Linear Elastic Response Research Articles

Comparing structural models of linear elastic responses to bending in inosculated joints

Key messageMechanical models of inosculations benefit from moderate geometric detail and characterisation of the structurally optimised area of interwoven tension-resistant fibres between the branches.Living architecture is formed by shaping and merging trees, often in combination with non-living technical elements. These structures often employ the mechanical and physiological adaptations of living trees to support structural loads. Designed and vernacular buildings utilise inosculations to redistribute forces, redirect growth, and provide redundancy. Mechanical models of inosculations in living architecture must be built according to the adaptations available to the tree. Here, mass allocation and fibre orientation are examined. Under typical gravity loads, a zone at the top of the inosculation is subject to tension. This is of particular interest because a trade-off in fibre orientation between mechanical and physiological optimisation is necessary. In tree forks, this results in specifically adapted interwoven fibres. In this study, Finite Element Analysis (FEA) is used to develop different mechanical models to fit bending experiments of four Salix alba inosculations, comparing the models’ accuracy in replicating rotations in the joint. Nine models were developed. Three levels of detail of mass allocation are considered for global isotropic (3 models) and orthotropic (3 models) mechanical properties as well as a model including the interwoven tension zone, a model of local branch and trunk orthotropy, and a model combining these two localised features. Results show significant accuracy gains come from moderate geometric accuracy and consideration of the tension-zone optimisation. The construction of the tension zone in FEA is simple and applicable to natural and artificially induced inosculations.

Finite elasticity of the vertex model and its role in rigidity of curved cellular tissues.

Using a mean field approach and simulations, we study the non-linear mechanical response of the vertex model (VM) of biological tissue to compression and dilation. The VM is known to exhibit a transition between solid and fluid-like, or floppy, states driven by geometric incompatibility. Target perimeter and area set a target shape which may not be geometrically achievable, thereby engendering frustration. Previously, an asymmetry in the linear elastic response was identified at the rigidity transition between compression and dilation. Here we show that the asymmetry extends away from the transition point for finite strains. Under finite compression, an initially solid VM can completely relax perimeter tension, resulting in a drop discontinuity in the mechanical response. Conversely, an initially floppy VM under dilation can rigidify and have a higher response. These observations imply that re-scaling of cell area shifts the transition between rigid and floppy states. Based on this insight, we calculate the re-scaling of cell area engendered by intrinsic curvature and write a prediction for the rigidity transition in the presence of curvature. The shift of the rigidity transition in the presence of curvature for the VM provides a new metric for predicting tissue rigidity from image data of curved tissues in a manner analogous to the flat case.

Anomalous linear elasticity of disordered networks.

Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We show, based on recent theoretical developments and extensive numerical computations, that disordered elastic networks near a critical rigidity transition, such as strain-stiffened fibrous biopolymer networks that are abundant in living systems, reveal an anomalous long-range linear elastic response below a correlation length. This emergent anomalous elasticity, which is non-affine in nature, is shown to feature a qualitatively different multipole expansion structure compared to ordinary continuum elasticity, and a slower spatial decay of perturbations. The potential degree of universality of these results, their implications (e.g. for cell-cell communication through biological extracellular matrices) and open questions are briefly discussed.

Computation of the homogenized linear elastic response of 2D microcellular re-entrant auxetic honeycombs based on modified strain gradient theory

Computation of the homogenized linear elastic response of 2D microcellular re-entrant auxetic honeycombs based on modified strain gradient theory

On global and local buckling response of structural angle sandwich panels

Having in mind the topic of industrialised construction and the benefits of modular construction, sandwich panels are investigated to be utilised as load-bearing wall elements. To assess its full potential, the present paper tackles the linear elastic buckling response of axially loaded angle sandwich panels, by means of numerical and analytical calculations, as the upper bound of its load bearing capacity. The failures modes are obtained and framed for concentrically loaded angle panels with fixed and pin-ended supports. A parametric study of the angle panel comprising a series of finite element models is undertaken where responses are compared with analytical calculations based on the theory of sandwich panels. Boundaries for local and global buckling are identified and framed.

