A geometrically inspired model for brittle damage in compressible elastomers

2021 ◽  
pp. 1-39
Author(s):  
Sanhita Das ◽  
Shubham Sharma ◽  
Ananth Ramaswamy ◽  
Debasish Roy ◽  
J.N. Reddy
Keyword(s):  
Phase Field ◽  
Scale Parameter ◽  
Damage Model ◽  
Continuum Damage ◽  
Surface Integral ◽  
Brittle Damage ◽  
Damage Models ◽  
Damaged Material ◽  
Isotropic Damage ◽  
Pure Compression

Abstract Regularized continuum damage models such as those based on an order parameter (phase field) have been extensively used to characterize brittle damage of compressible elastomers. However, the prescription of the surface integral and the degradation function for stiffness lacks a physical basis. In this article we propose a continuum damage model that draws upon the postulate that a damaged material could be mathematically described as a Riemannian manifold. Working within this framework with a well defined Riemannian metric designed to capture features of isotropic damage, we prescribe a scheme to prevent damage evolution under pure compression. The result is a substantively reduced stiffness degradation due to damage before the peak response and a faster convergence rate with the length scale parameter in comparison with a second order phase field formulation that involves a quadratic degradation function. We also validate this model using results of tensile experiments on double notched plates.

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

2011 ◽  
Vol 21 (5) ◽  
pp. 713-754 ◽  
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.

Experimental and FEA Investigations on the Fracture Properties of Pipe Structures Under Internal Pressure in DBTT Region

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Zhao-Xi Wang ◽  
Fei Xue ◽  
Hui-Ji Shi ◽  
Jian Lu
Keyword(s):  
Energy Density ◽  
Fracture Energy ◽  
Transition Region ◽  
Damage Model ◽  
Stress Triaxiality ◽  
Basic Material ◽  
Continuum Damage ◽  
Continuum Damage Model ◽  
Damage Models ◽  
Different Temperatures

The fracture behavior of pipes with penetrating cracks was experimentally investigated with the results of the load-deflection curves and crack length. J-R curves were obtained from the testing results for different temperatures. With the decrement in temperature, the critical J integral decreases and the tearing modulus increases. An updated continuum damage model was proposed, in which the fracture energy density as a function of the stress triaxiality, temperature and strain rate in the transition region was taken as the critical damage factor. The uni-axial tension experiments at different temperatures were carried out to obtain the basic material properties and the critical fracture energy density, to verify the validity of the damage model. Based on detailed finite element analyses with the proposed updated continuum damage model, the loading level of pipes with penetrating cracks was estimated and compared with the experimental results, meanwhile the fracture processes of the pipeline structure in the ductile-brittle-transition-temperature region were reproduced. It has been shown that the fracture process in the transition region strongly depends on both the stress and strain state, and can be effectively predicted using the continuum damage models incorporating with the stress state effect.

Influence of Ductile Damage Evolution on the Collapse Load of Frames

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Edwin L. Chica ◽  
Antolín L. Ibán ◽  
José M. G. Terán ◽  
Pablo M. López-Reyes
Keyword(s):  
Ductile Fracture ◽  
Damage Evolution ◽  
Damage Model ◽  
Ductile Failure ◽  
Ductile Material ◽  
Collapse Load ◽  
Local Criterion ◽  
Solid Materials ◽  
Damage Models ◽  
Isotropic Damage

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.

scholarly journals Rate Sensitive Continuum Damage Models and Mesh Dependence in Finite Element Analyses

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Goran Ljustina ◽  
Martin Fagerström ◽  
Ragnar Larsson
Keyword(s):  
Damage Model ◽  
Direct Consequence ◽  
Continuum Damage ◽  
Dynamic Failure ◽  
Failure Model ◽  
Damage Models ◽  
Rate Dependent ◽  
Orthogonal Machining ◽  
Element Size ◽  
Viscous Regularization

The experiences from orthogonal machining simulations show that the Johnson-Cook (JC) dynamic failure model exhibits significant element size dependence. Such mesh dependence is a direct consequence of the utilization of local damage models. The current contribution is an investigation of the extent of the possible pathological mesh dependence. A comparison of the resulting JC model behavior combined with two types of damage evolution is considered. The first damage model is the JC dynamic failure model, where the development of the “damage” does not affect the response until the critical state is reached. The second one is a continuum damage model, where the damage variable is affecting the material response continuously during the deformation. Both the plasticity and the damage models are rate dependent, and the damage evolutions for both models are defined as a postprocessing of the effective stress response. The investigation is conducted for a series of 2D shear tests utilizing different FE representations of the plane strain plate with pearlite material properties. The results show for both damage models, using realistic pearlite material parameters, that similar extent of the mesh dependence is obtained and that the possible viscous regularization effects are absent in the current investigation.

