We consider the hyperelastic response of semi‐crystalline ethylene–co‐butyl acrylate (EBA) samples filled with carbon black (CB) particles. Such material is structurally complex with its ...microstructure being characterized by many structural parameters including crosslink density, filler/matrix interfaces, crystallinity, filler network, and chain entanglement which have different degrees of influence on the effective mechanical properties. We evaluate the ability of a number of analytical models to correctly reproduce the non‐linear elastic mechanical response of these samples. We do this by considering either dry samples, or samples which are swollen by a non‐polar solvent (toluene) at equilibrium, and subjected to uniaxial tension at room temperature. As test cases, we focus on six physical models for the purpose of analyzing the stress–strain curves of samples with different cross‐linking densities. Among these frameworks, we show that the Mooney–Rivlin (MR), Ogden, and eight‐chain models accurately describe the stress–strain curves of both dry and swollen CB‐EBA samples. These findings highlight the possibility of attaining a diverse set of mechanical properties of filled polymer samples by tailoring their structural parameters.
A schematic illustration of the effect of solvent (shown by the blue color) absorption on the microstructure of CB‐EBA samples.
Meso-FE modelling of 3D textile composites is a powerful tool, which can help determine mechanical properties and permeability of the reinforcements or composites. The quality of the meso FE analyses ...depends on the quality of the initial model. A direct method based on X-ray tomography imaging is introduced to determine finite element models based on the real geometry of 3D composite reinforcements. The method is particularly suitable regarding 3D textile reinforcements for which internal geometries are numerous and complex. The approach used for the separation of the yarns in different directions is specialised because the fibres flow in three-dimensional space. An analysis of the image’s texture is performed. The homogeneity parameter has proved to be the most efficient criterion to separate the yarns numerically. A hyperelastic model developed for fibre bundles is used for the simulation of the deformation of the 3D reinforcement. Meso-FE simulations based on this approach are performed in the event of transverse compaction of a 3D orthogonal reinforcement. The deformation of the yarns’ geometry in the simulation is compared with real conditions.
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume ...complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for large displacements. We propose the concept of non-Euclidean plates to approximate many naturally formed thin elastic structures. We derive a thin plate theory, which is a generalization of existing linear plate theories, valid for large displacements but small strains, and arbitrary intrinsic geometry. We study a particular example of a hemispherical plate. We show the occurrence of a spontaneous buckling transition from a stretching dominated configuration to bending dominated configurations, under variation of the plate thickness.
•Dynamic governing equations for visco-hyperelastic dielectric elastomer actuators are built based on Gent model.•An analytical dynamic solution for a plane dielectric elastomer actuators under ...equal-biaxial deformation is proposed.•PID controller is employed to control the output of the dielectric elastomer actuators.
Dynamic analysis and active control are important bases for dielectric elastomer (DE) applications. Most of the DE materials exhibit significant viscoelasticity. Although the visco-hyperelastic constitutive relations of DEs have been studied before, the dynamic analysis of the DEs with the consideration of viscoelasticity has rarely been explored. In this study, we lay out the dynamic equations for the visco-hyperelastic DE structures. The Gent hyperelastic model is applied to take into account the strain-stiffening effect of the elastomer. Based on the model, we derive an analytical solution for the dynamic DE under homogeneous in-plane deformation. We show that the model can capture the nonlinear oscillation of the DE and allows us to investigate how the viscoelasticity and strain-stiffening effect influence the resonant frequencies and oscillation amplitudes of the system. Given the nonlinear and viscoelastic nature of the material, its dynamic response could be complicated and deviate from the desired harmonic oscillation pattern. To achieve precise control over the outputs, we employ a PID controller to build a closed-loop feedback control and demonstrate its feasibility to correct most of the undesired outputs such as nonlinear oscillation, beating phenomenon, phase lag and so on.
We provide an optimization framework that is capable of identifying the material parameters and contact traction field from two measured deformed geometries of a soft body in contact. The novelty of ...the framework is the idea of parametrizing the missing contact traction field and incorporating it into the inverse+forward hyper-elasticity formulation. We provide the continuum- and finite element formulation of the framework, as well as the direct differentiation method of sensitivity analysis to efficiently obtain necessary gradients for the BFGS optimizer. The correctness of the formulation and the excellent performance of the framework are confirmed by a series of benchmark numerical examples.
