Elasto-plastic Constitutive Law Research Articles

An improved two phases-two points SPH model for submerged landslide

This research proposes an improved two phases-two points SPH model designed to simulate interactions between water and soil, particularly suitable for scenarios such as submerged landslides. This model treats water as a weakly compressible Newtonian fluid and soil as a cohesive-frictional material following an elastoplastic constitutive law, utilizing two layers of SPH particles to separately represent these two phases. An adaptive drag force formula is proposed that automatically switches between linear and nonlinear seepage modes based on the motion state of the porewater. Additionally, to improve the precision and stability of the model, a modified solid boundary condition and a method for calculating soil volume fraction are proposed, along with an SPH discretization formula that incorporates the effects of the volume fraction in a more effective way. The reliability of the improved two phases-two points SPH model is initially verified through two cases: a dry granular landslide and a submerged soil mass subjected to gravitational loading. Then, the effectiveness of the proposed improvement methods is further tested and validated through three submerged landslide cases with different grain diameters, demonstrating the applicability of the current model in simulating submerged landslides and its superiority in accuracy and stability compared to previous models.

Homogenized finite element simulations can predict the primary stability of dental implants in human jawbone

Adequate primary stability is a pre-requisite for the osseointegration and long-term success of dental implants. Primary stability depends essentially on the bone mechanical integrity at the implantation site. Clinically, a qualitative evaluation can be made on medical images, but finite element (FE) simulations can assess the primary stability of a bone-implant construct quantitatively based on high-resolution CT images. However, FE models lack experimental validation on clinically relevant bone anatomy. The aim of this study is to validate such an FE model on human jawbones. Forty-seven bone biopsies were extracted from human cadaveric jawbones. Dental implants of two sizes (Ø3.5 mm and Ø4.0 mm) were inserted and the constructs were subjected to a quasi-static bending-compression loading protocol. Those mechanical tests were replicated with sample-specific non-linear homogenized FE models. Bone was modeled with an elastoplastic constitutive law that included damage. Density-based material properties were mapped based on μCT images of the bone samples. The experimental ultimate load was better predicted by FE (R2 = 0.83) than by peri-implant bone density (R2 = 0.54). Unlike bone density, the simulations were also able to capture the effect of implant diameter. The primary stability of a dental implant in human jawbones can be predicted quantitatively with FE simulations. This method may be used for improving the design and insertion protocols of dental implants.

Direct validation of 3D meso-scale fracture modelling of UHPFRC by in-situ micro X-ray CT wedge-split tests and parametric studies

3D meso-scale finite element models of ultra high performance fibre reinforced concrete (UHPFRC) based on in-situ micro X-ray Computed Tomography (CT) images are developed and validated in this study. The CT images at 16.9 μm voxel resolution from a progressive wedge-split test were converted into meso-scale 3D tetrahedron meshes. The short fibres, embedded in the mortar matrix, were modelled by truss elements with equivalent elastoplastic constitutive laws transformed from single fibre pullout load–displacement curves, so as to indirectly model the fibre–matrix interfaces. A concrete damage plasticity model was used to simulate damage and fracture in the mortar. The simulated load–displacement curves, final crack patterns, and load-crack opening curves were found in good agreement with the in-situ CT test results, and the non-vertical crack path was significantly affected by the overall orientation of fibres bridging the crack. Further simulations with all the fibres perpendicular to the tensile splitting direction showed that the peak load and fracture energy increased by 42 % and 45 % respectively from 1 % to 3 % fibre volume fraction. This indicates the need to optimize the fibre orientation for best mechanical performance according to the loading conditions.

