Isotropic Damage Law Research Articles

Effect of damage evolution on the auxetic behavior of 2D and 3D re-entrant type geometries

In this work, a mathematical formulation based on variational asymptotic method (VAM) has been proposed to determine the effect of damage on the auxetic properties of two-dimensional (2D) and three-dimensional (3D) re-entrant geometries. The influence of damage progression on the auxetic behavior was captured using a geometrically exact one-dimensional beam theory and an isotropic damage law, implemented in a nonlinear finite element framework. The effect of material degradation on the macroscale effective elastic properties such as the elastic modulus and Poisson’s ratio for the two-dimensional and three-dimensional re-entrant auxetic geometries was quantified. The mechanical behavior as predicted by the in-house Python-based implementation of the proposed VAM-based formulation is verified with the results from the commercial finite element solver Abaqus, wherein the user material subroutine was used to capture damage evolution. The numerical examples presented in this paper reveal that the macroscale auxetic behavior of the geometries was affected significantly by damage progression. The results of this research will provide insights into the design and analysis of auxetic materials for applications that warrant consideration of damage evolution.

Improved plastic-damage cap model for shear behavior predictions of plain and reinforced concrete members

In this article, an improved continuous surface cap model (ICSC) with isotropic plastic-damage algorithms is proposed, namely to predict more accurately the shear behavior of both plain and reinforced concrete members. For this, a suitable yield surface is implemented and the critical shear-to-compression transition parameter in the ductile damage law is scrutinized and determined. Firstly, the mathematical framework of the plastic-damage cap model is summarized, namely the formulations in plasticity, the returning mapping algorithms of cutting plane and the isotropic damage law. Then, the proposed constitutive parameters in ICSC model are presented. The plastic-damage algorithms flowchart is presented and described, and the new proposed ICSC model is implemented in the software LS-DYNA. Next, the proposed ICSC model is validated against the original CSC model (MAT159 in LS-DYNA) and also against the previously improved CSC model with crack closure behavior developed by the authors. For this, several simulations using the three CSC models are performed and the results are compared with experimental results, which involve single concrete element under various loading conditions, plain concrete structure under direct shear load and simply supported reinforced concrete (RC) beams with or without stirrups under a center-point load. The results are presented and discussed. They show the superiority of the proposed ICSC model for the prediction of the ultimate concrete behavior at the material level, and a better prediction of the shear behavior for plain concrete and reinforced concrete beams.

Multiscale design of nonlinear materials using a Eulerian shape optimization scheme

AbstractMotivated by recent advances in manufacturing, the design of materials is the focal point of interest in the material research community. One of the critical challenges in this field is finding optimal material microstructure for a desired macroscopic response. This work presents a computational method for the mesoscale‐level design of particulate composites for an optimal macroscale‐level response. The method relies on a custom shape optimization scheme to find the extrema of a nonlinear cost function subject to a set of constraints. Three key “modules” constitute the method: multiscale modeling, sensitivity analysis, and optimization. Multiscale modeling relies on a classical homogenization method and a nonlinear NURBS‐based generalized finite element scheme to efficiently and accurately compute the structural response of particulate composites using a nonconformal discretization. A three‐parameter isotropic damage law is used to model microstructure‐level failure. An analytical sensitivity method is developed to compute the derivatives of the cost/constraint functions with respect to the design variables that control the microstructure's geometry. The derivation uncovers subtle but essential new terms contributing to the sensitivity of finite element shape functions and their spatial derivatives. Several structural problems are solved to demonstrate the applicability, performance, and accuracy of the method for the design of particulate composites with a desired macroscopic nonlinear stress‐strain response.

Prediction of Failure in Ceramic Matrix Composites Using Damage-Based Failure Criterion

This paper presents a damage-based failure criterion and its implementation in order to predict failure in ceramic matrix composites (CMC) manufactured via filament winding. The material behavior of CMCs is anisotropic and strongly depends on the angle between fiber orientation and loading direction. The inelastic behavior of laminates with different fiber orientations under tension and shear is modeled with the help of continuum damage mechanics. The parameters required for the damage model are obtained from a standard tensile and shear test. An isotropic damage law determines the evolution of damage in thermodynamic space and considers the interaction of damage parameters in different principal material directions. A quadratic damage-based failure criterion inspired by the Tsai-Wu failure criterion is proposed. Failure stress and strain can be predicted with higher accuracy compared to the Tsai-Wu failure criterion in stress- or strain-space. The use of the proposed damage limits allows designing a CMC component based on the microstructural phenomenon of stiffness loss. With the help of results obtained from modeling and experiments, fracture mechanics during the Iosipescu-shear test of CMCs and its capability to determine the shear strength of the material is discussed.

