An isotropic damage model for ductile material

In this note we analyze the influence of four damage models on the collapse load of a structure. The models considered here have been developed using the hypothesis based on the concept of effective stress and the principle of strain equivalence and they were proposed by Lemaitre and Chaboche (1990, Mechanics of Solid Materials), Wang (1992, “Unified CDM Model and Local Criterion for Ductile Fracture—I. Unified CDM Model for Ductile Fracture,” Eng. Fract. Mech., 42, pp. 177–183), Chandrakanth and Pandey (1995, “An Isotropic Damage Model for Ductile Material,” Eng. Fract. Mech., 50, pp. 457–465), and Bonora (1997, “A Nonlinear CDM Model for Ductile Failure,” Eng. Fract. Mech., 58, pp. 11–28). The differences between them consist mainly in the form of the dissipative potential from which the kinetic law of damage is derived and also in the assumptions made about some parameters of the material.

Download Full-text

Failure Predictions for DP Steel Cross-die Test using Anisotropic Damage

International Journal of Damage Mechanics ◽

10.1177/1056789511407646 ◽

2011 ◽

Vol 21 (5) ◽

pp. 713-754 ◽

Cited By ~ 18

Author(s):

M. S. Niazi ◽

H. H. Wisselink ◽

T. Meinders ◽

J. Huétink

Keyword(s):

Strain Rate ◽

Damage Evolution ◽

Damage Model ◽

Anisotropic Damage ◽

Continuum Damage ◽

Anisotropic Plasticity ◽

Continuum Damage Model ◽

Damage Models ◽

Isotropic Damage ◽

Failure Predictions

The Lemaitre's continuum damage model is well known in the field of damage mechanics. The anisotropic damage model given by Lemaitre is relatively simple, applicable to nonproportional loads and uses only four damage parameters. The hypothesis of strain equivalence is used to map the effective stress to the nominal stress. Both the isotropic and anisotropic damage models from Lemaitre are implemented in an in-house implicit finite element code. The damage model is coupled with an elasto-plastic material model using anisotropic plasticity (Hill-48 yield criterion) and strain-rate dependent isotropic hardening. The Lemaitre continuum damage model is based on the small strain assumption; therefore, the model is implemented in an incremental co-rotational framework to make it applicable for large strains. The damage dissipation potential was slightly adapted to incorporate a different damage evolution behavior under compression and tension. A tensile test and a low-cycle fatigue test were used to determine the damage parameters. The damage evolution was modified to incorporate strain rate sensitivity by making two of the damage parameters a function of strain rate. The model is applied to predict failure in a cross-die deep drawing process, which is well known for having a wide variety of strains and strain path changes. The failure predictions obtained from the anisotropic damage models are in good agreement with the experimental results, whereas the predictions obtained from the isotropic damage model are slightly conservative. The anisotropic damage model predicts the crack direction more accurately compared to the predictions based on principal stress directions using the isotropic damage model. The set of damage parameters, determined in a uniaxial condition, gives a good failure prediction under other triaxiality conditions.

Download Full-text

Fracture simulations using edge-based smoothed finite element method for isotropic damage model via Delaunay/Voronoi dual tessellations

International Journal of Damage Mechanics ◽

10.1177/10567895211040549 ◽

2021 ◽

pp. 105678952110405

Author(s):

Young Kwang Hwang ◽

Suyeong Jin ◽

Jung-Wuk Hong

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Voronoi Tessellation ◽

Damage Model ◽

Time Integration ◽

Voronoi Cell ◽

Smoothed Finite Element Method ◽

Isotropic Damage ◽

Edge Based ◽

Element Method

In this study, an effective numerical framework for fracture simulations is proposed using the edge-based smoothed finite element method (ES-FEM) and isotropic damage model. The duality between the Delaunay triangulation and Voronoi tessellation is utilized for the mesh construction and the compatible use of the finite element solution with the Voronoi-cell lattice geometry. The mesh irregularity is introduced to avoid calculating the biased crack path by adding random variation in the nodal coordinates, and the ES-FEM elements are defined along the Delaunay edges. With the Voronoi tessellation, each nodal mass is calculated and the fractured surfaces are visualized along the Voronoi edges. The rotational degrees of freedom are implemented for each node by introducing the elemental formulation of the Voronoi-cell lattice model, and the accurate visualizations of the rotational motions in the Voronoi diagram are achieved. An isotropic damage model is newly incorporated into the ES-FEM formulation, and the equivalent elemental length is introduced with an additional geometric factor to simulate the consistent softening behaviors with reducing the mesh sensitivity. The full matrix form of the smoothed strain-displacement matrix is constructed for optimal use in the element-wise computations during explicit time integration, and parallel computing is implemented for the enhancement of the computational efficiency. The simulated results are compared with the theoretical solutions or experimental results, which demonstrates the effectiveness of the proposed methodology in the simulations of the quasi-brittle fractures.

