Strain-softening Materials Research Articles

Finite element simulation of an excavation-triggered landslide using large deformation theory

Numerical simulation of an excavation induced landslide in a strain softening material is presented and the results are compared with field measurements. The simulation is based on the methodology proposed to estimate the post-failure deformation of slopes in strain softening materials. The method includes: a) the Updated Lagrangian formulation which is essential in capturing the changing geometry and configuration of the slope during failure, b) a strain softening constitutive model which enables simulation of the progressive failure mechanisms, c) a stable solution scheme to prevent problems associated with numerical convergence in strain softening materials, and d) the h-adaptive mesh refinement technique to prevent excessive distortion of the finite element mesh due to large deformation and to increase the accuracy of the numerical solution.For the slope considered here, it is shown that failure initiated due to the excavation at the toe of the slope and propagated upward due to the strain softening behavior of the geomaterials which eventually led to the progressive failure of this slope. The failure surface is mainly within a thin layer of soil with substantial strain softening behavior but propagates to the surrounding soil as the excavation proceeds. The predicted crest settlement, toe movement, and deformed shape of the slope are lower than the observed behavior of the slope. However, the numerical analysis clearly predicts the triggering factor and the failure mechanism of the landslide and the impact of the large deformation of the soil mass on the houses at the toe of the slope.

Precast Fiber-Reinforced Concrete Barriers with Integrated Sidewalk

Three concepts of bridge barriers with integrated sidewalk were designed, built, and tested. Two precast barriers were designed with high-performance fiber-reinforced concrete (HPFRC)—the former with a tensile strain-softening material and the latter with a tensile strain-hardening material. Use of HPFRC allowed a significant reduction of concrete sections and reinforcement of precast barriers. Moreover, a new connection method was developed to anchor barriers to the bridge slab. One high-performance concrete (HPC) cast-in-place barrier was also designed as a reference. All barriers were submitted to quasi-static transverse loading up to failure and exceeded CSA PL2 and AASHTO TL4 design load requirements. Finite element models used at the design process provided an accurate reproduction of test results in terms of stiffness, ultimate strength, cracking pattern, and displacement. A numerical parametric study was conducted with the validated models to evaluate the effect of key economical and construction characteristics of the precast barriers.

Implicit Gradient Delocalization Method for Force-Based Frame Element

AbstractIn this study, a novel force-based frame element with delocalization is developed to address localization issues induced by material strain softening. A regularization procedure for section deformations is introduced on the basis of the concept of deformation gradient dependency. The internal length scale of the gradient-based regularization model is discussed and related to the plastic hinge length of the structural members. The weak form of the governing equation is derived, and a subscale numerical strategy is utilized within each element to implement the proposed model in the frame element. In addition, an adaptive scheme is developed for the RC members to determine the real-time gradient coefficient. Finally, two numerical examples are utilized and the results show that the proposed model can achieve an objective response for and excellent prediction of the nonlinear behavior of RC members.

DEM analyses of the whole failure process of shallow foundation in plate load test on dense sand

Shallow foundations are widely used in civil engineering practice, but the instability mechanism is still unclear yet. Previously, the Finite Element Method (FEM) was commonly used to analyze the failure process of shallow foundations, but it meets difficulty in properly simulating the whole failure process of shallow foundation on the strain-softening material. Hence, the Discrete Element Method (DEM) is employed in this paper to study the instability mechanism of the shallow foundation via numerical plate load test with focus on the microscopic features evolution during vertical loading. In the simulation, an amplified gravity was applied to a dense granular ground to reproduce a gravity stress state at a large scale. Then, a plate was put on the granular ground to simulate the plate load test. Deformation pattern, particle velocity and distribution of void ratio in the ground were examined to illustrate the microscopic features in the whole failure process of the granular ground. The results show that: 1) There are a marked peak value and a settlement softening branch in the stress-settlement relationship. 2) The grids close to the edge of the plate are peculiarly extended and twisted. 3) Four particle motion patterns were observed in the velocity fields and the percentage of each motion pattern changes during loading. 4) The void ratio field varies during loading, and the distinguishing interface tends to be similar to Terzaghi's shear failure surface.

Finite element implementation of the Hoek–Brown material model with general strain softening behavior

A numerical implementation of the Hoek–Brown criterion is presented, which is capable of modeling different post-failure behaviors observed in jointed rock mass. This is done by making the material parameters a function of the accumulated plastic strain. The implementation is for use in finite element calculations, and is based on the return mapping framework. The updated stress state together with the consistent constitutive matrix is found in principal stress space based on the principles of boundary planes. The implementation is verified through the simulation of a tunnel excavation for perfectly-plastic, brittle and strain softening material behavior and the results are compared with known solutions.