•The simultaneous calibration of material parameters and contact traction field is performed.•The framework is suitable for large deformations of soft bodies in contact.•No information about the unloaded configuration is needed.•The procedure combines inverse and forward elasticity formulations.•Noise is added to demonstrate the applicability to realistic measurements.
Maintaining vacuum integrity for the semi-conductor manufacturing processes is extremely important to improve semiconductor fab productivity. The expensive machinery and the enormous costs of ...production downtime require reliable sealing systems which are designed to operate the longest possible preventative maintenance (PM) cycles. Being able to predict the lifetime of the sealing systems can help determine the optimum maintenance periods and hence increase profitability in costly wafer processing. The present contribution describes a finite element method to predict the lifetime of vacuum sealing systems limited by aging effects of the elastomer. Several different applications are considered including isothermal and non-isothermal conditions. Furthermore, homogeneous and inhomogeneous temperature fields are analyzed. Finally, the model predictions are compared to experimental data.
Flexible foams are a class of materials often used in transportation systems to mitigate mechanical shocks and vibrations. Polydispersity causes these foams to have a complex microstructure composed ...of a matrix polymer material and nearly spherical voids. This structure leads to a complex material response upon loading where the load for a given displacement becomes highly dependent upon the current volume fraction of voids in the deformed foam. This complex behavior makes it challenging to develop constitutive models for flexible foams where typically only the homogenized response of the foam is considered during model development, calibration, and eventual deployment. To overcome these challenges we utilize a micromechanics finite element method simulation-informed machine learning framework to develop new constitutive models with idealized foam microstructures of moderate density in mind. Several different machine learned models will be presented and validated against micromechanics finite element simulation which were absent from the training dataset. Specifically, traditional data-driven machine learned regression models will be compared with machine learned models which learn the deviation of representative volume element data from a traditional homogenized constitutive model. A discussion on the strengths and weaknesses of each of the approaches will be presented.
•Machine learning is used to build constitutive models of large deformation of elastomeric foams.•A discrepancy formulation is developed to build off of traditional constitutive models.•The machine learned models are used in a material point driver to test their application performance.•The discrepancy models demonstrate robust performance in extrapolation from training data.
Mammography is a specific type of breast imaging that uses low-dose X-rays to detect cancer in early stage. During the exam, the women breast is compressed between two plates in order to even out the ...breast thickness and to spread out the soft tissues. This technique improves exam quality but can be uncomfortable for the patient. The perceived discomfort can be assessed by the means of a breast biomechanical model. Alternative breast compression techniques may be computationally investigated trough finite elements simulations.
The aim of this work is to develop and evaluate a new biomechanical Finite Element (FE) breast model. The complex breast anatomy is considered including adipose and glandular tissues, muscle, skin, suspensory ligaments and pectoral fascias. Material hyper-elasticity is modeled using the Neo-Hookean material models. The stress-free breast geometry and subject-specific constitutive models are derived using tissues deformations measurements from MR images.
The breast geometry in three breast configurations were computed using the breast stress-free geometry together with the estimated set of equivalent Young's modulus (Ebreastr = 0.3 kPa, Ebreastl = 0.2 kPa, Eskin = 4 kPa, Efascia = 120 kPa). The Hausdorff distance between estimated and measured breast geometries for prone, supine and supine tilted configurations is equal to 2.17 mm, 1.72 mm and 5.90 mm respectively.
A subject-specific breast model allows a better characterization of breast mechanics. However, the model presents some limitations when estimating the supine tilted breast configuration. The results show clearly the difficulties to characterize soft tissues mechanics at large strain ranges with Neo-Hookean material models.
•Modeling sliding conditions between pectoral muscle and breast improves the accuracy of the gravity loading simulations.•The stiffness of breast soft tissues is found to be relatively low then compared to other studies in the field.•The Neo-Hookean constitutive model cannot entirely describe the rich mechanical behavior of breast connective tissues.
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