Anisotropic Hyperelastic Constitutive Model Research Articles

A 2-D fabric anisotropic hyperelastic constitutive model based on micromechanics analysis

The analysis of the large deformation process of two-dimensional (2-D) fabrics helps to obtain the new distribution of yarns’ orientation and fiber in-plane density, which exert a considerable influence on the mechanical properties of the 2-D fabric composite component. By examining the underlying micromechanics involved in the shearing process, we developed a shear constitutive law within an anisotropic hyperelastic constitutive model framework, which is capable of capturing the large deformation of 2-D fabrics precisely. The constitutive law introduces parameters with specific physical meanings, facilitating their acquisition and modification. The proposed model was implemented in ABAQUS using a dedicated subroutine, UANISOHYPER_INV, for defining anisotropic hyperelastic material behavior through invariant formulation. The shear properties of 2/2 twill fabric were examined, and the parameters of the shear constitutive model were determined via bias-extension tests and corresponding finite element computations. The accuracy and reliability of the proposed model were validated through a hemispherical stamping test on the 2-D fabric and frame shear experiments performed by other researchers. This work contributes to the field by providing a robust method for characterizing and predicting the shear behavior of textile composites, thus enhancing the design and optimization of advanced fabric materials.

Dispersion‐type Anisotropic Viscoelasticity: Model Validation for Myocardium

AbstractThis contribution presents a novel constitutive model for rate‐dependent response of the passive myocardium. As a first step, we performed a comparative study on dispersion‐type anisotropic hyperelastic constitutive models [1–3] and assessed performance of various density distribution functions by fitting to experiments conducted on three distinct tissues [4]. Next, we proposed an angular integration type anisotropic viscoelastic constitutive model that uses bivariate von‐Mises distribution function to capture fiber dispersion in passive myocardium. The baseline hyperelasticity is described by a generalized structure tensor formulation proposed by GASSER ET AL. [1]. The non‐equilibrium part of the model utilizes a quadratic free energy function in the logarithmic strain space and a power‐type nonlinear evolution equation in orientation directions. The overstress response is then obtained by the numerical integration over the unit sphere by making use of 21 quadrature points. The proposed model parameters are obtained from cyclic triaxial shear and triaxial shear relaxation experiments on human passive myocardium [5].

Piezoelectric Response Analysis of Ferroelectret with Annular Configuration

Ferroelectric coaxial sensors (FCSs), one of the 1D thread-like electronics, offer a broad range of applications in the Internet of Things (IoT) fields. However, previously reported FCSs have limited prospects due to a lack of in-depth theoretical research. As a result, the ferroelectric annular configuration (FAC) was extracted as the fundamental structural configuration of the FCSs in this work. The anisotropic hyperelastic constitutive model was adopted to simulate the nonlinear mechanical deformation of ferroelectret. The materials parameters in the constitutive model for radiated cross-linked polypropylene (IXPP) ferroelectret were determined by fitting the experimental results of the uniaxial tensile, uniaxial compression, and picture frame shear tests orderly and simply. The numerical results of the piezoelectric response of FAC based on the constitutive model are almost the same as the experimental value, validating the model’s effectiveness. Finally, the effect of the material parameters in the constitutive model on the piezoelectric response of the ferroelectret film and FAC was further investigated.

Microstructural and damage parameter effect analysis on the failure mechanism of fibrous soft tissues with a structure-based unit cell model

The presence of hierarchical microstructures in natural materials, such as connective tissues, makes them possess exceptional mechanical performance and undergo complex damage behaviors. Accordingly, in this study, a structure-based unit cell model (UCM) in which controllable irregular crimped fiber is embedded into soft matrix is constructed for the analysis of microstructural effects. An anisotropic hyperelastic constitutive model enhanced with different damage parameters is applied in finite element program, and the effects of damage parameters on the mechanical responses of fibrous soft tissues are investigated. The numerical results indicate that the fiber waviness plays a significant role in determining the stiffness of the tissues and that the microstructure controlled by the fiber crimp amplitude H, waviness χ and number of inflection points ω, mainly determines the fluctuation of the nominal stress–strain curves of these tissues with damaged fibers. In addition, a damage parameter analysis indicates that the attenuation of the strength and amplitude of the stress strongly depend on the strain energy limiter, and the parameter m mainly determines the rate of damage accumulation by the fibers with smaller strain energy limiters. The results of this study deepen the understanding of the mechanical behaviors of such fibrous soft tissues and provides a template for the optimization of structural and material designs for bioinspired composites.

