Rate-dependent Damage Research Articles

Do blast induced skull flexures result in axonal deformation?

Subject-specific computer models (male and female) of the human head were used to investigate the possible axonal deformation resulting from the primary phase blast-induced skull flexures. The corresponding axonal tractography was explicitly incorporated into these finite element models using a recently developed technique based on the embedded finite element method. These models were subjected to extensive verification against experimental studies which examined their pressure and displacement response under a wide range of loading conditions. Once verified, a parametric study was developed to investigate the axonal deformation for a wide range of loading overpressures and directions as well as varying cerebrospinal fluid (CSF) material models. This study focuses on early times during a blast event, just as the shock transverses the skull (< 5 milliseconds). Corresponding boundary conditions were applied to eliminate the rotation effects and the resulting axonal deformation. A total of 138 simulations were developed– 128 simulations for studying the different loading scenarios and 10 simulations for studying the effects of CSF material model variance–leading to a total of 10,702 simulation core hours. Extreme strains and strain rates along each of the fiber tracts in each of these scenarios were documented and presented here. The results suggest that the blast-induced skull flexures result in strain rates as high as 150–378 s-1. These high-strain rates of the axonal fiber tracts, caused by flexural displacement of the skull, could lead to a rate dependent micro-structural axonal damage, as pointed by other researchers.

A constitutive model for frozen soil based on rate-dependent damage evolution

The deformation of frozen soil under impact loading is usually accompanied by the evolution of internal defects and microdamage. By taking the strain and strain rates into account, a rate-dependent damage evolution law is proposed in this study, under the assumption of equivalent strain. Subsequently, a damage-modified rate-dependent constitutive model is proposed to describe the dynamic mechanical properties of frozen soil. A split Hopkinson pressure bar is utilized to test the dynamic mechanical response of frozen soil at different temperatures and high strain rates. The experimental results show that frozen soil produces obvious strain rate and temperature effects, and that there is a linear relationship between the peak stress and temperature. The theoretical results of the proposed constitutive model agree well with the experimental results, verifying the applicability of the model.

Multi-Laminate Rate-Dependent Modelling of Static and Dynamic Concrete Behavior through Damage Formulation

Mathematical simulation of the nonlinear tri-dimensional mechanical behavior of quasi-brittle materials like concrete is one of the biggest challenges in the engineering science. It is vital to have the knowledge of the response of concrete specimens subjected to low and high strain rate deformation for the analysis of concrete structures under the static and dynamic loading cases. The behavior of this material is generally known to be strain rate sensitive. Among phenomena of different orientation, the multi plane models, like multi-laminate models using a constitutive equation in a vectorial form rather than tensorial form by means of capturing interactions, can meet this goal adequately. This paper suggests a robust rate dependent damage based model in the multi-planes framework accomplished with minimum parameters for calibration and appropriate for engineering purposes. This damage formulation has been built on the basis of two types of essential damage, axial damage and shear damage, that basically can happen on each sampling plane and based on this concept two new axial and shear damage functions are proposed. Model verification has been studied under different compressive and tensile loading rates, comparing the results of the proposed model with the experimental data and Mohr-Coulomb failure criterion envelope line.

Numerical mesoscopic investigations of dynamic damage and failure mechanisms of polymer bonded explosives

A damage elasto-viscoplastic model has been developed for cyclotetramethylenetetranitramine (HMX) crystals, which considers the anisotropy nature of HMX crystals and dislocation-mediated plasticity as well as the cleavage damage. A damage viscoelastic model has been developed for the polymer binder and the interface, which captures rate dependent damage due to binder rupture and binder debonding during the loading process. The proposed models were implemented in the finite element code ABAQUS by the user subroutine VUMAT. Macroscopic mechanical responses of Polymer Bonded explosives (PBXs) 9501 homogenized across the microstructure is generally in agreement with Split Hopkinson Pressure Bar (SHPB) experimental stress-strain responses at the strain rate of 2000 s−1. Microstructural heterogeneity is responsible for the non-uniform stress, strain and damage fields. Crystal fracture is the dominant failure mechanism under dynamic compression while interfacial debonding plays a more important role under dynamic tension. Mesoscale modeling results along with macroscopic responses are significantly important to have a better understanding of deformation, damage and failure mechanisms of PBX samples under dynamic loading and to improve our predictive ability.

