Effective Mechanical Response Research Articles

Incorporation of Defects in Finite Elements to Model Effective Mechanical Properties of Metamaterial Cells Printed by Selective Laser Melting

Additively printed mechanical metamaterial structures optimize material, energy and waste, producing more sustainable products. Their introduction in the production workflow depends on having proper tools for accurately predicting their performance. However, the additive manufacturing process incorporates significant defects which result in an important change of the effective properties of the metamaterial cell. Finite element predictions using perfect geometries and nominal base material properties result in important errors which may require excessive uncertainty-related safety design margins. This work presents a methodology to introduce the effect of the most common defects in finite element models to compute the effective mechanical response of different metamaterials printed by Selective Laser Melting. It is shown that even at elastic infinitesimal strains, the defects produce an important change in the effective mechanical capabilities of the metamaterial, which also depend on the type of the metamaterial cell studied and on the type and magnitude of defects. With the proposed methodology, which incorporates the distribution of defects in the finite element model, the predicted mechanical properties of the metamaterial better match the experimental ones. It is shown that the initial discrepancies in the order of 100% are reduced to an order of 5%.

Non-destructive evaluation of the curing of a polybenzoxazine nanocomposite blend for space applications using fluorescence spectroscopy and predictive mechanical modelling

In this study, we employ fluorescence spectroscopy to monitor the curing process of a novel polybenzoxazine (PBZ) resin blend containing a polyhedral oligomeric silsesquioxane (POSS) reagent in a non-destructive way and compare it with the differential scanning calorimetry data. Our resin blend has been carefully selected for study on the International Space Station in 2024 as part of the Euro Materials Ageing 1 Programme (AO-2020-EMA) supported by the European Space Agency (ESA) and the French Space Agency (CNES). Computational simulations of PBZ-POSS blend composites are investigated to determine their effective mechanical responses based on constituent micro-stresses with periodic boundary conditions and continuum-based analytical micromechanical models. Further investigations are focused on the development of different representative volume element models, including periodic, non-periodic, and overlap inclusions, and the comparison with experimental data. Fluorescence spectroscopy and computational and analytical methods can offer a non-destructive approach to gaining insights into polymerisation processes and effective mechanical responses.

Thermomechanical Coupling in Polydomain Liquid Crystal Elastomers

Abstract Liquid crystal elastomers (LCEs) are made of liquid crystal molecules integrated with rubber-like polymer networks. An LCE exhibits both the thermotropic property of liquid crystals and the large deformation of elastomers. It can be monodomain or polydomain in the nematic phase and transforms to an isotropic phase at elevated temperature. These features have enabled various new applications of LCEs in robotics and other fields. However, despite substantial research and development in recent years, thermomechanical coupling in polydomain LCEs remains poorly studied, such as their temperature-dependent mechanical response and stretch-influenced isotropic-nematic phase transition. This knowledge gap severely limits the fundamental understanding of the structure-property relationship, as well as future developments of LCEs with precisely controlled material behaviors. Here, we construct a theoretical model to investigate the thermomechanical coupling in polydomain LCEs. The model includes a quasi-convex elastic energy of the polymer network and a free energy of mesogens. We study the working conditions where a polydomain LCE is subjected to various prescribed planar stretches and temperatures. The quasi-convex elastic energy enables a “mechanical phase diagram” that describes the macroscopic effective mechanical response of the material, and the free energy of mesogens governs their first-order nematic-isotropic phase transition. The evolution of the mechanical phase diagram and the order parameter with temperature is predicted and discussed. Unique temperature-dependent mechanical behaviors of the polydomain LCE that have never been reported before are shown in their stress-stretch curves. These results are hoped to motivate future fundamental studies and new applications of thermomechanical LCEs.