Transverse seismic response of end‐bearing pipe piles to S‐waves

AbstractThis paper presents a method for the seismic analysis of open‐ended pipe piles subjected to vertically propagating S‐waves, that considers kinematic interaction between the pipe pile and its external and internal soil. Following the presentation of the elastodynamic continuum model, which is based on the assumptions of linear elastic soil response and uniform soil conditions, we employ the derived solution to investigate the sensitivity of the seismic response of pipe piles to certain key problem parameters, such as pile slenderness or the relative stiffness of the pipe pile compared to its surrounding soil. We demonstrate that the bending stiffness of pipe piles is governing their seismic response, and that thin‐walled pipe piles offer the best material usage versus seismic performance ratio. The presented solution offers a low‐cost alternative to complex numerical simulations for preliminary seismic design purposes, such as the selection of optimal pipe pile section geometry.

Integrated computational framework for modeling chopped fiber composites at the mesoscale

A new microstructure reconstruction algorithm, fully integrated with a non-iterative meshing algorithm named CISAMR, is introduced for synthesizing finite element (FE) models of chopped fiber composite (CFC) microstructures. This automated computational framework enables generating densely-packed CFC microstructures with desired statistical descriptors such as the volume fraction, diameter distribution, and spatial arrangement of fibers. The reconstruction process involves two main phases, starting with a virtual packing algorithm relying on Non-Uniform Rational B-Splines (NURBS) representation of fiber centerlines to efficiently detect/eliminate overlapping fibers. An explicit dynamic FE compression simulation is then pursued to increase the fiber volume fraction by modeling them as rigid shells and taking into account contact forces between fibers during the simulation. The shape/location of fibers excessively close to domain boundaries or intersecting them at sharp angles are then slightly modified in the resulting microstructure to ensure the construction of a high-quality conforming mesh using parallel CISAMR. Several example problems are provided to show the ability of this modeling framework for synthesizing and simulating the linear elastic response of polymer matrix CFCs with embedded glass fibers. We also demonstrate the application of high-fidelity FE models generated using CISAMR for simulating the nonlinear failure response of such composites.

Plasticity-Based Method for the Design and Analysis of Cold Recycled Pavement Layers

Abstract Asphalt cold recycling technologies allow the use of up to 100 % reclaimed asphalt pavement (RAP) from an existing asphalt pavement to construct new base layers and new subbase layers. Bituminous stabilized materials (BSM), obtained from cold recycling technologies, are susceptible to traffic-induced accumulation of permanent deformation. In the current design methods, BSM pavement layers are typically assumed to have a linear elastic response under traffic loading application, and this does not account for plasticity initiation and accumulation in the material. This research study provides insight on how to integrate plasticity behavior in numerical simulations of rehabilitated pavement structures with BSM. A BSM mixture prepared with 1.5 % cement by weight of total mixture and 1.5 % foamed asphalt binder content by weight of dry aggregates is characterized in the laboratory. Subsequently, a three-dimensional elastic-perfectly plastic finite element model is developed for the simulation of triaxial shear strength tests. Lab measured force-displacement curves are matched with the numerical simulations at different confining pressures. The calibrated mechanical properties are then used as input parameters in multilayer pavement models for pavement evaluation. Different pavement structures with and without BSM layers are compared in terms of a maximum allowable number of loading repetitions before reaching a 20-mm rut depth on the surface of the pavement. The results indicate that structures with BSM and traditional granular base layers yield comparable results in terms of rutting potential. In addition, the study presents a framework for the design and analysis of cold recycled pavement layers and a method to integrate the plasticity behavior of partially-bonded and unbounded layers for pavement evaluation.

Is It Possible to Directly Determine the Radius of a Spherical Indenter Using Force Indentation Data on Soft Samples?

An important factor affecting the accuracy of Young's modulus calculation in Atomic Force Microscopy (AFM) indentation experiments is the determination of the dimensions of the indenter. This procedure is usually performed using AFM calibration gratings or Scanning Electron Microscopy (SEM) imaging. However, the aforementioned procedure is frequently omitted because it requires additional equipment. In this paper, a new approach is presented that focused on the calibration of spherical indenters without the need of special equipment but instead using force indentation data on soft samples. Firstly, the question whether it is mathematically possible to simultaneously calculate the indenter's radius and the Young's modulus of the tested sample (under the restriction that the sample presents a linear elastic response) using the same force indentation data is discussed. Using a simple mathematical approach, it was proved that the aforementioned procedure is theoretically valid. In addition, to test this method in real indentation experiments agarose gels were used. Multiple measurements on different agarose gels showed that the calibration of a spherical indenter is possible and can be accurately performed. Thus, the indenter's radius and the soft sample's Young's modulus can be determined using the same force indentation data. It is also important to note that the provided accuracy is similar to the accuracy obtained when using AFM calibration gratings. The major advantage of this paper is that it provides a method for the simultaneous determination of the indenter's radius and the sample's Young's modulus without requiring any additional equipment.