A numerical study on crack branching in quasi-brittle materials with a new effective rate-dependent nonlocal damage model

This contribution presents a numerical study towards the propagation and branching of cracks in quasi-brittle materials, using a new effective rate-dependent damage model, enhanced by a stress-based nonlocal (SBNL) regularization scheme. This phenomenological model is mesh objective and reproduces the major phenomena associated with crack propagation and branching in quasi-brittle materials.It is discussed and demonstrated that the branching phenomenon is not controlled by a specific, material dependent, crack speed. Instead, it is governed by the evolution of the principal stresses at the crack tip, which are controlled by the evolution of damage. It is demonstrated that, with increasing crack speeds, the principal stresses at the crack tip tend to evolve from a mode-I to a mixed-mode state. Beyond a certain (critical) crack speed, the stress distribution around the crack tip reaches a critical state at which a single crack is no longer stable. When this condition is met, crack branching occurs whenever the stress field at the crack tip is destabilized by either a physical discontinuity or an interfering stress wave reflected at the specimen boundaries.

A new effective rate dependent damage model for dynamic tensile failure of concrete

From a macroscopic point of view, the dynamic tensile response of concrete is mainly due to the viscous behavior of the bulk material and inertia effects at multi-scale levels. It has been suggested that almost all of these mechanisms have to be considered as intrinsic material properties and explicitly included in the constitutive relations of the continuum model. It is discussed and demonstrated that the use of semi-empirical dynamic strength increase factor (DIF) functions to numerically describe rate effects do not characterize true constitutive relations of the material.A strain-rate dependent formulation is used to describe the strength and fracture energy increase of concrete under dynamic tensile loading conditions. However, instead of the commonly used ε̇ (instantaneous strain-rate) to update the constitutive law, an effective rate (R) is considered. With this new concept a time scale is introduced in the constitutive law which restrains the ‘evolution of rate’, to represent the inherent dynamic properties of concrete. This has a weak regularization effect and acts as a localization limiter. Mesh objectivity is recovered with the addition of a material length scale to the constitutive relations, here accomplished by an explicit stress-based nonlocal regularization scheme.Two sets of modified split Hopkinson bar tests are simulated for validation, using respectively notched and un-notched specimens. The results are objective and in good agreement with the experiments.

A mesoscale fracture model for concrete

We analyze the dynamic failure of concrete using two and three-dimensional finite-element models. In particular, the current results extend, using a unique parallel computing approach, previously published two-dimensional results. Concrete is treated at the mesoscale with an explicit representation of coarse aggregates and mortar paste. The propagation and coalescence of cracks are modeled with dynamically inserted cohesive elements. Stress-strain response, dissipated fracture energy and crack evolution are compared under tensile loading at several strain rates. The artifacts of the two-dimensional approach regarding microcrack coalescence are discussed in detail. Nonetheless, the dynamic increase factors for the peak strength and dissipated fracture energy show that in both two and three dimensions, micro-inertial effects are not enough to simulate the rate dependency in concrete with a simple rate-independent cohesive law. Rate-dependent damage parameters can be introduced to obtain a more accurate dynamic response.

Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach

We present a continuum model that incorporates rate-dependent damage and fracture, a material order-parameter field and temperature within a phase-field approach. The models covers partial damage as well as the formation of macro-cracks. For the material order parameter we assume a Cahn Larche-type dynamics, which makes the model in particular applicable to binary alloys. We give thermodynamically consistent evolution equations resulting from a unified variational approach. Diverse coupling mechanisms can be covered within the model, such as heat dissipation, thermal-expansion-induced failure and crack deflection due to inhomogeneities. With help of an adaptive finite element code we conduct numerical experiments of different complexity in order to study the possibilities and limitations of the presented model. We furthermore include anisotropic linear elasticity in our model and investigate the effect on the crack pattern.