Size-dependent mechanical behaviors of 3D woven composite under high strain-rate compression loads

Dynamic characterization of textile composites is confronted with great challenges due to its large unit-cell size and the inherent limitations in specimen size for the Hopkinson bar-based test system. The small specimen size will inevitably introduce variations in effective mechanical response and failure mechanism, and bring about additional problems in determining the realistic dynamic properties of the material. This work experimentally investigated the dynamic compression behavior of three-dimensional angle interlock woven composite (3DWC) using the split Hopkinson pressure bar (SHPB). Specimens with different sizes were designed to explore the size dependency, strain-rate dependency and orientation dependency for the compressive behavior of the 3DWC. A high-speed camera and an optical microscope were introduced to elaborate on the damage progressing process and fracture morphology under different loading conditions. With an increase in strain rate, the measured strength of warp-direction specimens increased by approximately 7.6%, 4.8%, and 2.6% for three different sizes of specimens, accompanied by more severe intra-tow damage. Different-sized dynamic specimens exhibited comparable failure processes but modest variations in measured properties. When the number of unit cells in a specimen increased from two to three and four, the strength was observed to rise by around 14.9% and 21.9% respectively. In comparison to the warp-direction specimen, the weft-direction specimens exhibited substantially higher strength and failure strain, as well as distinct dominant failure modes of yarns. This work provides valuable insights into the determination of dynamic properties for 3D woven composites, and the designing and interpretation of dynamic test methods.

Effective design and mechanical response of Gyroid lattice scaffold for orthopedic implants

Compared to solid metallic implants, lattice (porous) Ti-6Al-4 V scaffolds provide better osteointegration and minimize the stress shielding effect by bringing down the effective elastic modulus of implants closer to the natural bones. According to available literature, the pore shape, pore size and surface curvature of lattice structures strongly influence implants' osteointegration capacity and mechanical integrity. Triply periodic minimal surface (TPMS) based Gyroid lattice structure has been widely studied by researchers for orthopedic implant applications. In this research, Gyroid unit cells were designed for orthopedic implant applications, considering optimum lattice design parameters like pore shape and curvature (TPMS skeletal Gyroid), pore size (800–1000 µm), porosity (70–85 % with a variation of 5 %) and manufacturing constraints for additive manufacturing (AM), to obtain reduced stiffness of implants, equivalent to bone and better osteointegration. The lattice structures were manufactured using direct metal laser sintering (DMLS), an additive manufacturing technology. The mechanical stability of lattice structures was analyzed using the finite element method and mechanical testing under compressive loads. The compression analysis results indicate that lattice structures with 70–85 % porosity impose stiffness and strength on par with the trabecular bone, thus helping reduce stress shielding. For implantation near the regions where cortical bones are prominent, stiffness and strength need to be improved. The micro defects generated during additive manufacturing potentially reduced the mechanical strength.

Effective compressive behavior of functionally graded TPMS titanium implants with ingrown cortical or trabecular bone

This work investigates numerically the effect of gradient coefficient, partial ingrowth length of bone, topology, loading direction, and average relative density on the yield strength (YS) and effective stiffness of functionally graded (FG) triply periodic minimal surface (TPMS)-based titanium implant topologically interconnected with ingrown bone subjected to uniaxial compression. The partially or fully topologic interconnection of two bi-continuous phases including titanium TPMS and bone forms a partially or fully interpenetrating phase composites (IPCs), for which their effective mechanical response is determined by means of finite element analysis and computational homogenization. The numerical framework used for this purpose is conceptually validated against the experimental characterization of the effective mechanical properties of additively manufactured two-phase FG IPC samples consisting of a white Polylactic Acid (PLA)-based reinforcement phase and white porous Polyvinyl Alcohol Natural (PVA)-based matrix phase under the same conditions such as the topology, dimensions, boundary conditions, and material property. The results show that the effective yield strength of the titanium-bone IPC increases with the decreased absolute value of the gradient coefficient regardless of the loading direction. Comparison between homogenization results obtained using titanium implant TPMS architectures with gyroid, primitive, diamond, and IWP shows that IWP exhibits the highest effective yield strength for a given porosity level. Moreover, the effective yield strength of the bone-implant FG IPCs increases with a rise of partial ingrowth length of bone and higher average relative density of the implant. The effective yield strength is also found to be substantially dependent on the direction of the applied load.

