Unified Continuum Damage Model for Matrix Cracking in Composite Rotor Blades

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic

A gradient-enhanced continuum damage model for fibre-reinforced materials

Modelo de daño no local definido a materiales fibrados. Este modelo se aplica al estudio de problemas típicos en la biomecánica de los tejidos blandos, como las paredes arteriales.

A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

A gradient-enhanced continuum damage model with application to fibre-reinforced tissues at finite strains

A non-local gradient-based damage formulation within a geometrically non-linear set- ting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy function which is additively composed by an isotropic neo-Hookean matrix and by an anisotropic fibre-reinforced material based on the model proposed by T. Gasser, R. Ogden, and G. Holzapfel.

A continuum damage model characterization based on the soft tissue mesostructure

Material properties of soft tissues are highly conditioned by the hierarchical structure of this kind of composites. These collagen-based tissues present a complex framework of fibres, fibrils, tropocollagen molecules and amino-acids. As the structural mechanisms that control the degradation of soft tissues are related with the behaviour of its fundamental constituents, the relationship between the molecular and intermolecular properties and the tissue behaviour needs to be studied.

A regularised continuum damage model based on the mesoscopic scale for soft tissue

Material properties of soft fibrous tissues are highly conditioned by the hierarchical structure of this kind of composites. Collagen based tissues present, at decreasing length scales, a complex framework of fibres, fibrils, tropocollagen molecules and amino-acids. Understanding the mechanical behaviour at nano-scale level is critical to accurately incorporate this structural information in phenomenological damage models. In this work we derive a relationship between the mechanical and geometrical properties of the fibril constituents and the soft tissue material parameters at macroscopic scale. A Hodge–Petruska two-dimensional model has been used to describe the fibrils as staggered arrays of tropocollagen molecules. After a mechanical characterisation of each of the fibril components, two fibril failures modes have been defined related with two planes of weakness. A phenomenological continuous damage model with regularised softening was presented along with meso-structurally based definitions for its material parameters. Finally, numerical analysis at fibril, fibre and tissue levels are presented to show the capabilities of the model

Development of a transient gradient enhanced non local continuum damage mechanics model for masonry

Due to the advent of varied types of masonry systems a comprehensive failure mechanism of masonry essential for the understanding of its behaviour is impossible to be determined from experimental testing. As masonry is predominantly used in wall structures a biaxial stress state dominates its failure mechanism. Biaxial testing will therefore be necessary for each type of masonry, which is expensive and time consuming. A computational method would be advantageous; however masonry is complex to model which requires advanced computational modelling methods. This thesis has formulated a damage mechanics inspired modelling method and has shown that the method effectively determines the failure mechanisms and deformation characteristics of masonry under biaxial states of loading.

A micropolar cohesive damage model for delamination of composites

A micropolar cohesive damage model for delamination of composites is proposed. The main idea is to embed micropolarity, which brings an additional layer of kinematics through the micro-rotation degrees of freedom within a continuum model to account for the micro-structural effects during delamination. The resulting cohesive model, describing the modified traction separation law, includes micro-rotational jumps in addition to displacement jumps across the interface. The incorporation of micro-rotation requires the model to be supplemented with physically relevant material length scale parameters, whose effects during delamination of modes I and II are brought forth using numerical simulations appropriately supported by experimental evidences. (C) 2015 Elsevier Ltd. All rights reserved.

3D Anisotropic Elastoplastic-Damage Model and its Application in Simulating the Behavior of Rock Materials

A 3D anisotropic elastoplastic-damage model was presented based on continuum damage mechanics theory. In this model, the tensor decomposition technique is employed. Combined with the plastic yield rule and damage evolution, the stress tensor in incremental format is obtained. The derivate eigenmodes in the proposed model are assumed to be related with the uniaxial behavior of the rock material. Each eigenmode has a corresponding damage variable due to the fact that damage is a function of the magnitude of the eigenstrain. Within an eigenmodes, different damage evolution can be used for tensile and compressive loadings. This model was also developed into finite element code in explicit format, and the code was integrated into the well-known computational environment ABAQUS using the ABAQUS/Explicit Solver. Numerical simulation of an uniaxial compressive test for a rock sample is used to examine the performance of the proposed model, and the progressive failure process of the rock sample is unveiled.

Numerical considerations for the implementation of a comprehensive composite damage model

A comprehensive continuum damage mechanics model [1] had been developed to capture the detailed
behaviour of a composite structure under a crushing load. This paper explores some of the difficulties
encountered in the implementation of this model and their mitigation. The use of reduced integration
element and a strain softening model both negatively affect the accuracy and stability of the
simulation. Damage localisation effects demanded an accurate measure of characteristic length. A
robust algorithm for determining the characteristic length was implemented. Testing showed that this
algorithm produced marked improvements over the use of the default characteristic length provided
by Abaqus. Zero-energy or hourglass modes, in reduced integration elements, led to reduced
resistance to bending. This was compounded by the strain softening model, which led to the formation
of elements with little resistance to deformation that could invert if left unchecked. It was shown,
through benchmark testing, that by deleting elements with excess distortions and controlling the mesh
using inbuilt distortion/hourglass controls, these issues can be alleviated. These techniques
contributed significantly to the viability and usability of the damage model.

Validation of a 3D damage model for predicting the response of composite structures under crushing loads

A 3D intralaminar continuum damage mechanics based material model, combining damage mode interaction and material nonlinearity, was developed to predict the damage response of composite structures undergoing crush loading. This model captures the structural response without the need for calibration of experimentally determined material parameters. When used in the design of energy absorbing composite structures, it can reduce the dependence on physical testing. This paper validates this model against experimental data obtained from the literature and in-house testing. Results show that the model can predict the force response of the crushed composite structures with good accuracy. The simulated energy absorption in each test case was within 12% of the experimental value. Post-crush deformation and the damage morphologies, such as ply splitting, splaying and breakage, were also accurately reproduced. This study establishes the capability of this damage model for predicting the responses of composite structures under crushing loads.

Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Continuum damage interactions between tension and compression in osteonal bone

Skeletal diseases such as osteoporosis impose a severe socio-economic burden to ageing societies. Decreasing mechanical competence causes a rise in bone fracture incidence and mortality especially after the age of 65 y. The mechanisms of how bone damage is accumulated under different loading modes and its impact on bone strength are unclear. We hypothesise that damage accumulated in one loading mode increases the fracture risk in another. This study aimed at identifying continuum damage interactions between tensile and compressive loading modes. We propose and identify the material constants of a novel piecewise 1D constitutive model capable of describing the mechanical response of bone in combined tensile and compressive loading histories. We performed several sets of loading–reloading experiments to compute stiffness, plastic strains, and stress-strain curves. For tensile overloading, a stiffness reduction (damage) of 60% at 0.65% accumulated plastic strain was detectable as stiffness reduction of 20% under compression. For compressive overloading, 60% damage at 0.75% plastic strain was detectable as a stiffness reduction of 50% in tension. Plastic strain at ultimate stress was the same in tension and compression. Compression showed softening and tension exponential hardening in the post-yield regime. The hardening behaviour in compression is unaffected by a previous overload in tension but the hardening behaviour in tension is affected by a previous overload in compression as tensile reloading strength is significantly reduced. This paper demonstrates how damage accumulated under one loading mode affects the mechanical behaviour in another loading mode. To explain this and to illustrate a possible implementation we proposed a theoretical model. Including such loading mode dependent damage and plasticity behaviour in finite element models will help to improve fracture risk analysis of whole bones and bone implant structures.

A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory.