scholarly journals A VANISHING VISCOSITY APPROACH TO A RATE-INDEPENDENT DAMAGE MODEL

2013 ◽  
Vol 23 (04) ◽  
pp. 565-616 ◽  
Author(s):  
DOROTHEE KNEES ◽  
RICCARDA ROSSI ◽  
CHIARA ZANINI
Keyword(s):  
Damage Model ◽  
Energy Functional ◽  
Stored Energy ◽  
Vanishing Viscosity ◽  
Damage Models ◽  
Rate Dependent ◽  
Elastic Bodies ◽  
Viscosity Limit ◽  
Independent Effects ◽  
Independent Model

We analyze a rate-independent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional, which is assumed to be positively homogeneous of degree one. Since the energy is not simultaneously (strictly) convex in the damage variable and the displacements, solutions may have jumps as a function of time. The latter circumstance makes it necessary to recur to suitable notions of weak solution. However, the by-now classical concept of global energetic solution fails to describe accurately the behavior of the system at jumps. Hence, we consider rate-independent damage models as limits of systems driven by viscous, rate-dependent dissipation. We use a technique for taking the vanishing viscosity limit, which is based on arclength reparametrization. In this way, in the limit we obtain a novel formulation for the rate-independent damage model, which highlights the interplay of viscous and rate-independent effects in the jump regime, and provides a better description of the energetic behavior of the system at jumps.

scholarly journals Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

2020 ◽  
Author(s):  
Chuang Liu ◽  
Dongzhi Sun ◽  
Xianfeng Zhang ◽  
Florence Andrieux ◽  
Tobias Gerster
Keyword(s):  
Cast Iron ◽  
Constitutive Model ◽  
Strain Rate ◽  
Mechanical Behavior ◽  
Damage Model ◽  
Iron Alloys ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Damage Models ◽  
Rate Dependent

Abstract Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry. To study the mechanical behavior of a typical ductile cast iron (GJS-450) with nodular graphite, uni-axial quasi-static and dynamic tensile tests at strain rates of 10− 4, 1, 10, 100, and 250 s− 1 were carried out. In order to investigate the effects of stress state, specimens with various geometries were used in the experiments. Stress–strain curves and fracture strains of the GJS-450 alloy in the strain-rate range of 10− 4 to 250 s− 1 were obtained. A strain rate-dependent plastic flow law based on the Voce model is proposed to describe the mechanical behavior in the corresponding strain-rate range. The deformation behavior at various strain rates is observed and analyzed through simulations with the proposed strain rate-dependent constitutive model. The available damage model from Bai and Wierzbicki is extended to take the strain rate into account and calibrated based on the analysis of local fracture strains. The validity of the proposed constitutive model including the damage model was verified by the corresponding experimental results. The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys. The predictions with the proposed constitutive model and damage models at various strain rates agree well with the experimental results, which illustrates that the rate-dependent flow rule and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.

Comparison of Interfacial and Continuum Models for Dynamic Fragmentation Analysis

2018 ◽  
Author(s):  
Bahador Bahmani ◽  
Philip Clarke ◽  
Reza Abedi
Keyword(s):  
Damage Model ◽  
Compressive Load ◽  
Stochastic Field ◽  
Damage Models ◽  
Coupled Equations ◽  
Rate Dependent ◽  
Fracture Simulation ◽  
Microstructure Effects ◽  
Dynamic Brittle Fracture ◽  
Final System

The microstructural design has an essential effect on the fracture response of brittle materials. We present a stochastic bulk damage formulation to model dynamic brittle fracture. This model is compared with a similar interfacial model for homogeneous and heterogeneous materials. The damage models are rate-dependent, and the corresponding damage evolution includes delay effects. The delay effect provides mesh objectivity with much less computational efforts. A stochastic field is defined for material cohesion and fracture strength to involve microstructure effects in the proposed formulations. The statistical fields are constructed through the Karhunen-Loeve (KL) method. An advanced asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used to discretize the final system of coupled equations. Application of the presented formulation is shown through dynamic fracture simulation of rock under a uniaxial compressive load. The final results show that a stochastic bulk damage model produces more realistic results in comparison with a homogenizes model.

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.

Validation of Modified Lemaitre’s Anisotropic Damage Model with the Cross Die Drawing Test

2011 ◽  
Vol 488-489 ◽  
pp. 49-52 ◽  
Author(s):  
M.S. Niazi ◽  
H. H. Wisselink ◽  
T. Meinders
Keyword(s):  
Strain Rate ◽  
Automotive Industry ◽  
Damage Model ◽  
Anisotropic Damage ◽  
Rate Dependency ◽  
Damage Models ◽  
Rate Dependent ◽  
Drawing Test ◽  
Dp Steels ◽  
The Cross

Dual Phase (DP) steels are widely replacing the traditional forming steels in automotive industry. Advanced damage models are required to accurately predict the formability of DP steels. In this work, Lemaitre’s anisotropic damage model has been slightly modified for sheet metal forming applications and for strain rate dependent materials. The damage evolution law is adapted to take into account the strain rate dependency and negative triaxialities. The damage parameters for pre-production DP600 steel were determined. The modified damage models (isotropic and anisotropic) were validated using the cross die drawing test. The anisotropic damage model predicts the crack direction more accurately.

scholarly journals A Novel Damage Model for Strata Layers and Coal Mass

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1928 ◽  
Author(s):  
Faham Tahmasebinia ◽  
Chengguo Zhang ◽  
Ismet Canbulat ◽  
Samad Sepasgozar ◽  
Serkan Saydam
Keyword(s):  
Constitutive Model ◽  
Strain Energy ◽  
Damage Model ◽  
Rock Joint ◽  
Coal Mass ◽  
Stored Energy ◽  
Rock Interaction ◽  
Geological Factors ◽  
Coal Rock ◽  
Joint Quality

Coal burst occurrences are affected by a range of mining and geological factors. Excessive slipping between the strata layers may release a considerable amount of strain energy, which can be destructive. A competent strata is also more vulnerable to riveting a large amount of strain energy. If the stored energy in the rigid roof reaches a certain level, it will be released suddenly which can create a serious dynamic reaction leading to coal burst incidents. In this paper, a new damage model based on the modified thermomechanical continuum constitutive model in coal mass and the contact layers between the rock and coal mass is proposed. The original continuum constitutive model was initially developed for the cemented granular materials. The application of the modified continuum constitutive model is the key aspect to understand the momentum energy between the coal–rock interactions. The transformed energy between the coal mass and different strata layers will be analytically demonstrated as a function of the rock/joint quality interaction conditions. The failure and post failure in the coal mass and coal–rock joint interaction will be classified by the coal mass crushing, coal–rock interaction damage and fragment reorganisation. The outcomes of this paper will help to forecast the possibility of the coal burst occurrence based on the interaction between the coal mass and the strata layers in a coal mine.

Sign in / Sign up

Export Citation Format

Share Document