Improved incrementally affine homogenization method for viscoelastic-viscoplastic composites based on an adaptive scheme

We proposed an adaptive incrementally affine method, a micromechanics-based mean-field homogenization scheme for viscoelastic-viscoplastic particle-reinforced composites, which is applicable for predicting the mechanical response under complex loading conditions. The formulation is based on an incrementally affine scheme using algorithmic tangent operators while adaptively adjusting the mean strain of each constituent at every step of the loading process to reflect the changes in tangent operators and the shape of the reinforcing particles. We found that its prediction beyond the viscoelastic regime can be further improved by enforcing consistency between the accumulated strain states of each phase and the concentration tensors, excluding accumulated affine strain and stress. It was inevitable that the plastic deformation of the composite was initiated earlier than what was predicted by the mean-field theory owing to the local stress concentration near the particles. Hence, we proposed a yield reduction method that enforces the earlier initiation of plastic deformation in the matrix phase when obtaining an effective mechanical response. We observed that the predictions of the adaptive incrementally affine scheme adjusted with the yield reduction agreed well with various numerical simulations of particle-reinforced composites considering viscoelastic, elastic-viscoplastic, and viscoelastic-viscoplastic matrices under uniaxial, cyclic, and biaxial loadings.

The Mechanical Response of Epoxy–Sisal Composites Considering Fiber Anisotropy: A Computational and Experimental Study

Natural-fiber-reinforced composites are seen as a good alternative to traditional synthetic-fiber composites. However, to successfully implement these materials in engineering applications, along with these materials demonstrating satisfactory load-bearing capacity, it is necessary to provide engineers with effective material properties, as well as calculation methods that take into account the distinctive features of natural fibers. This study investigated the effective elastic properties and strength of materials composed of unidirectional sisal fibers within a thermosetting polymer matrix, containing 20%, 40% and 60% fiber-volume fraction. Experiments with axial and off-axis loads in conjunction with finite-element modeling were utilized to determine the effective mechanical response of the composites. Analytical and numerical models were considered, using both isotropic- and anisotropic-fiber approaches. It is shown that only by taking into account the sisal-fiber anisotropy can the experimental results of the off-axis experiments be reproduced. The influence of sisal-fiber transverse modulus on the overall mechanical response is a function of the sisal-fiber volume fraction. It has been shown that the longitudinal specific strength of sisal-fiber-reinforced composites is comparable to classical aluminum alloys or steel. Thus, this environmentally friendly composite can be considered as an alternative in some engineering applications, such as reinforcement in concrete composites.

Void-growth computational analysis in elastic-plastic porous materials

This study aims to model the effective mechanical response of highly porous materials using computational homogenisation. A two-phase material is considered here in the form of a von Mises elastic-plastic matrix that includes spherical identical voids. A wide range of void volume fractions from 0.1% to 24% is investigated. The representative volume element principle is adopted to determine the effective yield surface of each case. Its representativeness is checked from a statistical point of view and the mechanical response is set for each porosity rate considering a wide range of stress triaxiality ratios. The relation between void volume fraction and stress triaxiality is discussed and an analysis based on the unit cell computation is proposed to examine the void shape evolution according to these parameters. Therefore, an improvement of the Gurson–Tvergaard–Needleman (GTN) model considering a wide range of void volume fractions is presented. The computational data are subsequently used to enhance the original GTN model. The parameter q1 is translated as a linear function of the porosity while q2 is kept equal to 1. This makes the model simpler and more suitable for a wide range of porous materials.