A Constitutive Law Modeling the Mixed Hardening Behavior of Particle-Reinforced Composites

Abstract A homogenized elasto-plastic constitutive law (including both constitutive equations and inversed constitutive equations) is proposed in an incremental form for the particle-reinforced composites based on the flow theory of plasticity and the asymptotic homogenization method. The constitutive law can be used to predict the mixed hardening behavior of particle-reinforced composites under arbitrary loading conditions if the uniaxial tension test curve of matrix materials is known. It is found that the constitutive law of particle-reinforced composites is similar in form to the law of matrix materials. There is a simple proportional relationship between the yield stress, the plastic modulus, and the deviatoric back stress of particle-reinforced composites and the corresponding parameters of matrix materials, which is equal to the ratio of the shear modulus of composites to the shear modulus of matrix materials. The tangent modulus of particle-reinforced composites can be calculated using a simple arithmetic formula according to the tangent modulus of matrix materials. A numerical algorithm is suggested.

Multiple nonlinearities in the process of embedding and pulling out of nails: A numerical approach

This paper presents a numerical approach to analyze the embedding and withdrawal process of nails. Multiple nonlinearities are considered: law of orthotropic large strain elasto-plastic materials and contact with friction. The Uzawa algorithm based on the bi-potential method is used to describe the nonlinearity of boundary conditions. A return mapping algorithm is applied to deal with the elasto-plastic constitutive laws. On the basis of the Updated Lagrangian formulation, we adopt a Rotationally Neutralized Objective hypothesis to describe the geometrically nonlinear behavior. The Newton–Raphson iterative method is employed to solve the nonlinear equation. The simulation results show the deformation and the stress distribution of wood in the process of the nail embedding and withdrawal. The effectiveness and accuracy of the numerical scheme are proved by comparing with the existing engineering experiments. The influence of friction coefficients on the nail embedding and withdrawal strength is also explored.

Thermodynamically consistent concurrent material and structure optimization of elastoplastic multiphase hierarchical systems.

The concept of concurrent material and structure optimization aims at alleviating the computational discovery of optimum microstructure configurations in multiphase hierarchical systems, whose macroscale behavior is governed by their microstructure composition that can evolve over multiple length scales from a few micrometers to centimeters. It is based on the split of the multiscale optimization problem into two nested sub-problems, one at the macroscale (structure) and the other at the microscales (material). In this paper, we establish a novel formulation of concurrent material and structure optimization for multiphase hierarchical systems with elastoplastic constituents at the material scales. Exploiting the thermomechanical foundations of elastoplasticity, we reformulate the material optimization problem based on the maximum plastic dissipation principle such that it assumes the format of an elastoplastic constitutive law and can be efficiently solved via modified return mapping algorithms. We integrate continuum micromechanics based estimates of the stiffness and the yield criterion into the formulation, which opens the door to a computationally feasible treatment of the material optimization problem. To demonstrate the accuracy and robustness of our framework, we define new benchmark tests with several material scales that, for the first time, become computationally feasible. We argue that our formulation naturally extends to multiscale optimization under further path-dependent effects such as viscoplasticity or multiscale fracture and damage.

Non-iterative stress projection method for anisotropic hardening

In this paper, a fully explicit non-iterative stress projection method for the instant stress integration of advanced plasticity models that account for the history-dependent deformation is proposed. In this non-iterative stress projection method, the stress increment is directly determined based on the elastoplastic constitutive law. Generalized formulations of the elastoplastic tangent moduli for anisotropic hardening models are discussed considering the morphological yield surface changes in the context. Precise integrations of the stress tensor, effective plastic strain, and other state variables are accomplished for kinematic- and distortional hardening models. The implemented plasticity hardening models are validated through a series of non-proportional loadings and a sheet metal forming simulation to check the fidelity, numerical robustness, and computational efficiency of the suggested non-iterative stress projection method. Consequently, the computation cost for a large-scale metal forming simulation is reduced up to 50%.