Two-Way Coupled Multiscale Model for Predicting Mechanical Behavior of Bone Subjected to Viscoelastic Deformation and Fracture Damage

This paper presents a two-way linked computational multiscale model and its application to predict the mechanical behavior of bone subjected to viscoelastic deformation and fracture damage. The model is based on continuum thermos-mechanics and is implemented through the finite element method (FEM). Two physical length scales (the global scale of bone and local scale of compact bone) were two-way coupled in the framework by linking a homogenized global object to heterogeneous local-scale representative volume elements (RVEs). Multiscaling accounts for microstructure heterogeneity, viscoelastic deformation, and rate-dependent fracture damage at the local scale in order to predict the overall behavior of bone by using a viscoelastic cohesive zone model incorporated with a rate-dependent damage evolution law. In particular, age-related changes in material properties and geometries in bone were considered to investigate the effect of aging, loading rate, and damage evolution characteristics on the mechanical behavior of bone. The model successfully demonstrated its capability to predict the viscoelastic response and fracture damage due to different levels of aging, loading conditions (such as rates), and microscale damage evolution characteristics with only material properties of each constituent in the RVEs.

Damage Induced by High-Velocity Impact on Composite Structures Using Finite Element Simulation

In the current study, a finite element model was established to simulate the penetration process of composite laminates under high-velocity impact. A 3D rate-dependent damage constitutive model was developed to simulate the ballistic response of unidirectional fiber-reinforced composite laminate. Numerical models were built based on a damage model where cohesive contact method was involved. The user-developed FORTRAN subroutine (VUMAT) was written and implemented in ABAQUS/Explicit 6.11 version. The ballistic resistance and damage characteristics of composite laminate were discussed, and the damage model was validated. The results of the FEM were observed to agree well with experimental observation. According to the results, the ply angle of the laminate had great influence on the damage distribution; thus, when the ply angle increases, the ballistic resistance and damage areas on both front and rear side of the laminate decrease. Again, the result shows that increasing the thickness of the laminate was advantageous to the ballistic resistance and damage characteristics of the composite laminates. The prediction of the model was proved to have good accuracy and efficiency.

An experimental and numerical study on scaling effects in the low velocity impact response of CFRP laminates

Scaling effects in the low velocity impact response of plain weave carbon-fibre-reinforced plastic (CFRP) panels have been investigated both experimentally and numerically. The experimental tests were undertaken using an instrumented drop-weight impact tower and the numerical simulations were conducted using the commercially-available finite element (FE) solver ABAQUS/Explicit. Here a rate-dependent damage model was implemented through the ABAQUS user-defined material interface, VUMAT, to describe the mechanical behaviour of the composite laminates. The experimental tests and numerical simulations both indicate that at energies above the damage threshold, damage does not obey a simple scaling law, becoming more severe as the scale size is increased. An examination of the damaged samples in the tests and numerical simulations indicated that, for a given scaled impact energy, fibre damage, in the form of large cracks extending in the warp and weft directions, was more severe in the larger samples. It is argued that the energy absorbed in fibre fracture scales with the square of the scale factor, i.e. n2, whereas the initial impact energy scales as n3. This discrepancy results in increased levels of energy needing to be absorbed in larger scale sizes, leading to greater levels of impact damage in the larger scale sizes.

A rate-dependent damage model for elastomers at large strain

The ability to predict rate and deformation dependent damage in elastomers is important for many applications. To model the rate dependent damage processes we introduce chain scission, predicted using concepts of mechanochemistry, into hyperelastic constitutive models (Arruda–Boyce as an example). The result is a model capable of handling large strain and rate dependent damage. Additionally, polydispersity is incorporated by considering a distribution of chain lengths, which gives the model the capability to predict progressive material damage. To demonstrate the application of the model, uniaxial tensile deformation with constant extension rates is examined. The tensile stress is found to first reach a peak and then decrease due to scission, and faster rates of deformation result in larger peak stress. Under cyclic loading the polydispersity results in progressive material damage which mirrors the Mullins effect at high deformation rates. In addition, the damage model predicts interesting rate-dependent behavior, such as significant hysteresis during unloading and reloading, as the loading rate is decreased. Finally, the model is shown to be capable of fitting experimental data for a variety of materials.