Viscoelastic truss metamaterials as time-dependent generalized continua

Mechanical metamaterials provide tailorable functionality based on a careful combination of base material and structural architecture. Truss-based metamaterials, e.g., exploit structural topology and beam geometry to achieve beneficial mechanical and physical properties from stiffness and wave dispersion to strength and toughness. While the focus to date has been primarily on static metamaterial properties or elastic wave motion, 3D-printed polymeric base materials naturally come with significant viscoelasticity, making the effective truss response time- and rate-dependent. Here, we report a theoretical-numerical-experimental study which (i) deploys a linear viscoelastic corotational beam description (capturing finite rotations at small strains), (ii) implements the latter in a finite element framework, (iii) calibrates a generalized Maxwell model based on viscoelastic experiments on 3D-printed polymer samples, (iv) validates the theory and implementation through experimental truss benchmark tests, and (v) introduces a generalized continuum formulation for the efficient simulation of viscoelastic truss metamaterials containing large numbers of structural members. We show that the viscoelastic beam approach, calibrated via tension tests on individual strut samples, performs well when applied to complex truss lattices undergoing time-dependent stress relaxation — as verified by the effective mechanical response and full-field deformation maps. The resulting variational generalized continuum framework uses on-the-fly periodic homogenization based on a representative unit cell and is extended to dynamics by including inertial effects. By comparison to discrete numerical simulations we demonstrate the accuracy of the continuum approach, which is promising for modeling and optimizing 3D-printed truss metamaterials for engineering applications from shock-absorbing structures to rate-dependent architected materials and soft robotics.

Mechanical performance of zirconia-silica bilayer coating on aluminum alloys with varying porosities: Deep learning and microstructure-based FEM

Despite significant efforts in multiscale modeling of multiphase materials, the effective mechanical response of the thin surface layers still remains elusive due to the complexity of heterogeneous microstructures and composition. This work presents a multiscale modeling approach for determining the effective elastic properties and mechanical behavior of heterogeneous materials such as thin multilayered oxides. This approach is specifically tailored for identifying the mechanical performance of porous solid oxides as the outermost layer. A generative adversarial network (GAN) is used to generate microstructure with varying porosities, complex pore shapes, and randomly distributed pores. The multiscale modeling framework is based on the Mechanics of Structure Genome (MSG) to concurrently derive micromechanics and structural analysis models from heterogeneous structures. We have evaluated the modeling approach based on the available experimental data in the literature. By resorting to the presented framework, not only the effective mechanical properties but also the global and local fields within the macro- and micro-structures, respectively, can be quantitatively predicted for a wide range of heterogeneous systems. A thorough investigation of the mechanical performance of aluminum alloys with deposited porous ZrO2 – SiO2 bilayer is presented to demonstrate the efficacy and applicability of this approach. Results show that the elastic properties of silica and zirconia are dramatically reduced when porosity exceeds 5% and 3%, respectively.

Constitutive modeling for linear viscoelastic fiber-reinforced composites

In this paper, a micromechanics-based constitutive model is proposed for linear viscoelastic fiber-reinforced composites via a homogenization procedure in the time domain. Based on an additive decomposition, a general deformation is split into four simple deformations, namely, longitudinal tension/compression, transversely hydrostatic deformation, along-fiber shear and transverse shear. For each simple deformation, the mechanical response of the composite is reformulated utilizing the effective time-dependent relaxation functions and the effective referred elastic (time-independent) stresses, which are computed based on micromechanics. The constitutive equations for the linear viscoelastic fiber-reinforced composites are then derived through superposing the effective stresses for all the four simple deformations. The constitutive model has a simple form, which facilitates to study the effective mechanical behaviors of the composites in both the time and frequency domains. The representative volume element (RVE) models with different fiber volume fractions are created to simulate the effective viscoelastic behaviors of the fiber-reinforced composites. The comprehensive numerical simulation results reveal that the constitutive model can offer quite consistent effective mechanical responses with the finite element simulations. The experimental results in the literature are also employed to validate the constitutive model, and the findings show that the constitutive model can offer satisfactory prediction accuracy.