A microstructurally-based internal length for strain localization problems in dynamics

Classical finite element method including strain-softening materials suffers from a mesh-dependency solution. The thickness of the bands in which strains are localized is arbitrarily narrow and may lead to a rupture without energy consumption. This is the case in quasi-static as well as in dynamics problems. The present paper uses a two-scale dynamic damage law that is based on an intrinsic length at micro-scale, corresponding to the inter-distance between two adjacent micro-cracks, that regularizes the strain localization problem in dynamics. The material response is time-dependent due to the inertial effect of the micro-crack propagation. This produces a natural, microstructurally-based, delayed response of the material that, in turn, removes the mesh-sensitivity in dynamics. As a consequence, the size of the strain localization band is controlled by the internal length of the material.

Nano-mechanical behaviour of lithium metasilicate glass–ceramic

This paper reports the first study on the mechanical behavior of lithium metasilicate glass–ceramic using nanoindentation and in situ scanning probe imaging techniques. Indentation contact hardness, Hc, and Young’s modulus, E, were measured at 10mN peak load and 0.1–2mN/s loading rates to understand the loading rate effect on its properties. Indentation imprints were analysed with the in situ scanning probe imaging to understand indentation mechanisms. The average contact hardness increased by 112% with the loading rate (ANOVA, p<0.05) while the Young’s modulus showed the loading rate independence (ANOVA, p>0.05). A strain rate sensitivity model was applied to determine the intrinsic contact hardness. Extensive discontinuities and largest maximum, contact and final depths were also observed at the lowest loading rate. These phenomena corresponded to inhomogeneous shear-band flow and densification leading to the material strain softening. The in situ scanning probe images of indentation imprints showed plastic deformation at all loading rates and shear band-induced pileups at the lowest loading rate. With the increase in loading rate, the induced pile-ups decreased. The continuum model predicted the largest densified shear zone at the lowest loading rate. Finally, these results provide scientific insights into the abrasive machining responses of lithium metasilicate glass–ceramic during dental CAD/CAM processes using sharp diamond abrasives.

The Rate Dependent Tensile Response of Polycarbonate and Poly-methylmethacrylate

The tensile mechanical response of polycarbonate and polymethyl-methacrylate is investigated across a range of strain rates from 0.001 to 1600 s−1. Traditional standard ASTM tensile experiments are limited to low strain rates and do not give quantitative data for plastic behavior for strain softening materials. In this study, a novel specimen and gripping geometry is designed and verified to mitigate wave reflections present in previous high strain rate tensile experiments. Digital image correlation is used to extract local deformation measurements, and a Kolsky bar technique typically used for fiber experiments is adapted for soft polymers. The insights gathered in this study will provide a further step toward a high fidelity material model for both ductile and brittle polymers.

A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model

The failure of carbon fiber reinforced epoxy laminates is studied using an anisotropic gradient-enhanced continuum damage model embedded in a mean-field homogenization scheme.In each ply, a homogenized material law is used to capture the intra-laminar failure. The anisotropy of the homogenized material model results from the homogenization method and from the reformulation of the non-local continuum damage theory to account for the material anisotropy. As a result the damage propagation direction in each ply is predicted with accuracy as compared to the experimental results, while the problems of losing uniqueness and strain localization, which occur in classical finite element simulations when strain softening of materials is involved, can be avoided.To model the delamination process, the hybrid discontinuous Galerkin/extrinsic cohesive law method is introduced at the ply interfaces. This hybrid method avoids the need to propagate topological changes in the mesh with the propagation of the delamination while it preserves the consistency and stability in the un-cracked interfaces.As a demonstration, open-hole coupons with different stacking sequences are studied numerically and experimentally. Both the intra- and inter-laminar failure patterns are shown to be well captured by the computational framework.

H-Adaptive Updated Lagrangian Approach for Large-Deformation Analysis of Slope Failure

AbstractThis paper presents a novel approach to improving our understanding of complicated slope failure mechanisms that can occur in strain-softening material as well as to evaluating the accompanying postfailure deformation of slopes. Three cutting-edge technologies were integrated into one numerical analysis tool: (1) a large-deformation analysis using the updated Lagrangian formulation, (2) a stable numerical algorithm for the solution of progressive failure in strain-softening materials, and (3) an h-adaptive mesh refinement algorithm. The significance of this study is mainly in the adoption of a proper numerical discretization for cases of slope failure in which large deformations lead to distortion of the finite-element mesh, unreliable results, and lack of convergence. The h-adaptive remeshing technique is used to refine the finite-element mesh around the area of large shear strain, thereby improving the accuracy and convergence of numerical solutions. This study presents a method that can be used...