Experimental and numerical investigation of increased formability in combined quasi-static and high-speed forming processes

The formability of deep drawing can be extended by combining it with a subsequent high-speed forming method such as electromagnetic forming. However, up to now, no sufficient systematic understanding of the underlying principles or of a successful design of such coupled processes has been gained. Hence, in this work, a methodology for the analysis and design of such process chains is presented. This approach comprises a new method for the experimentally based determination of quasi-static and high-speed forming limits along close to proportional strain paths, a constitutive visco-plastic, anisotropic material model with a rate dependent ductile damage formulation, which allows for the accurate numerical prediction of forming limits for complicated forming operations under a largely varying strain rate, and finally the actual application of both to a combined quasi-static and high-speed forming operation. In doing so, material areas are identified that are deep drawn up to a degree immediately before necking occurs and then electromagnetically be formed beyond the quasi-static forming limit without damage. This proves that an extension of formability is here achieved due to a change in strain rate rather than in the strain path.

A Prony-series type viscoelastic solid coupled with a continuum damage law for polar ice modeling

Predicting the time-dependent behavior of polar ice is a significant challenge especially when damage effects are considered. In the present work, ice is modeled by a generalized Maxwell type viscoelastic solid and coupled to a continuum damage model. Viscoelastic behavior is obtained by a Prony-series expansion where the shear components of the deviatoric stress are time dependent while the volumetric part remains purely elastic. A semi-analytical integration scheme of the convolution integral allow for fast computation of stresses. Damage initiation and propagation is captured by a Murakami rate dependent damage law, where the state of damage is updated at each time step based on the current values of stress. The model is shown to be thermodynamically consistent.A rigorous gradient-based constrained optimization approach is employed to calibrate the model parameters against some published experimental data. Validation tests which include tensile creep, compressive creep and biaxial failure contours under compression are then carried out and good agreement is demonstrated. Furthermore, the model is implemented in a finite element code and is used to investigate surface crevasse propagation in grounded marine-terminating glaciers. The simulations, on idealized rectangular ice slabs in contact with the ocean, examine the depth and rate of damage propagation with increasing seawater depth near the terminus. The predictions and computational efficiency of the proposed model are highlighted when compared to another recently published ice model.

Finite element analysis of combined forming processes by means of rate dependent ductile damage modelling

Sheet metal forming is an inherent part of todays production industry. A major goal is to increase the forming limits of classical deep-drawing processes. One possibility to achieve that is to combine the conventional quasi-static (QS) forming process with electromagnetic high-speed (HS) post-forming. This work focuses on the finite element analysis of such combined forming processes to demonstrate the improvement which can be achieved. For this purpose, a cooperation of different institutions representing different work fields has been established. The material characterization is based on flow curves and forming limit curves for low and high strain rates obtained by novel testing devices. Further experimental investigations have been performed on the process chain of a cross shaped cup, referring to both purely quasi-static and quasi-static combined with electromagnetic forming. While efficient mathematical optimization algorithms support the new viscoplastic ductile damage modelling to find the optimum parameters based on the results of experimental material characterization, the full process chain is studied by means of an electro-magneto-mechanical finite element analysis. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine into the commercial finite element package LS-DYNA.

Stability and well-posedness of a rate-dependent damage model for brittle materials based on crack mechanics

This paper presents an investigation of the stability and well-posedness of a rate-dependent damage model for brittle materials. The model is based on the response of an ensemble of distributed microcracks under a general, three-dimensional state of stress. The stability and well-posedness of the model are studied by examining the behavior of dynamic perturbations to the steady-state solution of uniaxial-stress loading. It is shown that as a result of incorporating the strain-rate effect in the model, perturbations of all wave lengths remain bounded for finite times, making the problem well-posed. It is also shown that the corresponding rate-independent model is ill-posed in that perturbations grow unbounded with the wave number, even for finite times.