Tangent second-order homogenisation estimates for incompressible hyperelastic composites with fibrous microstructures and anisotropic phases

This work presents new estimates for the effective mechanical response of composites with fibrous microstructures and hyperelastic, anisotropic, incompressible phases. The composites are two-phase materials consisting of aligned cylindrical fibres of circular cross section that are randomly distributed in the transverse plane of the matrix phase. The proposed homogenisation is based on the tangent second-order method proposed by Avazmohammadi and Ponte Castañeda (2013), which utilises variational principles and a suitably chosen “linear comparison material” to provide estimates for effective strain energies of nonlinear materials. To take into account the incompressibility of the fibre phase, we employed an appropriate asymptotic expansion of the fibre deformation field. By doing so, a constraint pressure is identified as the consistent limit of emerging indeterminate forms in the dilatational part of the fibre stress tensor. Furthermore, we performed an asymptotic analysis to obtain regular expressions of the underlying equations in the incompressible matrix limit. While we addressed the general case of incompressible and generally anisotropic phases, we put particular emphasis on composites with transversely isotropic phases whose symmetry axes are collinear with the fibre direction. For such materials, we derived estimates for the effective strain energies in terms of macroscopic strain invariants. In addition, for composites that are described by isotropic phase energies augmented with J4-invariant-based anisotropic terms, which is the case for many biological materials, we show that the anisotropic part of the energy can be easily homogenised by means of a simple Voigt-type average. Moreover, we present closed-form results for composites with isotropic Neo-Hookean phases augmented by transversely isotropic energy contributions. Finally, it is shown that the new estimates correspond to certain exact results under longitudinal shear deformation and that they properly linearise for small strains by recovering the corresponding linear-elastic estimates.

A computational multiscale modeling framework for investigating the mechanical properties of meat

The present work presents a novel computational multiscale modeling framework for estimating the mechanical properties of meat, based entirely on the microstructural properties of its constituents. In order to achieve this, a numerical homogenization approach is used to bridge the micro-scale to the macro-scale of a meat structure and obtain its effective mechanical response under three-dimensional loading conditions. The effective properties of meat are obtained by solving numerically, in the context of the finite element method, a boundary value problem of a representative volume element of meat’s microstructure under periodic boundary conditions. A real meat microstructure is virtually represented by eroded Voronoi unit cells, which provide the appropriate flexibility to capture the effects of microstructural variability on the macroscopic mechanical properties of meat. The model analysis suggests that the intramuscular connective tissue plays the most critical role in the overall mechanical response of meat, even if it accounts for only a small fraction of the whole material’s volume. The present microstructurally-based modeling framework can be used to tailor meat microstructures in order to manage material properties related to specific food quality characteristics. • Multiscale modeling is used to estimate the mechanical properties of meat. • A computational homogenization method is used to bridge the length scales. • Meat properties depend on mechanical aspects of its microstructural constituents. • Intramuscular connective tissue plays a critical role on meat’s properties. • Modeling tool to tailor meat microstructures and manage material properties.

Effective Mechanical Responses of a Class of 2D Chiral Materials

Effective Mechanical Responses of a Class of 2D Chiral Materials

Effective Mechanical Responses of a Class of 2D Chiral Materials

Chiral materials may exhibit negative Poisson's ratio and deformation‐mode coupling phenomena. The finite element numerical method is adopted to analyze a class of 2D chiral and nonchiral materials and to show the effects of microstructural geometry on their effective elastic properties and coupling between tension/compression and bending. With the same area fraction (AF), nonchiral samples show larger effective moduli than chiral ones. The number of unit cells may reduce negativity in effective Poisson's ratio of the chiral samples due to nonuniform lateral deformation under uniaxial straining. Increasing AF in a hierarchical pattern in the chiral samples makes their Poisson's ratio more negative. Bending occurs in the chiral samples when they are under uniform, uniaxial, tensile, or compressive straining due to the coupling of deformation modes. The sensibility of tension–bending coupling may be controlled by the chiral microstructure. Optimization of the coupling sensitivity may help develop novel mechanical sensors.

