Continuum-based Analysis Research Articles

Macroscopic characterization of modern masonry

This publication presents a study aiming a macro characterization of the mechanical properties, suitable for future macro-scale numerical continuum-based analyses of a structured masonry bond, employing modern hollow bricks. The experiments themselves were initially simulated across different configurations, sizes and loading scenarios to determine the minimal specimen size invariant to boundary and size effects that scales consistently. From these simulations, a numerically informed experimental program was executed across compression, tension, shear, triplet shear, and out-of-plane bending conditions to fully quantify orthotropic material parameters of the masonry pattern suitable for aimed macro-scale simulation. The outcome of this publication is a comprehensive quantitative understanding of the apparent masonry type for engineering design purposes.

Energy-Based Approach: Analysis of a Laterally Loaded Pile in Multi-Layered Non-Linear Elastic Soil Strata

Several studies have been reported in published literature on analytical solutions for a laterally loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. The present study describes a new continuum-based analysis or energy-based approach for predicting the pile displacement responses subjected to static lateral loads and moments considering the soil non-linearity. This analytical analysis treats the pile as an elastic Euler–Bernoulli beam and the soil as a three-dimensional (3D) continuum in which the non-linear elastic properties are described by a modulus degradation relationship. The principle of virtual work was applied to the energy equation of a pile–soil system in order to obtain the governing differential equation for the pile and soil displacements. An iterative procedure was adopted to solve the equations numerically using a finite difference method (FDM). The pile displacement response was obtained using the software MATLAB R2021a, and the results from the energy-based method were compared with those obtained from the field test data as well as the finite element analysis (FEA) based on the software ANSYS Workbench 2021R1. The present study investigated the effect of explicit incorporation of soil properties and layering through a parametric study in order to understand the importance of predicting appropriate pile displacement responses in a linear elastic soil system. The responses indicated that the effect of soil layers and their thicknesses, pile properties and the variation in soil moduli have a direct impact on the displacements of piles subjected to lateral loading. Hence, a proper emphasis has to be given to account for the soil non-linearity. Considering the effect of soil non-linearity, it is observed that the results obtained from the energy-based method agreed well with the field measured values and those obtained from the FEA. The results indicated a difference of approximately less than 7% between the proposed method and the FEA. The approach presented in this study can be further extended to piles embedded in multi-layered soil strata subjected to the combined action of axial loads, lateral loads and moments. Furthermore, the same approach can be extended to study the response of the soil to group piles.

Modeling cell membrane electrodeformation by alternating electric fields.

With the aim of characterizing and gaining insight into the frequency response of cells suspended in a fluid medium and deformed with a controlled alternating electric field, a continuum-based analysis is presented for modeling electrodeformation (ED) via Maxwell stress tensor (MST) calculation. Our purpose here is to apply this approach to explain the fact that the electric field anisotropy and electrical conductivity ratio Λof the cytoplasm and the extracellular medium significantly impact the MST exerted on the cytoplasm-membrane interface. One important finding is that the modulation of electrical cues and MST force by the frequency of the applied electric field provides an extremely rich tool kit for manipulating cells. We show the extreme sensitivity of proximity-induced capacitive coupling arising concomitantly when the magnitude of the MST increases as the distance between cells is decreased and the spatial anisotropy becomes important. Moreover, our model highlights the strongly localized character of the electrostatic field effect emanating from neighboring cells and suggests the possibility of exploiting cell distribution as a powerful tool to engineer the functional performance of cell assemblies by controlling ED and capacitive coupling. We furthermore show that frequency has a significant impact on the attenuation-amplification transition of MST, suggesting that shape anisotropy has a much weaker influence on ED of the cell membrane compared to the anisotropy induced by the orientation angle itself.

Micromechanics of defects in functional materials

We report on the unified approach to the classification of defects in continuum-based analysis of the defect self-distortions. Defects of various dimensionality including point, linear, surface, and volume defects are considered depending on the domain of self-distortion definition. The results of analytical calculations of elastic fields and the energies of dislocations, disclinations, and inclusions in bodies of various geometries with internal and external boundaries are considered. Examples of defects in modern functional materials, e.g., graphene, are given. It is discussed how the presence of defects and associated elastic fields affects the properties of modern functional materials and the characteristics of devices based on them.