Multi-scale damage framework for textile composites: Application to plain woven composite

A damage mechanics-based progressive damage analysis (PDA) of plain woven textile composite (PWTC) is performed in this work. The primary objective is to identify the micro-scale and meso-scale failure modes, and compute the ultimate strength of PWTC under in-plane loadings. Multi-scale PDA is performed on an equivalent cross-ply laminate (ECPL) model by maximum stress theory to predict the meso-scale failure modes of PWTC. The damaged stiffness is computed by 3 different ways: 1) hypothesis of strain energy equivalence by proposed 4th order anisotropic damage tensor, 2) applying isotropic damage law, and 3) eliminating the stiffness terms. Novel multi-scale PDA approaches, applying Mori-Tanaka (MT) theory on ECPL model and on the quarter portion of representative volume element of PWTC, are performed to predict micro-scale failure modes. The macro-scale constitutive behaviour of PWTC is theoretically predicted and the corresponding strengths are computed. A user material (UMAT) subroutine is developed to validate the proposed constitutive behaviour of PWTC solving macro-scale boundary value problems in ABAQUS®. The PDA simulation results of 3D PWTC bar model are found to be reasonably matching with the in-house experiments.

Damage modeling employing strain gradient continuum theory

A damage model for quasi-brittle materials embedded into the two dimensional C1 continuity triangular finite element formulation based on the strain gradient continuum theory is considered. The isotropic damage law is applied to the higher-order stress-strain constitutive model, which enables the analysis of both homogeneous and heterogeneous materials. Such softening formulation also ensures a decrease of the intensity of the material nonlocality associated with the damage growth, which is necessary for the correct description of the narrow localized deformation. In order to obtain the required constitutive matrices, the second-order homogenization procedure is applied to the various representative volume elements in the frame of a multiscale approach. The derived finite element formulation is implemented into the finite element program ABAQUS by means of user subroutines. The superior regularization capabilities, as well as the accuracy and efficiency of the proposed higher-order gradient damage model are demonstrated by the standard benchmark examples.

Plasticity constitutive modeling of partially confined concrete with steel jacketing

Current research offers experimental and numerical investigation on concrete blocks with partial steel jackets, which endures axial compression. Experimental procedure provides the primary data for calibration of proposed model. Specimens have various steel jacketing ratios and the load is axial compression. The recorded data are strain components, elongation and the resisted force in experiment. A continuous cap plasticity surface expresses the non-uniform expansion and contraction of concrete beside an isotropic damage law that models the strength degradation using Abaqus® code. In presented mathematical model, the contraction and dilation of concrete is function of lateral pressure provided by steel jackets. The confining pressure is non-uniform due to discrete arrangement of steel ties in jacket and yielding of steel as concrete expands. Model provides parametric curves in order to design the confined-to-unconfined strength and ductility capacities of confined concrete. The presented numerical model is in close agreement with experimental results based on acquired results. We derive finally parametric curves for ductility and strength of confined concrete for various jacketing ratios.

Plastic-damage smeared crack model to simulate the behaviour of structures made by cement based materials

This work proposes a constitutive model to simulate nonlinear behaviour of cement based materials subjected to different loading paths. The model incorporates a multidirectional fixed smeared crack approach to simulate crack initiation and propagation, whereas the inelastic behaviour of material between cracks is treated by a numerical strategy that combines plasticity and damage theories. For capturing more realistically the shear stress transfer between the crack surfaces, a softening diagram is assumed for modelling the crack shear stress versus crack shear strain. The plastic-damage model is based on the yield function, flow rule and evolution law for hardening variable, and includes an explicit isotropic damage law to simulate the stiffness degradation and the softening behaviour of cement based materials in compression. This model was implemented into the FEMIX computer program, and experimental tests at material scale were simulated to appraise the predictive performance of this constitutive model. The applicability of the model for simulating the behaviour of reinforced concrete shear wall panels submitted to biaxial loading conditions, and RC beams failing in shear is investigated.