New strain energy-based thermo-elastoviscoplastic isotropic damage–self-healing model for bituminous composites—Part I: Formulations

New initial strain energy-based thermo-elastoviscoplastic isotropic damage–self-healing formulations for bituminous materials are developed and implemented for numerical predictions of experimental measurements. A class of elastoviscoplastic constitutive damage–self-healing model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation. An Arrhenius-type temperature term is uncoupled with Helmholtz free energy potential to account for the effect of temperature. In particular, the governing incremental damage and healing evolutions are coupled and characterized through the net stress concept in conjunction with the hypothesis of strain equivalence. The viscoplastic flow is introduced by means of an additive split of the stress tensor. The (undamaged) energy norm of strain tensor is redefined and employed as equivalent strain. A rate-dependent (viscous) damage model with a structure analogous to viscoplasticity of the Perzyna type is used for rate sensitivity of bituminous materials. In net space, Drucker–Prager yield function and Perzyna viscoplastic model are employed. Completely new computational algorithms are systematically developed in Part II of this sequel, based on the two-step operator splitting methodology. Comparisons with experimental results and numerical simulations are undertaken in Part II of this work.

Three‐dimensional cell model analysis of ductile damage under dynamic loading condition

AbstractThe paper deals with the damage and fracture behavior of ductile metals under dynamic loading conditions. The in [1–3] presented phenomenological continuum damage and fracture model, which takes into account the rate‐ and temperature‐dependence of the material, provides reasonable results of experiments with high strain rates while the identification of the corresponding material parameters results difficult from the available experimental data. This lack of information can be resolved by micro‐mechanical numerical simulations of void containing unit‐cells. In this context results of dynamic micro‐mechanical simulations are presented which can be used to study the damage effects on the micro‐scale and to validate the rate‐dependent continuum damage model. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Prediction of crack propagation and arrest in X100 natural gas transmission pipelines with a strain rate dependent damage model (SRDD). Part 2: Large scale pipe models with gas depressurisation

Part 1 of this paper described a specimen for the measurement of high strain rate flow and fracture properties of pipe material and for tuning a strain rate dependent damage model (SRDD). In part 2 the tuned SRDD model is used for the simulation of axial crack propagation and arrest in X100 natural gas pipelines. Linear pressure drop model was adopted behind the crack tip, and an exponential gas depressurisation model was used ahead of the crack tip. The model correctly predicted the crack initiation (burst) pressure, the crack speed and the crack arrest length. Strain rates between 1000 s−1 and 3000 s−1 immediately ahead of the crack tip are predicted, giving a strong indication that a strain rate material model is required for the structural integrity assessment of the natural gas pipelines. The models predict the stress triaxiality of about 0.65 for at least 1 m ahead of the crack tip, gradually dropping to 0.5 at distances of about 5–7 m ahead of the crack tip. Finally, the models predicted a linear drop in crack tip opening angle (CTOA) from about 11−12° at the onset of crack propagation down to 7−8° at crack arrest. Only the lower of these values agree with those reported in the literature for quasi-static measurements. This discrepancy might indicate substantial strain rate dependence in CTOA.

Rate-dependent damage model for polymeric composites under in-plane shear dynamic loading

The present study aims at rate-dependent damage modeling for polymeric composite materials with the rate-dependent constitutive model using a multi-scale approach. Phenomenologically, the nonlinear response of a composite under the in-plane shear loading condition is originated from the viscoplasticity of a matrix and the damage behavior of composite materials. In case of dynamic loading conditions, the strain-rate effects the change of the damage behavior of composite materials, as well as the behavior of the matrix. The enhanced micromechanical model which improves the in-plane shear behavior, is used for analyzing the rate-dependent behaviors of the fiber and matrix constituents. The rate-dependent elastic damage model based on orthotropic continuum damage mechanics theory at the macromechanical level is applied to improve the accuracy of the analysis model. Predictions by presented model are shown to agree fairly well with experimental results over a wide range of strain rates.