Dynamics of creeping landslides controlled by inelastic hydro-mechanical couplings

Slow-moving landslides affect proximal infrastructures and communities, often causing extensive economic loss. While many of these landslides exhibit slow and episodic sliding for decades or more, they sometimes accelerate rapidly and fail catastrophically. Although it is known that the landslide dynamics are controlled by hydro-mechanical processes, few analytical models enable a versatile incorporation of the inelastic behavior of the shear zone materials, thus hindering an accurate quantification of how their properties modulate the magnitude and rate of coupled fluid flow and landslide motion. To address this problem, we develop a simulation framework incorporating rainfall-induced, deformation-mediated pore-water pressure transients at the base of active landslides. The framework involves the computation of two sequential diffusion processes, one within an upper rigid-porous landslide block, and another within the inelastic shear zone. Although the framework can be linked to any elastoplastic constitutive laws, here we model landslide motion through an elastic-perfectly plastic frictional model, which enables us to account for standard properties of earthen materials such as elastic moduli, friction angle, dilation angle, and hydraulic conductivity. Numerical case studies relevant to slow-moving landslides in the California Coast Ranges show that the proposed formulation captures different temporal patterns of movement induced by precipitation. In each of the case, we achieved a relatively accurate match between data and simulations by incorporating positive dilation coefficients, which leads to spontaneous generation of negative excess pore-water pressure and self-regulating motion. Conversely, simulations with no dilation (hence, reflecting the approach of critical state) produce sharp acceleration, typical of catastrophic runaway acceleration. Our findings encourage the use of the proposed framework in conjunction with constitutive laws tailored to site-specific geomaterial properties and data availability, thus favoring a versatile representation of the variety of creeping landslide trends observed in nature.

Local buckling on large sandwich panels applied to light aviation: Experimental and computation dialogue

Wrinkling is a local buckling phenomenon in sandwich structures subjected to compression and shear loading that is challenging for the aircraft design engineer. Numerous wrinkling models are proposed in the literature but historical formulas developed after the Second World War are still widely used by the industry with important knock down factors. Theory-experiment correlation should be the final step in validating and evaluating the models. This article presents an experimental-computational dialogue on structural tests on large sandwich panels of dimensions 558 × 536 mm2 representative of the design used in light aviation. The panels were subjected to compressive and shear loading by using the VERTEX test bench and wrinkling failures were observed. Comparisons are first made with linear wrinkling models. Despite correlations are quite encouraging, the imperfection-sensitivity of the experimentally observed wrinkling failure questions the pertinence of a linear bifurcation approach. A nonlinear Finite Element Model (FEM) of the sandwich panels is then developed. Initial imperfections measured by Stereo Digital Image Correlation (SDIC) are directly introduced in the mesh and an elastoplastic constitutive law for the core is implemented. Dynamic explicit computation is used to access the highly nonlinear behaviour and matches the test observations very well. The nonlinear FEM provides an improved, conservative prediction of wrinkling loads over the linear models.

Patient-specific finite element simulation of peripheral artery percutaneous transluminal angioplasty to evaluate the procedure outcome without stent implantation.

The purpose of this work is to present a patient-specific (PS) modeling approach for simulating percutaneous transluminal angioplasty (PTA) endovascular treatment and assessing the balloon sizing influence on short-term outcomes in peripheral arteries, i.e. without stent implantation. Two 3D PS stenosed femoral artery models, one with a dominant calcified atherosclerosis while the other with a lipidic plaque, were generated from pre-operative computed tomography angiography images. Elastoplastic constitutive laws were implemented within the plaque and artery models. Implicit finite element method (FEM) was used to simulate the balloon inflation and deflation for different sizings. Besides vessel strains, results were mainly evaluated in terms of the elastic recoil ratio (ERR) and lumen gain ratio (LGR) attained immediately after PTA. Higher LGR values were shown within the stenosed region of the lipidic patient. Simulated results also showed a direct and quantified correlation between balloon sizing and LGR and ERR for both patients after PTA, with a more significant influence on the lumen gain. The max principal strain values in the outer arterial wall increased at higher balloon sizes during inflation as well, with higher rates of increase when the plaque was calcified. Results show that our model could serve in finding a compromise for each stenosis type: maximizing the achieved lumen gain after PTA, but at the same time without damaging the arterial tissue. The proposed methodology can serve as a step toward a clinical decision support system to improve angioplasty balloon sizing selection prior to the surgery.

Mechanical properties of 3D printed polylactic acid elements: Experimental and numerical insights

The mechanical behaviour of polylactic acid (PLA) samples printed via material extrusion is experimentally and numerically addressed. An experimental program comprising tensile and three-point bending tests is carried out. Some filament printing orientations and different values of flow rate percentage are considered and their influence on the mechanical performance is investigated. From a numerical point of view, a new two-level model for the multiscale analysis is considered. The macroscopic structural behaviour of the 3D printed component is described with a laminate finite element model based on the first-order shear deformation theory. Each layer of the laminate is described with an elasto-plastic constitutive law and the geometrical and mechanical properties are derived from the experimental results. The micromechanical analysis is conducted only when inelastic strain occurs performing a non-linear analytical homogenization technique based on the Transformation Field Analysis. The obtained numerical results are compared with the experimental results highlighting the effectiveness of the proposed modelling approach.

Comparison of the effects of traditional and innovative tie-rods in reducing the seismic vulnerability of church façades: the case of San Francesco in Mirandola (Italy)

This contribution discusses the effect of steel tie-rods installed in a church façade subjected to 60 recorded earthquakes. The church façade is firstly analysed as a two-sided and a one-sided rocking SDOF system. For the one-sided rocking, sidewalls are modelled through either elastic or rigid contact to compare the two modelling techniques. Secondly, two configurations of tie-rods are investigated: (i) traditional tie-rods with a specific elasto-plastic constitutive law and (ii) innovative tie-rods with a dissipative component. The chosen case study is the San Francesco Church located in Mirandola, hit by the 2012 Emilia Romagna earthquake. The results of nonlinear dynamic analyses are presented in terms of median and standard deviation of maximum normalised displacements for each of the 60 seismic inputs. The results show the great benefit introduced by both traditional and dissipative tie-rods, with remarkable reductions of maximum rotations up to an order of magnitude with respect to the unrestrained façade. Moreover, the increment of damping coefficient is associated to a reduction of the standard deviation of the amplitude peaks, which is a positive aspect for the reliability of the response of the damped wall. Finally, the two models, rigid and elastic contact, of sidewalls provide results in excellent agreement in terms of median and standard deviation of the maximum normalised rotations.

A voxels-based Rayleigh-Ritz method for the post-buckling elasto-plastic analysis of restrained steel columns in fire

The paper presents a novel numerical strategy to analyse steel columns in fire, based on the concept of voxel. The material obeys to an elasto-plastic constitutive law that degrades with temperature. The member's internal strain energy is computed through an original methodology: the column is considered to be a grid of small and perfectly packed parallelepipeds, denominated as voxels. Any quantity is constant along any voxel and equal to its value at the voxel's geometric centre. The coordinates of each voxel's geometric centre are inferred by the voxel's ordering in the global grid, and its constitutive law depends solely on the strains and on the temperature at the voxel's geometrical centre, and is independent of the neighbouring voxels. The total internal strain energy is given by the sum of all internal energies along the grid and depends solely on the temperature and of the degrees of freedom. The strategy is able to deal with complex behaviours, such as snap-back and spread of plasticity, and requires a smaller number of degrees of freedom to a given accuracy, when compared to alternative methodologies. It enables new and transformative insights on the behaviour of columns in fire and can be incorporated in other methodologies.

Multiscale bridging method to characterize elasto-plastic properties of polymer nanocomposites

A multiscale bridging method is proposed to describe the elasto-plastic behavior of polymer nanocomposites affected with the interphase elasto-plastic constitutive law (near the nanoparticle). The inverse characterization method of the interphase elasto–plastic constitutive law was proposed by combining full atomistic molecular dynamics and finite element homogenization. Based on the proposed multiscale bridging method, the influences of the crosslink ratio of the epoxy network and radius of nanoparticles on the elasto-plastic behavior of the interphase were investigated. Additionally, a multiscale homogenization analysis of the representative volume element of the multi-particulate systems was conducted using the elasto–plastic constitutive law of interphase.

Non-iterative stress integration method for anisotropic materials

A non-iterative stress update method is proposed to accelerate finite element simulations while retaining the numerical robustness and accuracy in rate-independent plasticity. The stress tensor is directly integrated on the basis of the elastoplastic constitutive law without a recursive root-finding process such as the Newton-Raphson method. The iterative return mapping process for stress integration is avoided by first introducing an equation that guarantees the positive-definite nature of the effective plastic strain increment. Furthermore, the uncertainty of the yield condition fulfillment in a non-iterative stress update method is completely resolved by employing a stress projection technique. The numerical robustness, accuracy, and computational efficiency are comprehensively assessed through a wide range of strain increments in both implicit and explicit finite element analyses. Consequently, the computation time is remarkably reduced by more or less 50% with high fidelity in a variety of finite element simulation examples.

The influence of microstructure on the tensile properties of a creped tissue paper: Modeling and experiments

Low density tissue papers are soft fiber networks with a folded internal microstructure—deliberately imparted during a widely used manufacturing process, called dry creping. The folded crepe structure enhances a tissue paper’s specific volume, stretchability, and softness. The influence of the micron-scale crepe structure on nonlinear tensile response is studied using experiments and a discrete elasto-plastic model (DEM). First, ‘Crepe Index (CI)’ is defined to quantify the crepe structure. An optical method to obtain high resolution edge images is developed to measure the CI. The relationship between the CI and tensile failure strain and initial elastic stiffness is assessed: the failure strain is observed to be proportional to CI, while the dependence of initial stiffness on CI is unclear–presumably due to the damage induced through the de-densification of fiber layers during the manufacturing. The effect of CI on initial stiffness and failure strain is assessed using DEM by idealizing the creped paper as a segmented triangular wave—each segment governed by a bilinear elastoplastic constitutive law and a strength-based failure criterion. The model reveals that the initial stiffness of a creped sheet depends not only on the CI but also on sheet-thickness to crepe-wavelength ratio, and the stiffness of the uncreped sheet. The failure strain is found to be stretching dominated at low CI, and bending dominated at higher CI. Qualitative agreement is found between the DEM and experiments. The significance of both the material and the geometric non-linearity on the macroscale tensile response of a creped tissue paper emerges from this study.

A unified general framework for small and finite strain two-invariants elastoplasticity

PurposeThis paper proposes a unified original general framework, designed to theoretically develop and to extremely easily implement elastoplastic constitutive laws defined in the so called two-invariants space, both in small and finite strain regime.Design/methodology/approachA general return mapping algorithm is proposed, and particularly a standard procedure is developed to compute the two algorithmic tangent operators, required to solve the Newton–Raphson scheme at the local and global level and thus cast the elastoplastic algorithm within a FEM code.FindingsThis work demonstrates that the proposed procedure is fully general and can be applied whatever is the elastic law, the yield surface, the plastic potential function and the hardening law. Several numerical examples are reported, not only to demonstrate the accuracy and robustness of the algorithm, but also explain how to use this general algorithm also in other applications.Originality/valueThe proposed algorithm and its numerical implementation into a FEM code is new and original. The usefulness and the value of the algorithm is twofold: (1) it can be implemented in a small and finite strain simulation FEM code, in order to handle different types of constitutive laws in the same modular way, thus fully leveraging on modern object-oriented coding approach; (2) it can be used as a framework to develop (and then to implement) new constitutive models, since the researcher can simply define the relevant functions (and its main derivatives) and automatically get the numerical algorithm.

Experimental study of compaction localization in carbonate rock and constitutive modeling of mechanical anisotropy

AbstractSedimentary rocks are inherently anisotropic and prone to strain localization. While the influence of rock anisotropy on the brittle/dilative regime has been studied extensively, its influence on the ductile/compactive regime is much less explored. This paper discusses the anisotropic behavior of a high‐porosity carbonate rock from central Europe (the Maastricht Tuffeau). A set of triaxial tests with concurrent x‐ray tomography has been performed at different confining pressures. The anisotropic characteristics of this rock have been investigated by testing samples cored at different inclinations of the bedding, thus revealing non‐negligible effects of the coring direction on yielding and compaction behavior. Specifically, samples cored perpendicular to bedding display higher strength and longer stages of post‐yielding deformation before manifesting re‐hardening. Despite such alterations of the inelastic response, Digital Image Correlation has revealed that the strain localization mode is independent of the coring direction, thus being primarily affected by the confinement level. To capture the observed interaction between material anisotropy and compaction behavior at the continuum‐scale, an elastoplastic constitutive law has been proposed. For this purpose, a set of tensorial bases has been introduced to replicate how the oriented rock fabric modulates the yielding and plastic flow characteristics of the material. The analyses show that the impact of the coring direction on yield function and plastic flow rule is fundamentally different, thus requiring the use of distinct projection strategies (a strategy here defined heterotopic mapping). The performance of the model, studied through parametric analyses and by calibrating the experimental results, illustrates the improved capability of the proposed constitutive approach when applied to strongly anisotropic porous rocks.

Mesoscale simulation of frost damage to rock material based on Rigid Body Spring Method

Frost damage is one of the most important deterioration factors for porous materials in cold and wet region. In this study, a mesoscale numerical study is conducted to estimate the frost damage of rock materials based on the Rigid Body Spring Method. The mesoscale elastoplastic constitutive law is presented cooperated with the ice formation model for the rock material. Then, the cyclic expansion of selected marble during multiple freeze-thaw cycles (FTC) is simulated, resulting in different values of residual strain. It is found that using the residual strain as a link between freezing process and mechanical degradation, the damaged compressive behaviors after different numbers of FTC can be successfully explained and reproduced, including the crack recovery phenomenon. The findings in this study are beneficial for the further simulation of frost deterioration history, considering the large variability in properties of rock material.

Experimental and numerical study on open-hole tension/compression properties of carbon-fiber-reinforced thermoplastic laminates

The stress-strain responses and damage initiation/propagation mechanisms of T700G/LM-PAEK, an open-hole carbon-fiber-reinforced thermoplastic were investigated experimentally and numerically. To obtain the mechanical properties necessary for numerical simulations, uniaxial tensile/compressive, double cantilever beam, and end notched flexure tests were conducted. T700G/LM-PAEK was found to have comparable or higher Young’s modulus, strength, and interlaminar fracture toughness relative to thermoset CFRPs with carbon fiber of a similar grade. These superior mechanical properties are mainly attributable to the higher toughness and ductility of the thermoplastic resin. The interfacial fracture toughnesses were evaluated by finite element analysis with the cohesive zone model to determine the interlaminar fracture toughnesses for crack initiation and propagation. Based on the above experimental and numerical results, the stress strain response and damage evolution of open-hole specimens were analyzed by a quasi-3D extended finite element method (XFEM) and compared with the experimental results. The computational model with the elastoplastic constitutive law provided an accurate prediction of the stress-strain response in both open-hole tension and compression (OHT and OHC, respectively), suggesting that the elastoplastic constitutive law should be considered in XFEM to guarantee the accuracy of strength prediction for both OHT and OHC. The OHT model showed that the Weibull criterion was satisfied without any delamination at the failure strain, corresponding to the brittle failure mode due to fiber breakage. For the OHC simulation, the damage initiation of 0°-ply kinking was observed at 88% of the peak stress. These predicted damage mechanisms agreed reasonably well with the experimental observations.