Numerical simulation of the non-linear deformation of 5-harness satin weaves

The mechanical behaviour of a polymer composite reinforced by 5-harness satin weave is modelled using a micromechanical approach in which each of its constituents is characterised by a constitutive damage model. The epoxy matrix is modelled using an elasto-plastic with isotropic damage law while the fibrous reinforcements follow a transversely isotropic damage law. A representative unit cell of a 5-harness satin weave has been generated and a set of periodic boundary conditions implemented in order to run micromechanical analyses. Volumetric homogenisation is performed on the obtained micro-stress and -strain fields in order to study stiffness degradation and damage evolution of the satin weave under different in-plane multiaxial loading conditions.

The effect of anisotropic damage evolution on the behavior of ductile and brittle matrix composites

Anisotropic damage evolution laws for ductile and brittle materials have been coupled to a micromechanical model for the prediction of the behavior of composite materials. As a result, it is possible to investigate the effect of anisotropic progressive damage on the macroscopic (global) response and the local spatial field distributions of ductile and brittle matrix composites. Two types of thermoinelastic micromechanics analyses have been employed. In the first one, a one-way thermomechanical coupling in the constituents is considered according to which the thermal field affects the mechanical deformations. In the second one, a full thermomechanical coupling exists such that there is a mutual interaction between the mechanical and thermal fields via the energy equations of the constituents. Results are presented that illustrate the effect of anisotropic progressive damage in the ductile and brittle matrix phases on the composite’s behavior by comparisons with the corresponding isotropic damage law and/or by tracking the components of the damage tensor.

Computationally optimized formulation for the simulation of composite materials and delamination failures

The numerical simulation of complex failure modes of composite materials, such as delamination, can be computationally very demanding, as it requires special elements and/or numerical strategies to characterize damage onset and propagation. This work presents several formulations developed to optimize the computational performance of an explicit finite element code designed specifically for the simulation of large scale composite structures. The composite mechanical performance is obtained with the matrix-reinforced mixing theory, a simplified version of the serial/parallel mixing theory that does not require an iterative procedure or the calculation of the tangent stiffness matrix. The number of elements required to perform the simulation is reduced by stacking several layers inside a single finite element. This work also proposes a modification of the isotropic damage law, capable of taking into account the residual strength provided by friction in type II fracture modes. The ability of these formulations to successfully predict the mechanical performance of composite materials is assessed with the ply drop-off test. In this test a laminate with a change of thickness in its mid-span is loaded until it breaks due to a delamination process. The formulation proposed obtains a very accurate prediction of the experimental response of the test, as it provides a very good characterization of the initial laminate stiffness, the delamination onset, and its propagation along the specimen.

Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces

The cohesive surface methodology is used in a numerical study of fracture of concrete. The traction vs. separation response is governed by an isotropic damage law in which damage evolves according to a prescribed one-dimensional linear or exponential softening law. Cohesive surfaces are immersed in the continuum to allow for a maximum freedom of crack path selection. The single edge notched four point shear beam and the double edge notched tensile bar are used to study: (i) the influence of the tangential cohesive response on the development of the fracture path and (ii) the mesh alignment sensitivity. It is shown that in the present formulation, the tangential cohesive response has a minor influence on both crack path and global characteristics. Mesh alignment does have a significant influence on the outcome of the numerical analysis.

Sur l'endommagement et les matériaux standard implicites

The class of implicit standard materials, based on the introduction of a bipotential, has been proposed by de Saxcé. The kinetic isotropic damage law of Lemaitre is presented here as a new example of application.

Steel‐Concrete Bond Analysis with Nonlocal Continuous Damage

This paper deals with the application of continuum damage mechanics to the description of the response of reinforced concrete members. Two simplifying assumptions are made: (1) The constitutive law of concrete is the isotropic damage law; and (2) there are no displacement discontinuities at the interface between steel and concrete (this last statement is probably true only if ribbed reinforcing bars are considered). Numerical implementations face the same pathological difficulties related to strain softening and damage localization in shear bands near the steel bars. This problem and its consequence, mesh‐dependency, were solved by using the “nonlocal continuum with local strain” approach. Predictions of pull‐out tests are in very good agreement with test data, including size effect data. The study shows that it is possible to extend the nonlocal damage approach easily to the prediction of the response of reinforced concrete structures.