Effective response of heterogeneous materials using the recursive projection method

This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various fixed-point methods to solve the problem on the periodic unit cell. These have proven extremely powerful in a range of problems ranging from image-based modeling to dislocation plasticity. However, the fixed-point iterations can converge very slowly, or not at all, if the elastic properties have high contrast, such as in the case of voids. The paper examines the reasons for slow, or lack of convergence, in terms of a variational perspective. In particular, when the material contains regions with zero or very small stiffness, there is lack of uniqueness, and the energy landscape has flat or shallow directions. Therefore, in this work, the fixed-point iteration is replaced by the RPM iteration. The RPM uses the fixed-point iteration to adaptively identify the subspace on which fixed-point iterations are unstable, and performs Newton iterations only on the unstable subspace, while fixed-point iterations are performed on the complementary stable subspace. This combination of efficient fixed-point iterations where possible, and expensive but well-convergent Newton iterations where required, is shown to lead to robust and efficient convergence of the method. In particular, RPM-FFT converges well for a wide range of choices of the reference medium, while usual fixed-point iterations are usually sensitive to this choice.

Effective mechanical response of non-linear heterogeneous materials comprising bimodular phases

In this study, the effective constitutive behavior of heterogeneous materials comprising bimodular phases is investigated through a computational approach and by referring to Curnier-type bimodularity. Different microstructures characterized by spherical inclusions or voids are addressed, by analyzing different loading scenarios. Numerical results, obtained via an iterative finite-element scheme, highlight the influence of intraphase constitutive non-linearities induced by the tension/compression transition of the local material stiffness. Moreover, coupling effects between hydrostatic and deviatoric states are elucidated. The macroscale material response results dependent on the loading condition, and it is driven by perturbative effects of heterogeneous fields locally induced by pores or inclusions.

A Mechanics Based Surface Image Interpretation Method for Multifunctional Nanocomposites.

Graphene nanosheets and thicker graphite nanoplatelets are being used as reinforcement in polymeric materials to improve the material properties or induce new functional properties. By improving dispersion, de-agglomerating the particles, and ensuring the desired orientation of the nano-structures in the matrix, the microstructure can be tailored to obtain specific material properties. A novel surface image assisted modeling framework is proposed to understand functional properties of the graphene enhanced polymer. The effective thermal and mechanical responses are assessed based on computational homogenization. For the mechanical response, the 2-D nanoplatelets are modeled as internal interfaces that store energy for membrane actions. The effective thermal response is obtained similarly, where 2-D nanoplatelets are represented using regions of high conductivity. Using the homogenization simulation, macroscopic stiffness properties and thermal conductivity properties are modeled and then compared to the experimental data. The proposed surface image assisted modeling yields reasonable effective mechanical and thermal properties, where the Kapitza effect plays an important part in effective thermal properties.

A microstructurally-based, multi-scale, continuum-mechanical model for the passive behaviour of skeletal muscle tissue

This work presents a novel microstructurally-based, multi-scale model describing the passive behaviour of skeletal muscle tissue. The model is based on the detailed description of the mechanically relevant parts of the microstructure. The effective constitutive material response is obtained by a homogenisation of mechanical energies and stresses from the micro- to the macroscale. The key feature of the new model is that it does not require any constitutive assumptions or calibration on the macroscale. The effective mechanical response is a pure consequence of the stiffness and structural arrangement of microscopic components. In this sense, the model inherits its direction-dependent properties directly from the microstructure. This is achieved by employing a Voigt-type homogenisation and by utilising for the complex collageneous network of the extracellular matrix an angular integration method. For physiologically realistic microscopic model parameters, this model reveals that muscle tissue exhibits a tensile stiffness that is larger transverse to the muscle fibre than in muscle fibre direction. This highlights that muscle tissue in general does not obey a classical fibre-reinforcement solely for tensile stretches of the muscle fibres but rather a general transversely isotropic behaviour. Moreover, the formulation of the effective macroscopic energy is provided in terms of well-known macroscopic strain invariants, which allows for an easy application of the model in standard numerical settings.