Ground reaction curves for circular excavations in non-homogeneous, axisymmetric strain-softening rock masses

Fast methods to solve the unloading problem of a cylindrical cavity or tunnel excavated in elasto-perfectly plastic, elasto-brittle or strain-softening materials under a hydrostatic stress field can be derived based on the self-similarity of the solution. As a consequence, they only apply when the rock mass is homogeneous and so exclude many cases of practical interest. We describe a robust and fast numerical technique that solves the tunnel unloading problem and estimates the ground reaction curve for a cylindrical cavity excavated in a rock mass with properties depending on the radial coordinate, where the solution is no longer self-similar. The solution is based on a continuation-like approach (associated with the unloading and with the incremental formulation of the elasto-plastic behavior), finite element spatial discretization and a combination of explicit sub-stepping schemes and implicit techniques to integrate the constitutive law, so as to tackle the difficulties associated with both strong strain-softening and elasto-brittle behaviors. The developed algorithm is used for two practical ground reaction curve computation applications. The first application refers to a tunnel surrounded by an aureole of material damaged by blasting and the second to a tunnel surrounded by a ring-like zone of reinforced (rock-bolted) material.

An implicit-gradient-enhanced incremental-secant mean-field homogenization scheme for elasto-plastic composites with damage

This paper presents an incremental-secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the proposed method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme. When strain softening of materials is involved, classical finite element formulations lose solution uniqueness and face the strain localization problem. To avoid this issue the model is formulated in a so-called implicit gradient-enhanced approach, with a view toward macro-scale simulations. The method is then used to predict the behavior of composites whose matrix phases exhibit strain softening, and is shown to be accurate compared to unit cell simulations and experimental results. Then the convergence of the method upon strain softening, with respect to the mesh size, is demonstrated on a notched composite ply. Finally, applications consisting in a stacking plate, successively without and with a hole, are given as illustrations of the possibility of the method to be used in a multiscale framework.

Evaluation of varying ductile fracture criterion for 7075 aluminum alloy

As one of the principal failures, ductile fracturing restricts metal forming process. Cockcroft-Latham type fracture criterion is suited for ductile fracture in bulk metal-forming simulation. Finding a way to evaluate the ductile fracture criterion (DFC) and identify the relationship between DFC and deformation conditions for a strain-softening material, 7075 aluminum alloy; however, it is a non-trivial issue that still needs to be addressed in a greater depth. An innovative approach is brought forth that the compression tests and numerical simulations provide mutual support to evaluate the ductile damage cumulating process and determine the DFC diagram. One of the results shows that for a fixed temperature, the maximum cumulated damage decreases regularly with increasing strain rate. The most important result shows that DFC of 7075 aluminum alloy at temperatures of 573–723 K and strain rates of 0.01-10 s−1 is not a constant but a change in a range of 0.255-0.453, thus it has been defined with varying ductile fracture criterion (VDFC) and characterized by a function of strain rate and temperature. According to VDFC diagram, the exact fracture moment and position during various forming processes will be predicted conveniently, in addition to which, the deformation domains with lower fracture risk corresponding to higher VDFC can be identified.

The Evaluation of Varying Ductile Fracture Criteria for 3Cr20Ni10W2 Austenitic Heat-Resistant Alloy

Most bulk metal forming processes may be limited by ductile fracture, such as an internal or surface fracture developing in the workpiece. Finding a way to evaluate the ductile fracture criteria (DFC) and identify the relationships between damage evolution and strain-softening behavior of 3Cr20Ni10W2 heat-resistant alloy is very important, which, however, is a nontrivial issue that still needs to be addressed in greater depth. Based on cumulative damage theory, an innovative approach involving heat physical compression experiments, numerical simulations, and mathematical computations provides mutual support to evaluate ductile damage cumulating process and DFC diagram along with deformation conditions. It is concluded that, as for strain-softening material, ductile damage starts at work hardening phase, and the damage cumulation is more sensitive in work hardening phase than in work softening phase. In addition, DFC of 3Cr20Ni10W2 heat-resistant alloy in a wide temperature range of 1203∼1403 K and the strain rate of 0.01∼10 s−1 are not constant but change in a range of 0.099∼0.197; thus they have been defined as varying ductile fracture criteria (VDFC) and characterized by a function of strain rate and temperature. According to VDFC diagram, the exact fracture moment and position during various forming processes will be predicted conveniently.