Micromechanics Approach for the Overall Elastic Properties of Ceramic Matrix Composites Incorporating Defect Structures

Abstract The initial mechanical response of ceramic matrix composites (CMCs) is linear until the proportional limit. This initial response is characterized by linear elastic properties, which are anisotropic due to the orientation and arrangement of fibers in the matrix. The linear elastic properties are needed during various phases of analysis and design of CMC components. CMCs are typically made with ceramic unidirectional (UD) or woven fiber preforms embedded in a ceramic matrix formed via various processing routes. The matrix processing of interest in this work is the polymer impregnation and pyrolysis (PIP) process. As this process involves pyrolysis to convert a preceramic polymer into ceramic, considerable volume shrinkage occurs in the material. This volume shrinkage can lead to significant defects in the final material in the form of porosity of various size, shape, and volume fraction. These defect structures can have a significant impact on the elastic and damage response of the material. In this paper, a multiscale micromechanics modeling framework is developed to study the effects of processing-induced defects on the linear elastic response of a PIP-derived CMC. A combination of analytical and computational micromechanics approaches is used to derive the overall elastic tensor of the CMC as a function of the underlying constituents and/or defect structures. It is shown that the volume fraction and aspect ratio of porosity at various length scales play an important role in accurate prediction of the elastic tensor. Specifically, it is shown that the through-thickness elastic tensor components cannot be predicted accurately using the micromechanics models unless the effects of defects are considered.

The Hertzian theory in AFM nanoindentation experiments regarding biological samples: Overcoming limitations in data processing

Atomic Force Microscopy (AFM) nanoindentation is a powerful tool for the mechanical nano-characterization of biological samples. However, the range of Young’s modulus values for the same type of samples usually varies significantly in the literature. This fact is partly related to the inhomogeneity of biological samples at the nanoscale and partly to significant mistakes during data processing. This review depicts that common errors related to (i) the real shape of the AFM tip, (ii) the range of data for which the sample presents an approximate linear elastic response, (iii) the sample’s viscoelasticity, (iv) the sample’s shape and (v) the substrate effects can be easily avoided without increasing the complexity of data processing. Thus, the present review paper focuses on the procedures that should be followed for the accurate processing of force-indentation curves regarding experiments on biological samples.

Ground motion of the Ms7.0 Jiuzhaigou earthquake

Abstract Eighty-eight free-field strong ground motion observation datasets obtained by the National Strong Motion Observation Network System of China for the Jiuzhaigou Ms7.0 earthquake were used to study the characteristics of the strong ground motion and the site response. In this study, we calculated the VS30 of the near field station and compared the observed values of the horizontal peak acceleration and peak velocity with the CB2014 ground motion prediction models developed by Campbell et al. (2014). The results indicate that the observed values of the horizontal peak acceleration and peak velocity of the Jiuzhaigou earthquake are both smaller than the predicted values obtained from the ground motion prediction equations. By regressing the spatial variation curves of the D SR (5–95%) and D SR (5–75%) ground motion durations, and comparing them with Bommer’s (2009) ground motion duration prediction curve, it was found that the duration of the Jiuzhaigou earthquake was greater than that obtained from the global empirical prediction equation. The scope of the source duration corresponding to the D SR (5–75%) duration is 2.76–4.28 s, and the scope of the source duration corresponding to the D SR (5–95%) duration is 8.88–10.36 s, which are close to the peak time and completion time of the seismic moment release during the source rupture process. The linear elastic acceleration response spectra of 11 stations within 100 km of the fault were calculated for comparison with the design spectrum. It was concluded that the range of the predominant period of the response spectrum was 0.05–0.26 s, which is less than the natural vibration period of the local multistory building. However, the response spectrum value recorded by station 51JZZ is greater than the design spectrum of the 8° rare earthquake and the observation values of the nearby strong ground motion stations. Through analysis of the H/V spectrum ratio and the case of station 51JZZ, which is closest to the epicenter, this phenomenon was concluded to be related to the magnification effect of the near-surface soil layer and the nonlinear response of the site under the action of strong earthquakes.