Computational modeling of the out-of-plane behavior of unreinforced irregular masonry

The vulnerability of stone masonry structures to seismic loading constitutes one of the main application areas of research in the field of structural engineering. This paper focuses on the analysis of the out-of-plane response of unreinforced masonry structures. Although successful in many applications, traditional continuum-based analysis, as well as simplified analytical models, fail to a large extent in correctly capturing complex failure mechanisms occurring for this type of structures. To overcome this issue, this study adopts a discrete model, the so-called Lattice Discrete Particle Model (LDPM), to describe the structural behavior of a variety of stone masonry structures up to their collapse. LDPM simulates the behavior of masonry at the stone level. The interaction between stones that are bounded by weak layers of mortar is governed by specific constitutive equations describing tensile fracturing with strain-softening, cohesive and frictional shearing, and compressive response with strain-hardening. This manuscript aims to validate the proposed model with experimental data available in the literature. Furthermore, overturning walls with and without openings are simulated, the associated local collapse mechanisms are analyzed and compared with the classical kinematic analysis. Finally, more complex mechanisms are numerically investigated to reproduce the behavior of systems of panels included within the continuity of a facade. The results show that LDPM is able to capture the damage evolution and the fracture propagation that lead to the overall collapse and it can be used confidently as an alternative method to perform the limit analysis of local collapse mechanisms. The proposed numerical approach provides engineers with a powerful modeling tool for the analysis of the behavior of stone masonry structures with a variety of geometrical configurations and under very general loading conditions.

Variational approach for settlement analysis of circular plate on multilayered soil

• A semi-analytical method is developed for the analysis of a uniformly-loaded circular plate on a multilayered soil. • The method can analyze a thin circular plate's flexural behavior on any number of soil layers. • A parametric study on two- and three-layered soils highlights important insights about plate-layered soil interactions. • Charts that can facilitate the analysis of differential settlement of concrete tanks are provided. A continuum-based analysis method is developed to analyze a uniformly-loaded circular plate founded on a multilayered soil deposit. The multilayered soil deposit forms a semi-infinite half space, and the behavior of each soil layer is assumed to be linear elastic. The plate is considered to be isotropic, homogeneous, and linear elastic. We apply variational principles to obtain the governing differential equations of the plate-layered soil system and solve them semi-analytically. We then compare results from the present analyses with those from finite element analysis. Using the proposed analysis method we perform a parametric study, results from which provide important insights into the effects of soil layering – such as the thicknesses and stiffness ratios of multiple soil layers – on the flexural behavior of the circular plate. Analyses for wide ranges of plate-to-soil stiffness ratios provide further insights on plate-soil interactions.

A patchy continuum? Stream processes show varied responses to patch- and continuum-based analyses.

Many conceptual syntheses in ecology and evolution are undergirded by either a patch- or continuum-based model. Examples include gradualism and punctuated equilibrium in evolution, and edge effects and the theory of island biogeography in ecology. In this study, we sought to determine how patch- or continuum-based analyses could explain variation in concentrations of stream macronutrients and system metabolism, represented by measures of productivity and respiration rates, at the watershed scale across the Kanawha River Basin, USA. Using Strahler stream order (SSO; continuum) and functional process zone (FPZ; patch) as factors, we produced statistical models for each variable and compared model performance using likelihood ratio tests. Only one nutrient (i.e., ) responded better to patch-based analysis. Both models were significantly better than a null model for ecosystem respiration; however, neither outperformed the other. Importantly, in most cases, a combination model, including both SSO and FPZ, best described observed variation in the system. Our findings suggest that several patch- and continuum-based processes may simultaneously influence the concentration of macronutrients and system metabolism. Nutrient spiral- ing along a continuum and the patch mosaic of land cover may both alter macronutrients, for example. Similarly, increases in temperature and discharge associated with increasing SSO, as well as the differences in light availability and channel morphology associated with different FPZs, may influence system metabolism. For these reasons, we recommend a combination of patch- and continuum-based analyses when modeling, analyzing, and interpreting patterns in stream ecosystem parameters.

Fragility analysis of continuous pipelines subjected to transverse permanent ground deformation

The structural integrity of buried continuous pipelines can be jeopardized by transverse permanent ground deformation (PGD) induced by landslides. A probabilistic analysis can facilitate understanding the likelihood of damage to pipelines in landslide regions, further minimizing the risk. However, empirical fragility curves for the landslide-pipeline interaction problem are not available due to the lack of field data. The problem can be addressed by numerical approaches. In this study, a simplified two-dimensional numerical model is developed. It characterizes the pipes as beam-type structures and the surrounding soil as Winkler springs. It is compared here against three-dimensional continuum-based analyses, which could save extensively on computational efforts. All input parameters were sampled randomly and paired with the displacement demands to form a limited set of statistically significant, yet nominally identical, pipeline samples, and the demand models for the maximum tensile strain were evaluated. A supervised machine learning technique, called Lasso regression, was then used to establish a predictive relation between the input and the output using the limited dataset, based on which a large dataset (one million) was calculated for the fragility analysis. The use of a Winkler-based analysis and the supervised machine learning technique makes it possible to generate fragility curves for pipelines subjected to transverse PGD for the first time.

Response of Laterally Loaded Rectangular and Circular Piles in Soils with Properties Varying with Depth

Continuum-based analyses for laterally loaded piles with rectangular and circular cross sections are presented using solutions that can be obtained quickly without requiring any elaborate inputs for the geometry and numerical mesh. The analysis is developed by solving the differential equations governing the displacements of the pile-soil system derived using the variational principles of mechanics. Parametric studies are performed to investigate the influence of the pile cross-sectional shape, soil layering, pile slenderness ratio, and pile-soil modulus ratio on the response of laterally loaded piles in heterogeneous soil in which the soil shear modulus varies continuously or discretely with depth. The results show that piles with the same second moment of inertia have similar lateral-load response. The lateral responses of piles in two-layer systems were mainly affected by the thickness and stiffness of the top soil layer. Soil layering also influences the lateral response of piles in three-layer soil deposits consisting of two thin layers overlying the third layer. Algebraic equations for estimating the pile-head deflection and maximum bending moment are proposed that can be readily used in design. A user-friendly spreadsheet program is developed as a tool to perform calculations of pile response using the analysis. Numerical examples demonstrating the use of the analysis are provided.

Numerical Investigation of Stress Distribution during Die Compaction of Food Powders

A numerical method is presented to determine the internal stress distribution in powder compacts during uniaxial die compaction using the finite element method. A continuum-based analysis was carried out considering the powder body forming a tablet as an elastic-plastic continuum. Compaction behavior and mechanical material properties were defined using a modified density-dependent Drucker-Prager cap (DPC) material model. In addition, a nonlinear elasticity law was adopted to describe the nonlinear unloading behavior observed for the tested amorphous and crystalline food powders. The constitutive model was calibrated using an experimental procedure based on uniaxial die compaction experiments. All material-dependent parameters were determined experimentally using a fully instrumented hydraulic tablet press with a single-ended compaction profile. Numerical simulations of the compaction process were carried out by the commercial finite element software package ABAQUS using the calibrated material model and experimental friction data. The simulation results were in good agreement with experimental data, which demonstrated the suitability of this method to investigate internal processes during tableting.

Modeling of CNTs and CNT–Matrix Interfaces in Continuum-Based Simulations for Composite Design

Abstract A series of molecular dynamic (MD), finite element (FE) and ab initio simulations are carried out to establishsuitable modeling schemes for the continuum-based analysis of aluminum matrix nanocomposites reinforced with carbonnanotubes (CNTs). From a comparison of the MD with FE models and inferences based on bond structures and electrondistributions, we propose that the effective thickness of a CNT wall for its continuum representation should be related to thegraphitic inter-planar spacing of 3.4 A. We also show that shell element representation of a CNT structure in the FE modelsproperly simulated the carbon-carbon covalent bonding and long-range interactions in terms of the load-displacement behaviors.Estimation of the effective interfacial elastic properties by ab initio simulations showed that the in-plane interfacial bond strengthis negligibly weaker than the normal counterpart due to the nature of the weak secondary bonding at the CNT-Al interface.Therefore, we suggest that a third-phase solid element representation of the CNT-Al interface in nanocomposites is not physicallymeaningful and that spring or bar element representation of the weak interfacial bonding would be more appropriate as in the casesof polymer matrix counterparts. The possibility of treating the interface as a simply contacted phase boundary is also discussed.Key wordscarbon nanotube, molecular dynamic simulation; ab initio simulation; nanocomposite.

333 連続体モデルを用いた接着細胞の力学構造に関する解析(OS4-3:細胞のバイオメカニクス(3),OS4:細胞のバイオメカニクス)

333 連続体モデルを用いた接着細胞の力学構造に関する解析(OS4-3:細胞のバイオメカニクス(3),OS4:細胞のバイオメカニクス)

Micromechanical modeling of stress transfer in carbon nanotube reinforced polymer composites

A micromechanics model is developed for assessing the interfacial shear stress transfer in carbon nanotube reinforced polymer (NRP) composites. The model employs three concentric cylinders, each of a different length, as the representative volume element (RVE). A capped, hollow nanotube is utilized as the innermost cylinder that is completely surrounded by a matrix cylinder, which is, in turn, embedded in a composite cylinder. The atomistic structure of the nanotube is incorporated in the model by determining the Young's modulus of the nanotube using the molecular structural mechanics approach. A continuum-based analysis is performed using the elasticity theory for the axisymmetric RVE problem to obtain an analytical solution for computing the average axial normal stress in the nanotube and the interfacial shear stress across the matrix/nanotube interface. Parametric studies are conducted to illustrate the applications of the present model. The numerical results indicate that using sufficiently long and large nanotubes and a small nanotube volume fraction improves the efficiency of stress transfer in NRP composites. The predictions made by the current model are in favorable agreement with existing analytical, experimental, and computational studies.

Analysis of tablet compaction. I. Characterization of mechanical behavior of powder and powder/tooling friction

In this first of two articles on the modeling of tablet compaction, the experimental inputs related to the constitutive model of the powder and the powder/tooling friction are determined. The continuum-based analysis of tableting makes use of an elasto-plastic model, which incorporates the elements of yield, plastic flow potential, and hardening, to describe the mechanical behavior of microcrystalline cellulose over the range of densities experienced during tableting. Specifically, a modified Drucker-Prager/cap plasticity model, which includes material parameters such as cohesion, internal friction, and hydrostatic yield pressure that evolve with the internal state variable relative density, was applied. Linear elasticity is assumed with the elastic parameters, Young's modulus, and Poisson's ratio dependent on the relative density. The calibration techniques were developed based on a series of simple mechanical tests including diametrical compression, simple compression, and die compaction using an instrumented die. The friction behavior is measured using an instrumented die and the experimental data are analyzed using the method of differential slices. The constitutive model and frictional properties are essential experimental inputs to the finite element-based model described in the companion article.34

Examining Stage and Continuum Models of Flake Debris Analysis: An Experimental Approach

Flake debris produced from a number of flintknapping experiments is used to explore stage and continuum models of lithic reduction. Using metric attributes, flakes produced during core reduction are separated from those produced during tool production. Theoretically, this should allow the utilization of continuum approaches in the analysis of archaeological assemblages that represent a mix of reduction strategies (i.e., core reduction and tool production). Further, continuum based analyses are refined by providing a standardized scale. Although this work demonstrates the potential utility of a continuum based model for analysing archaeological lithic assemblages, stage analyses retain utility and can be fruitfully used in conjunction with the refined continuum model developed here.

Natural Vibrations Of Shear Deformable Cantilevered Skew Thick Plates

The natural vibrations of thick and thin cantilevered skew plates are analyzed using C0 continuous finite element assemblages of nine-node Lagrangian isoparametric quadrilateral plates based on three shear deformable thick plate theories. Finite elements based on the widely used first order Reissner-Mindlin plate theory are compared to those derived from two higher order shear deformable plate theories. Here, additional nodal displacement degrees of freedom are derived by retaining higher order powers of the thickness coordinate in the in-plane displacement fields. Essential rotary inertia terms are derived and included in the present analysis. An extensive amount of non-dimensional frequencies and mode shapes are calculated for thick and thin skew cantilevered plates having various thickness ratios and arbitrary degrees of skewness. The efficacy of using higher order shear deformable plate finite elements for predicting the in-plane vibration modes of skew plates is found to increase as the thickness ratio decreases and the skew angle increases. The present work shows that higher order shear deformable finite elements essentially eliminate the over-correction of thick skew plate frequencies that is produced when first order shear deformable finite elements are utilized. Results using the present finite element analysis are compared with those obtained using three-dimensional finite element and continuum-based analyses, and experimental methods.

Effects of shear stresses on crack-growth microstructures in transformation-toughened ceramics

Abstract In accordance with a prior study, transformation toughening of zirconia-reinforced ceramics is simulated by treating regions of particles surrounding quasi-statically advancing cracks as Mode-I symmetric distributions of circular spots that undergo a ‘supercritical’ dilatant transformation when a critical stress criterion is satisfied. Three stress criteria are considered: mean stress, maximum in-plane shear stress, and an equal mixture of these two. Simulations with the mean-stress criterion show good agreement with results of previous continuum-based analyses, as the profile of the transformed region ahead of the tip approximates a partial cardioid. In contrast, simulations for the other criteria display claw-like transformed regions extending far ahead of the crack tip. This difference in behaviour is conjectured to arise from the presence of direct spot-to-spot interaction terms in the shear stress and may account for large (i.e. mm size) transformed regions seen in some materials.

Evaluation of finite element analysis for prediction of the strength reduction due to metastatic lesions in the femoral neck

Between 30 and 70% of almost one million new cancer patients diagnosed each year will develop osseous metastases. Clinicians are faced with the difficult task of determining which patients require prophylactic stabilization to prevent pathologic fracture. The objective of this study was to test the ability of macroscopic finite element models to predict the fracture strength of the proximal femur with a lesion in the femoral neck. Drill hole defects in human cadaver femora were used to simulate lesions that penetrate one cortex of the femoral neck. Based on the first of two series of in vitro experiments, the fracture strength of a femur with a lesion that penetrates either the inferior-medial or superior-lateral cortex of the neck is approximately 45% less than the fracture strength of the paired intact femur; based on the second series, the fracture strength with the inferior-medial lesion is approximately 20% less than the fracture strength with the superior-lateral lesion. A series of three-dimensional finite element models were used to predict the fracture strength for anterior and posterior lesions, as well as the inferior-medial and posterior-lateral lesions tested in vitro. Based on a direct comparison of the strengths predicted by the finite element models to the measured in vitro fracture strengths, the finite element models performed poorly. In particular, the application of an anisotropic strength criterion to the stresses predicted by the models resulted in a considerable underestimation of the percentage reduction in the in vitro fracture strength. This may reflect a fundamental inability of a linear, macroscopic continuum-based analysis to predict accurately the fracture strength of a bone structure as complex as the proximal femur. However, despite this lack of agreement in absolute fracture strength, the general trends for gait and stair ascent loading for the inferior-medial and superior-lateral lesions were consistent with the in vitro data. The greatest reduction in strength was predicted for the inferior-medial lesion, followed by the anterior lesion and then the superior-lateral lesion, and the least reduction in strength was predicted for the posterior lesion. Most importantly, the predicted strength ratio varied considerably as a function of the applied loads. Any metastatic lesions of the femoral neck may be especially sensitive to some particular activity, making it difficult to determine precisely the risk of fracture.