Download Full-text

An Application of Bi-Directional Evolutionary Structural Optimisation for Optimising Energy Absorbing Structures Using a Material Damage Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.553.836 ◽

2014 ◽

Vol 553 ◽

pp. 836-841 ◽

Cited By ~ 2

Author(s):

Daniel Stojanov ◽

Brian G. Falzon ◽

Xin Hua Wu ◽

Wen Yi Yan

Keyword(s):

Finite Element ◽

Damage Model ◽

Ductile Material ◽

Topology Optimisation ◽

Material Damage ◽

Structural Optimisation ◽

Element Analysis ◽

Element Mesh ◽

Beso Method ◽

Energy Absorbing

The Bi-directional Evolutionary Structural Optimisation (BESO) method is a numerical topology optimisation method developed for use in finite element analysis. This paper presents a particular application of the BESO method to optimise the energy absorbing capability of metallic structures. The optimisation objective is to evolve a structural geometry of minimum mass while ensuring that the kinetic energy of an impacting projectile is reduced to a level which prevents perforation. Individual elements in a finite element mesh are deleted when a prescribed damage criterion is exceeded. An energy absorbing structure subjected to projectile impact will fail once the level of damage results in a critical perforation size. It is therefore necessary to constrain an optimisation algorithm from producing such candidate solutions. An algorithm to detect perforation was implemented within a BESO framework which incorporated a ductile material damage model.

Download Full-text

Lifetime Prediction of Rocket Combustion Chamber Wall by Means of Viscoplasticity Coupled With Ductile Isotropic Damage

Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control ◽

10.1115/esda2012-82748 ◽

2012 ◽

Cited By ~ 2

Author(s):

Vivian Tini ◽

Ivaylo N. Vladimirov ◽

Stefanie Reese

Keyword(s):

Combustion Chamber ◽

Copper Alloy ◽

Kinematic Hardening ◽

Damage Model ◽

Chamber Wall ◽

Lifetime Prediction ◽

Viscoplastic Model ◽

Material Parameters ◽

Isotropic Damage ◽

Wall Materials

This paper presents the application of a viscoplastic damage model for the lifetime prediction of a typical rocket combustion chamber structure. The material modeling is motivated by extension of the classical rheological model for elastoplasticity with Armstrong-Frederick kinematic hardening into a viscoplastic model. The coupling with damage is performed using the concept of effective stress and the principle of strain equivalence. The material parameters are identified based on experimental results for the high temperature copper alloy NARloy-Z, which is one of the typical combustion chamber wall materials. Finally the applicability of the model will be shown by means of sequentially coupled thermomechanical analyses.

Download Full-text

Cyclic Loading of Beams Based on Kinematics Hardening Behavior Coupled With Isotropic Damage

Volume 4: Fatigue and Fracture, Heat Transfer, Internal Combustion Engines, Manufacturing, and Technology and Society ◽

10.1115/esda2006-95239 ◽

2006 ◽

Cited By ~ 1

Author(s):

Ali Nayebi ◽

Kourosh H. Shirazi

Keyword(s):

Cyclic Loading ◽

Strain Hardening ◽

Kinematic Hardening ◽

Damage Model ◽

Mapping Algorithm ◽

Return Mapping ◽

Tension And Compression ◽

Computational Aspects ◽

Isotropic Damage ◽

Path Dependent

The kinematic hardening theory of plasticity based on the Prager model and incremental isotropic damage is used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. This allows damage to be path-dependent. The damage and inelastic deformation are incorporated and they are used for the analysis of the beam. The beam material is assumed to follow linear strain hardening property coupled with isotropic damage. The material strain hardening curves in tension and compression are assumed to be both identical for the isotropic material. Computational aspects of rate independent model is discussed and the constitutive equation of the rate independent plasticity coupled with the damage model are decomposed into the elastic, plastic and damage parts. Return Mapping Algorithm method is used for the correction of the elastoplastic state and for the damage model the algorithm is used according to the governed damage constitutive relation. The effect of the damage phenomenon coupled with the elastoplastic kinematic hardening is studied for deformation and load control loadings.

Download Full-text

A Multi-Level Superelement Technique for Damage Analysis

Materials: Processing, Characterization and Modeling of Novel Nano-Engineered and Surface Engineered Materials ◽

10.1115/imece2002-39190 ◽

2002 ◽

Author(s):

J. P. Fan ◽

C. Y. Tang ◽

C. L. Chow

Keyword(s):

Damage Model ◽

Tensile Loading ◽

Volume Element ◽

Damage Analysis ◽

Two Dimensional ◽

Element Computation ◽

Isotropic Damage ◽

Multi Level ◽

Abaqus Code ◽

Finite Element Computation

A multi-level superelement technique is applied to model the effects of circular voids on the effective elastic properties of a material. A two-dimensional representative volume element with a circular void in its center is initially modeled by a superelement. Using this superelement, a thin planar material with circular voids is constructed. The finite element computation is then conducted to estimate the effective Young’s modulus, Poisson’s ratio and the shear modulus of the material using the ABAQUS code for different void sizes. The values of the isotropic damage variables, DE and DG, under various degree of damage are hence determined. These values are compared with those calculated by using a conventional micromechanics damage model. A new isotropic damage model is proposed based on the results of this analysis. To demonstrate the applicability of this damage model, an example case of a notched cylindrical bar under tensile loading is investigated.

Download Full-text