Three-dimensional anisotropic hyperelastic constitutive model describing the mechanical response of human and mouse cervix

The mechanical function of the uterine cervix is critical for a healthy pregnancy. During pregnancy, the cervix undergoes significant softening to allow for a successful delivery. Abnormal cervical remodeling is suspected to contribute to preterm birth. Material constitutive models describing known biological shifts in pregnancy are essential to predict the mechanical integrity of the cervix. In this work, the material response of human cervical tissue under spherical indentation and uniaxial tensile tests loaded along different anatomical directions is experimentally measured. A deep-learning segmentation tool is applied to capture the tissue deformation during the uniaxial tensile tests. A 3-dimensional, equilibrium anisotropic continuous fiber constitutive model is formulated, considering collagen fiber directionality, fiber bundle dispersion, and the entropic nature of wavy cross-linked collagen molecules. Additionally, the universality of the material model is demonstrated by characterizing previously published mouse cervix mechanical data. Overall, the proposed material model captures the tension–compression asymmetric material responses and the remodeling characteristics of both human and mouse cervical tissue. The pregnant (PG) human cervix (mean locking stretch ζ=2.4, mean initial stiffness ξ=12 kPa, mean bulk modulus κ=0.26 kPa, mean dispersion b=1.0) is more compliant compared with the nonpregnant (NP) cervix (mean ζ=1.3, mean ξ=32 kPa, mean κ=1.4 kPa, mean b=1.4). Creating a validated material model, which describes the role of collagen fiber directionality, dispersion, and crosslinking, enables tissue-level biomechanical simulations to determine which material and anatomical factors drive the cervix to open prematurely. Statement of significanceIn this study, we report a 3D anisotropic hyperelastic constitutive model based on Langevin statistical mechanics and successfully describe the material behavior of both human and mouse cervical tissue using this model. This model bridges the connection between the extracellular matrix (ECM) microstructure remodeling and the macro mechanical properties change of the cervix during pregnancy via microstructure-associated material parameters. This is the first model, to our knowledge, to connect the the entropic nature of wavy cross-linked collagen molecules with the mechanical behavior of the cervix. Inspired by microstructure, this model provides a foundation to understand further the relationship between abnormal cervical ECM remodeling and preterm birth. Furthermore, with a relatively simple form, the proposed model can be applied to other fibrous tissues in the future.

Robotic-Assisted Measurement of Fabrics for the Characterization of the Shear Tension Coupling

Industrial use of composite materials requires an increasingly advanced knowledge of technical textiles mechanical properties to control the manufacturing process and guarantee the performances of the finished products. Among the qualities that influence greatly the shaping process, theshear deformability is key for the forming of complex composite parts with double curves geometries. On the other hand, the stiffening of the behavior as the shearing rise is responsible for the occurrence of the wrinkling defect. This shearing behavior of the textile reinforcement is difficult to determinebecause it is non-linear and it coexists with a tensile stiffness of the fibers that is several orders of magnitude higher. Furthermore, shear and tension are coupled due to the weaving of the textiles. Now, few experimental methods have been proposed to measure the tension behavior of fabric as a function of its shear level because dedicated devices are needed for this investigation, capturing the shear-tension coupled behavior of fabric is then a difficult task. This paper deals with the robotization of the fabric shear-tension effect characterization. A KUKA robot associated with a force/torque sensor is utilized, taking advantage of its benefits in the ability to control the state of yarn tensions during shear tests while keeping track of the desired trajectory as enabled by the hybrid position-force control feature. This ensures precise positioning of a sample fabric and accurate contact forces. An anisotropic hyperelastic constitutive model for fabrics, based on the continuum theory of mechanics that takes into account the shear-tension coupling effect was formulated analytically and numerically simulated using Matlab software. An experimental test was then implemented to validate the proposed model. The results from a uni-axial tensile test and shear test under constant uni-axial tensile loading were obtained and analyzed to characterize the test sample. The model parameter identification was performed and presented in detail.