Reinforced Concrete Beam under Support Removal-Parametric Analysis.

This paper investigates the behaviour of a reinforced concrete beam under a support removal. A detailed parametric analysis is carried out, covering the effect of support removal rate on dynamic response. The linear elastic and nonlinear inelastic responses are computed and studied in detail. Critical parameters during the structural response are identified. In order to determine the ultimate load, the vertical pushover analysis is performed. The key parameters driving the beam response are assumed as random variables, and respective reliability study makes it possible to check the overall uncertainty of the dynamic response. In particular, the response spectrum measuring the effect of support removal rate has been computed. It has been demonstrated that the critical vertical response occurs when the time of support removal is up to to 17% of the first natural period. The vertical pushover analysis results in obtaining capacity curves and showed the order in which two plastic hinges occur for various load patterns. Finally, the reliability-based sensitivity analysis indicates the geometric cross-section cover and height are the most sensitive parameters of the beam response.

A Multifeatured Data-Driven Homogenization for Heterogeneous Elastic Solids

A computational homogenization of heterogeneous solids is presented based on the data-driven approach for both linear and nonlinear elastic responses. Within the Double-Scale Finite Element Method (FE2) framework, a data-driven model is proposed to substitute the micro-level Finite Element (FE) simulations to reduce computational costs in multiscale simulations. The heterogeneity of porous solids at the micro-level is considered in various material properties and geometrical attributes. For material properties, elastic constants, which are Lame’s coefficients, are subjected to be heterogeneous in the linear elastic responses. For geometrical features, different numbers, sizes, and locations of voids are considered to reflect the heterogeneity of porous solids. A database for homogenized microstructural responses is constructed from a series of micro-level FE simulations, and machine learning is used to train and test our proposed model. In particular, four geometrical descriptors are designed, based on N-probability and lineal-path functions, to clearly reflect the geometrical heterogeneity of various microstructures. This study indicates that a simple deep neural networks model can capture diverse microstructural heterogeneous responses well when given proper input sources, including the geometrical descriptors, are considered to establish a computational data-driven homogenization scheme.

Multipole classification in 122 magnetic point groups for unified understanding of multiferroic responses and transport phenomena

Mutual interplay between the electronic degrees of freedom in solids, such as charge, spin, orbital, sublattice, and bond degrees of freedom, is a source of cross-correlated phenomena with unconventional electronic ordered states. Such degrees of freedom can be described by four types of multipoles (electric, magnetic, magnetic toroidal, and electric toroidal) in a unified way, which enable us to tightly connect the microscopic degrees of freedom with macroscopic physical responses in a transparent manner. We complete a classification of the multipoles in all 122 magnetic point groups based on group theory. The classification is useful to identify potentially active multipoles, not only in ordinary ferromagnetic and antiferromagnetic orderings but also in exotic orderings breaking time-reversal symmetry, e.g., a loop-current state. Moreover, the classification gives an insight into the microscopic origin of the multiferroic responses and quantum transports. By analyzing response functions up to the second order, we summarize the indispensable multipole moments for various responses, such as the linear magnetoelectric, piezoelectric, and elastic responses, and the nonlinear conductivity and Nernst coefficient. Our results highly promote a further discovery of functional multiferroic materials, guided by the bottom-up material design based on the symmetry-adapted multipoles.

Designing inelastic geotechnical systems on the basis of single design elastic response spectrum