Nonlinear modeling of concentrically loaded reinforced blockwork masonry columns

2004 ◽  
Vol 31 (6) ◽  
pp. 1012-1023 ◽  
Author(s):  
Hasan Orhun Köksal ◽  
Bilge Doran ◽  
Ayse Elif Ozsoy ◽  
Sema Noyan Alacali
Keyword(s):  
Finite Element ◽  
Yield Criterion ◽  
Nonlinear Modeling ◽  
Damage Model ◽  
Three Dimensional ◽  
Mesh Size ◽  
Simple Relation ◽  
Damage Parameter ◽  
Damage Models ◽  
Isotropic Damage

Since only a limited number of experimental and analytical studies have been carried out for the purpose of developing strength design procedures for reinforced blockwork masonry columns, there is a certain need for further studies that reflect material properties and behavior of blockwork masonry more closely. This paper deals with a nonlinear finite element modeling of the concentrically loaded reinforced blockwork masonry columns making use of both elasto-plastic and isotropic damage models. If the damage model is enriched with the introduction of a simple relation for the material damage parameter that accounts for the mesh size effect, three-dimensional finite element analyses of columns for the well-known experimental works in the literature are accomplished. Finally, the predictions from both the numerical analyses and the existing expressions for the ultimate load of the masonry columns are compared with the experimental results.Key words: compressive strength, reinforced blockwork masonry column, finite element method, Drucker-Prager yield criterion, isotropic damage theory.

Geometry Transferability of Lemaitre's Continuum Damage Mechanics Model in the Plane Stress Specimens

2013 ◽  
Vol 592-593 ◽  
pp. 266-270 ◽  
Author(s):  
Nima Allahverdizadeh ◽  
Andrea Manes ◽  
Marco Giglio ◽  
Andrea Gilioli
Keyword(s):  
Plane Stress ◽  
Damage Mechanics ◽  
Numerical Models ◽  
Damage Model ◽  
High Strength ◽  
Experimental Tests ◽  
Continuum Damage Mechanics ◽  
Failure Behavior ◽  
Continuum Damage ◽  
Damage Models

Different damage mechanics models have been proposed by researchers to calibrate the failure behavior of materials. Continuum damage mechanics (CDM) models are one of the main categories of damage models that can be exploited in numerical simulations. In this paper Lemaitres damage model, has been applied to finite element models of flat specimens. These models allow assessing the geometry transferability of the previously calibrated CDM model investigating in different geometry and loading conditions. Four different types of plane stress specimens have been designed to get different stress triaxialities which cover shear dominant and high triaxiality failure. Experimental tests were also done and the obtained data were critically compared with the results from numerical models. The tested material is Ti-6Al-4V titanium alloy which is a widely used material in aerospace industry because of its high strength and low density.

scholarly journals A Modified Phase-Field Damage Model for Metal Plasticity at Finite Strains: Numerical Development and Experimental Validation

Metals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 47
Author(s):  
Jelena Živković ◽  
Vladimir Dunić ◽  
Vladimir Milovanović ◽  
Ana Pavlović ◽  
Miroslav Živković
Keyword(s):  
Phase Field ◽  
Damage Evolution ◽  
Deformation Gradient ◽  
Damage Model ◽  
Steel Structures ◽  
Plasticity Model ◽  
Metal Plasticity ◽  
Damage And Fracture ◽  
Von Mises ◽  
Von Mises Plasticity

Steel structures are designed to operate in an elastic domain, but sometimes plastic strains induce damage and fracture. Besides experimental investigation, a phase-field damage model (PFDM) emerged as a cutting-edge simulation technique for predicting damage evolution. In this paper, a von Mises metal plasticity model is modified and a coupling with PFDM is improved to simulate ductile behavior of metallic materials with or without constant stress plateau after yielding occurs. The proposed improvements are: (1) new coupling variable activated after the critical equivalent plastic strain is reached; (2) two-stage yield function consisting of perfect plasticity and extended Simo-type hardening functions. The uniaxial tension tests are conducted for verification purposes and identifying the material parameters. The staggered iterative scheme, multiplicative decomposition of the deformation gradient, and logarithmic natural strain measure are employed for the implementation into finite element method (FEM) software. The coupling is verified by the ‘one element’ example. The excellent qualitative and quantitative overlapping of the force-displacement response of experimental and simulation results is recorded. The practical significances of the proposed PFDM are a better insight into the simulation of damage evolution in steel structures, and an easy extension of existing the von Mises plasticity model coupled to damage phase-field.

