steel rebar-concrete interface in RC structures. The proposed method considers the introduction of massive elasto-plastic isotropic bond element as steel rebarconcrete interface. Stress-strain behaviour curve required for elasto-plastic isotropic material is obtained by performing conventional pull-out tests on concrete. For plain concrete matrix, an orthotropic damage model based on plasticity and damage theories was adopted for finite element modelling in Finite Element (FE) code CASTEM. In order to validate the proposed approach, a comprehensive experimental program was designed and carried out. Under this program, pure tension test on RC prisms and flexural test on RC beams were performed. Testing of proposed steel rebar-concrete interface bond model in numerical simulation of RC prism subjected to pure tension and RC beam in flexure, and comparison of numerical simulation results with experimental data is also discussed in this paper.

Low velocity impact response of 3D angle-interlock Kevlar/basalt reinforced polypropylene composites

Experimental and numerical investigations are carried out to determine the low velocity impact (LVI) response of three different polypropylene (PP) composites. Three dimensional (3D) angle-interlock fabrics with Kevlar, basalt and a hybrid combination of both are produced. 3D composites are manufactured with these three fabrics using vacuum-assisted compression molding process with PP resin. LVI tests are conducted using a drop-weight impact equipment at the energy level of 240J. The LVI response of the three 3D-PP composites is compared in terms of peak force, energy absorption and damage modes. The experimental results indicate that the basalt 3D composites showed 6.62–13.73% higher peak force and H3D composites absorbed 7.67-48.49% more energy than the remaining composites. Results indicate that there is a considerable enhancement in the energy absorbing capability of hybrid composites as compared to Kevlar/PP and basalt/PP composites. Numerical simulations are carried out using the commercial finite element (FE) code ABAQUS/Explicit. A user-defined material subroutine (VUMAT) based on Chang-Chang linear orthotropic damage model, is implemented into the FE code. Good agreement between experimental and numerical simulations is achieved in terms of impact response characteristics.