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.

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)

Prediction of masonry compressive behaviour using a damage mechanics inspired modelling method

Masonry under compression is affected by the properties of its constituents and their interfaces. In spite of extensive investigations of the behaviour of masonry under compression, the information in the literature cannot be regarded as comprehensive due to ongoing inventions of new generation products – for example, polymer modified thin layer mortared masonry and drystack masonry. As comprehensive experimental studies are very expensive, an analytical model inspired by damage mechanics is developed and applied to the prediction of the compressive behaviour of masonry in this paper. The model incorporates a parabolic progressively softening stress-strain curve for the units and a progressively stiffening stress-strain curve until a threshold strain for the combined mortar and the unit-mortar interfaces is reached. The model simulates the mutual constraints imposed by each of these constituents through their respective tensile and compressive behaviour and volumetric changes. The advantage of the model is that it requires only the properties of the constituents and considers masonry as a continuum and computes the average properties of the composite masonry prisms/wallettes; it does not require discretisation of prism or wallette similar to the finite element methods. The capability of the model in capturing the phenomenological behaviour of masonry with appropriate elastic response, stiffness degradation and post peak softening is presented through numerical examples. The fitting of the experimental data to the model parameters is demonstrated through calibration of some selected test data on units and mortar from the literature; the calibrated model is shown to predict the responses of the experimentally determined masonry built using the corresponding units and mortar quite well. Through a series of sensitivity studies, the model is also shown to predict the masonry strength appropriately for changes to the properties of the units and mortar, the mortar joint thickness and the ratio of the height of unit to mortar joint thickness. The unit strength is shown to affect the masonry strength significantly. Although the mortar strength has only a marginal effect, reduction in mortar joint thickness is shown to have a profound effect on the masonry strength. The results obtained from the model are compared with the various provisions in the Australian Masonry Structures Standard AS3700 (2011) and Eurocode 6.

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.

Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

A multi-scaling approach to predict hydraulic damage of poromaterials

The purpose of this paper is to introduce the concept of hydraulic damage and its numerical integration. Unlike the common phenomenological continuum damage mechanics approaches, the procedure introduced in this paper relies on mature concepts of homogenization, linear fracture mechanics, and thermodynamics. The model is applied to the problem of fault reactivation within resource reservoirs. The results show that propagation of weaknesses is highly driven by the contrasts of properties in porous media. In particular, it is affected by the fracture toughness of host rocks. Hydraulic damage is diffused when it takes place within extended geological units and localized at interfaces and faults.

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

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.

Orientation-based Continuum Damage Models for Rocks

A general formulation of the Helmholtz free energy used in thermodynamics of damage process of rocks is derived within a multi-scale framework. Such a physically-based thermodynamic state potential has a hybrid, discrete/continuum, nature in the sense tha