Cross-Ply Laminates under Static Three-Point Bending: A Numerical Development Model

2012 ◽  
Vol 498 ◽  
pp. 42-54 ◽  
Author(s):  
S. Benbelaid ◽  
B. Bezzazi ◽  
A. Bezazi
Keyword(s):  
Numerical Model ◽  
Damage Mechanics ◽  
Progressive Failure ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Failure Criteria ◽  
Continuum Damage ◽  
Damage Development ◽  
Element Analysis ◽  
Progressive Failure Analysis

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical model. Under static three points bending, two modes of damage progression in cross-ply laminates are predominated: transverse cracking and delamination. However, this second mode of damage is not accounted in our numerical model. After a general review of experimental approaches of observed behavior of laminates, the focus is laid on predicting laminate behavior based on continuum damage mechanics. In this study, a continuum damage model based on ply failure criteria is presented, which is initially proposed by Ladevèze. To reveal the effect of different stacking sequence of the laminate; such as thickness and the interior or exterior disposition of the 0° and 90° oriented layers in the laminate, an equivalent damage accumulation which cover all ply failure mechanisms has been predicted. However, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized. The results of the numerical computation have been justified by the previous published experimental observations of the authors.

Numerical Investigation on Shear Failure of Concrete Beam Strengthened by Bonded Steel Plate

2013 ◽  
Vol 351-352 ◽  
pp. 1552-1557
Author(s):  
Da Guo Wang ◽  
Zhi Xiu Wang ◽  
Bing Xu
Keyword(s):  
Numerical Investigation ◽  
Concrete Beam ◽  
Shear Failure ◽  
Steel Plate ◽  
Damage Model ◽  
Adhesive Layer ◽  
Aggregate Gradation ◽  
Brittle Damage ◽  
Plastic Yield ◽  
Final Failure

Based on micromechanics, an elastic-plastic-brittle damage model of concrete beam reinforced with stick steel is proposed by considering the aggregate gradation curve algorithms and the heterogeneity. In the model, the concrete beam reinforced with stick steel is taken as a five-phase composite material that consists of the mortar matrix, coarse aggregate, bonds between mortar and aggregate, steel plate, and the adhesive layer between steel plate and concrete beam. Through the numerical investigation on shear failure of concrete beam reinforced with stick steel under external force, the results show that the model can clearly simulate microscopic plastic yield, and the initiation and extension of crack. The strength of the steel plate is relatively stronger, so it cant enhance the shear capability of the each side of the beam and the concrete beam bears the larger shear stress, which results that a large number of elements, from the supports to the load points, begin to yield. When the strain of the elements exceeds the yield strength, the elements will produce failure until the failure of the whole specimen. The final failure mode of concrete beam reinforced with stick steel is the shear failure.

Study of the progressive failure of concrete by phase field modeling and experiments

2021 ◽  
pp. 105678952110014
Author(s):  
Jichang Wang ◽  
Xiaoming Guo ◽  
Nailong Zhang
Keyword(s):  
Phase Field ◽  
Progressive Failure ◽  
Failure Process ◽  
Damage Model ◽  
Concrete Fracture ◽  
Opening Displacement ◽  
Three Point Bending ◽  
Edge Notch ◽  
Modeling And Experiments ◽  
Crack Faces

In this research, experiments and numerical simulations are employed to research the failure process of concrete. Fracture experiments on three-point bending (TPB) concrete beams with a prefabricated edge notch at the middle of the beam bottom are performed using a modified rigid testing instrument. The characteristics of the crack and section are analyzed, including the crack tensile opening displacement, crack length and width, and crack faces characteristics. Also, the full curves of the force-crack tensile opening displacement (CMOD) and force-deflection of the TPB beams with the prefabricated edge notch after breakage are obtained. The phase field (PF) damage model is applied to the mixed-mode and mode-I failure processes of concrete structures through the ABAQUS subroutine user defined element (UEL). The crack path and the full curves of force-CMOD and force-deflection obtained by numerical calculations are consistent with the experimental results and the calculated results of other researchers. The influences of the mesh sizes, initial lengths, and notched depths on the TPB beam of concrete are also analyzed.

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