A large deformation analysis for the assessment of failure induced deformations of slopes in strain softening materials

This paper presents a numerical method that can be used to evaluate the post-failure deformation of slopes and embankments. The method is based on a large deformation finite element analysis employing the updated Lagrangian formulation. It can simulate the changing geometry of slopes during failure. An extended Mohr–Coulomb constitutive model represents the strain softening behaviour of slope material. The results of a series of analyses show that the post-failure deformation of slopes is a function of the rate of strength reduction and also the stiffness of the slope material. These two factors influence the initiation of progressive failure of slopes. The validity of the method is evaluated by simulation of a test embankment failure and comparison of the predicted results with the observed record of the failure.

An internal state variable material model for predicting the time, thermomechanical, and stress state dependence of amorphous glassy polymers under large deformation

This paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress state dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation (Bouvard et al., 2010), developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by Coleman and Gurtin (1967) in which physically-based internal state variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for (i) the material strain softening induced by the polymer chain slippage; (ii) the material strain hardening at large strains induced by chain stretching between entanglement points; (iii) the time, temperature, and stress state dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress states. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions.

Damage regularisation with inertia gradients

Abstract A gradient enhanced model is formulated which simulates micro-structurally induced wave dispersion and is capable of achieving mesh objective results when modelling strain-softening materials. Length scale parameters are introduced to incorporate both micro-inertial effects and strain smoothing. The model is formulated such that all the gradient enhancement terms are contained within the kinetic energy functional, whilst all non-linear terms are linked to the strain energy functional. In addition, discretisation of the governing equations is performed in a manner such that only C 0 -continuity is required and is symmetric in the elastic range. Dispersion analysis is performed to show the correct format that a constitutive model must conform to in order that regularisation of strain-softening material models will occur. This dispersion analysis is then used to explore how the two length scales may influence the width of the zone in which strain localisation takes place. The efficacy of the model in simulating strain-softening behaviour in a mesh objective manner and the effects of wave dispersion on damage initiation and accumulation are demonstrated in numerical examples.

Simulating damage and delamination in fibre metal laminate joints using a three-dimensional damage model with cohesive elements and damage regularisation

This paper investigates the capability of a three-dimensional finite element model with damaging material behaviour, cohesive elements and damage regularisation to simulate complex damage patterns in fibre metal laminate (FML) joints. The model incorporates a three-dimensional continuum damage mechanics approach for the composite plies, a plasticity model for the aluminium layers, and a delamination model between layers. A nonlocal averaging scheme is implemented to mitigate the mesh sensitivity that occurs with strain-softening material models. Bearing stress–strain responses and variations in stiffness are calculated, and damage progression is described in detail for all plies and interfaces. Microscopy and stress–strain data from a parallel series of experimental tests are presented, and damage and failure phenomena observed in the tests are compared with the model. Generally, good agreement between model and tests was achieved but certain limitations of the numerical model were observed and are discussed. The combined numerical and experimental information provide a detailed understanding of the failure sequence of FML joints.

Ultimate bearing capacity of concrete dam involved in geometric and material nonlinearity

To get the actual ultimate bearing capacity of concrete dam, the effect of geometric nonlinearity and strain softening on it, which appears in the failure process of concrete dam, is studied. Overload method is adopted to obtain the bearing capacity of a concrete dam by taking into consideration strain softening in the material constitutive law, geometric nonlinearity in geometric equation and equilibrium differential equation. Arc-length method is used to find the extreme point and descending branch of the load-displacement curve of the dam. The results present that the effect cannot be ignored. And geometric nonlinearity of structure and strain softening of materials should be considered for numerical analysis of ultimate bearing capacity of a concrete dam.

Predicting the effects of geometry on the behaviour of fibre metal laminate joints

Abstract The effects of geometry on the bearing response of fibre metal laminate (FML) joints are numerically investigated. Specimens designed to fail in bearing, net-tension and shear-out are analysed using a continuum damage mechanics approach. Plasticity in the aluminium layers, fibre and matrix damage in the composite plies and, importantly, delamination between the plies of the laminate are accounted for. The effects of mesh sensitivity, associated with strain-softening material models, are mitigated using a nonlocal averaging scheme. Results are compared to experimental bearing stress–strain and bearing stiffness–strain responses, and surface strain measurements. Variations in the development of damage for the different joints are investigated, and the effect of damage on the joint responses is discussed. Very good agreement was achieved for the specimens of interest, without varying the model parameters for the different joint configurations, which highlighted the suitability of the model for FML structural analysis. The combined numerical and experimental information provide an in-depth understanding of the failure sequences of FML joints.