AbstractOne of the greatest uncertainties in earthquake‐resistant design is the proper selection of ground motions to be used as excitations. The universally accepted way to confront this is the establishment of the design linear elastic response (LER) spectrum as the basis of excitation for all types of man‐made and natural systems — elastic and inelastic. By demonstrating that the “critical” ground motions are fundamentally different for elastic and inelastic systems, the paper challenges the usefulness of the concept of design LER spectrum for strongly inelastic geotechnical systems, as well as for specific inelastic structural systems such as base‐isolated structures on friction bearings. While dogmatically respecting such a spectrum may be appropriate for elastic or mildly‐inelastic systems, it is shown to be of secondary relevance for strongly inelastic systems, which are vulnerable to acceleration and velocity pulses of long duration, as the late Professor Vitelmo Bertero had demonstrated 40 years ago. Attributed primarily to forward‐rupture directivity effects in near fault recordings and somewhat less frequently to fling steps appearing close to dip‐slip and strike‐slip faults emerging on the ground surface, such acceleration and/or velocity pulses are not always adequately reflected in current design elastic spectra. It is also shown that to such motions, highly‐asymmetric geotechnical systems like slopes and retaining walls may exhibit a striking sensitivity not only to near‐fault characteristics of excitations but also to the "polarity" of motions, an outcome of inelasticity which cannot be anticipated on the basis of current design LER spectra.

Measuring Surface Tensions of Soft Solids with Huge Contact-Angle Hysteresis

The equilibrium contact angle of a droplet resting on a solid substrate can reveal essential properties of the solid's surface. However, when the motion of a droplet on a surface shows significant hysteresis, it is generally accepted that the solid's equilibrium properties cannot be determined. Here, we describe a method to measure surface tensions of soft solids with strong wetting hysteresis. With independent knowledge of the surface tension of the wetting fluid and the linear-elastic response of the solid, the solid deformations under the contact line and the contact angle of a single droplet together reveal the difference in surface tension of the solid against the liquid and vapor phases. If the solid's elastic properties are unknown, then this surface tension difference can be determined from the change in substrate deformations with contact angle. These results reveal an alternate equilibrium contact angle, equivalent to the classic form of Young-Dupr\'{e}, but with surface tensions in place of surface energies. We motivate and apply this approach with experiments on gelatin, a common hydrogel.

Activated Ductile CFRP NSMR Strengthening.

Significant strengthening of concrete structures can be obtained when using adhesively-bonded carbon fiber-reinforced polymer (CFRP) systems. Challenges related to such strengthening methods are; however, the brittle concrete delamination failure, reduced warning, and the consequent inefficient use of the CFRP. A novel ductile near-surface mounted reinforcement (NSMR) CFRP strengthening system with a high CFRP utilization is introduced in this paper. It is hypothesized that the tailored ductile enclosure wedge (EW) end anchors, in combination with low E-modulus and high elongation adhesive, can provide significant strengthening and ductility control. Five concrete T-beams were strengthened using the novel system with a CFRP rod activation stress of approximately 980 MPa. The beam responses were compared to identical epoxy-bonded NSMR strengthened and un-strengthened beams. The linear elastic response was identical to the epoxy-bonded NSMR strengthened beam. In addition, the average deflection and yielding regimes were improved by 220% and 300% (average values), respectively, with an ultimate capacity comparable to the epoxy-bonded NSMR strengthened beam. Reproducible and predictable strengthening effect seems obtainable, where a good correlation between the results and applied theory was reached. The brittle failure modes were prevented, where concrete compression failure and frontal overload anchor failure were experienced when failure was initiated.

Architected material analogs for shape memory alloys

Architected material analogs for shape memory alloys

Effect of matrix architecture on the elastic behavior of an emulsion-filled polymer gel

This work aimed to address the effect of network architecture on the small deformation mechanical properties of emulsion-filled gelatin gels as a fat- or oil-filled composite food matrix. Through pH adjustment, filled gels could be produced with either a homogeneous or heterogeneous network architecture; the latter being characterized by droplet-rich, protein dense domains. Both systems displayed a characteristic filler-mediated reinforcement in the relative elastic modulus (Er), which was dependent on both droplet and matrix stiffness. The homogeneous system was affected by the filler modulus, but showed no dependence on gelator concentration. This trend followed the general behavior of the van der Poel model of particle reinforcement, but was also indicative of imperfect interfacial adhesion. Er of the heterogeneous composites could not be described by the van der Poel model, but exhibited power law scaling with filler content. This was attributed to an increase in the connectivity of the load-bearing network which translates stress through the material. The scaling factor decreased with increasing gelator concentration, indicating an interplay between the connectivity introduced by filler-rich domains and increasing crosslink density of the embedding network. This work demonstrates that network architecture plays a central role in determining the linear elastic response of fat-filled composite soft materials.