Biomechanical characterization and constitutive modeling of the layer-dissected residual strains and mechanical properties of abdominal porcine aorta

We analyze the residual stresses and mechanical properties of layer-dissected infrarenal abdominal aorta (IAA). We measured the axial pre-stretch and opening angle and performed uniaxial tests to study and compare the mechanical behavior of both intact and layer-dissected porcine IAA samples under physiological loads. Finally, some of the most popular anisotropic hyperelastic constitutive models (GOH and microfiber models) were proposed to estimate the mechanical properties of the abdominal aorta by least-square fitting of the recorded in-vitro uniaxial test results.The results show that the residual stresses are layer dependent. In all cases, we found that the OA in the media layer is lower than in the whole artery, the intima and the adventitia. For the axial pre-stretch, we found that the adventitia and the media were slightly stretched in the environment of the intact arterial strip, whereas the intima appears to be compressed. Regarding the mechanical properties, the media seems to be the softest layer over the whole deformation domain showing high anisotropy, while the intima and adventitia exhibit considerable stiffness and a lower anisotropy response. Finally, all the hyperelastic anisotropic models considered in this study provided a reasonable approximation of the experimental data. The GOH model showed the best fitting.

A direct Jacobian total Lagrangian explicit dynamics finite element algorithm for real‐time simulation of hyperelastic materials

AbstractThis article presents a novel direct Jacobian total Lagrangian explicit dynamics (DJ‐TLED) finite element algorithm for real‐time nonlinear mechanics simulation. The nodal force contributions are expressed using only the Jacobian operator, instead of the deformation gradient tensor and finite deformation tensor, for fewer computational operations at run‐time. Owing to this proposed Jacobian formulation, novel expressions are developed for strain invariants and constant components, which are also based on the Jacobian operator. Results show that the proposed DJ‐TLED consumed between 0.70× and 0.88× CPU solution times compared to state‐of‐the‐art TLED and achieved up to 121.72× and 94.26× speed improvements in tetrahedral and hexahedral meshes, respectively, using GPU acceleration. Compared to TLED, the most notable difference is that the notions of stress and strain are not explicitly visible in the proposed DJ‐TLED but embedded implicitly in the formulation of nodal forces. Such a force formulation can be beneficial for fast deformation computation and can be particularly useful if the displacement field is of primary interest, which is demonstrated using a neurosurgical simulation of brain deformations for image‐guided neurosurgery. The present work contributes towards a comprehensive DJ‐TLED algorithm concerning isotropic and anisotropic hyperelastic constitutive models and GPU implementation.

Anisotropic hyperelastic constitutive modeling of in-plane finite deformation responses of commercial composite hexagonal honeycombs

This research presents the adaptation of an anisotropic hyperelastic constitutive model for predicting the experimentally observed in-plane, orthotropic, bi-modular and nonlinear-elastic responses of a commercial adhesively bonded HRP-C fiberglass/phenolic hexagonal honeycomb core. The hyperelastic constitutive model is evaluated under simple states of loading using single-element finite element analysis. The predictions of the model, including stress-strain behavior, Poisson effects, and strain energy densities, are compared with test data for the in-plane uniaxial tension/compression responses of the honeycomb core as well as the single-element model with a linear orthotropic constitutive model to highlight the effectiveness of the hyperelastic model at high strain levels. Good agreement is observed between the model predictions and test data. Tension tests in ribbon and transverse directions with the full-scale honeycomb core are also simulated to ensure the suitability of the single element model for simulations of the simple loading cases and preliminary validation process.

Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approaches with application to cubic lattice metamaterials

This work investigates the capabilities of anisotropic theory-based, purely data-driven and hybrid approaches to model the homogenized constitutive behavior of cubic lattice metamaterials exhibiting large deformations and buckling phenomena. The effective material behavior is assumed as hyperelastic, anisotropic and finite deformations are considered. A highly flexible analytical approach proposed by Itskov (Int J Numer Methods Eng 50(8): 1777–1799, 2001) is taken into account, which ensures material objectivity and fulfillment of the material symmetry group conditions. Then, two non-intrusive data-driven approaches are proposed, which are built upon artificial neural networks and formulated such that they also fulfill the objectivity and material symmetry conditions. Finally, a hybrid approach combing the approach of Itskov (Int J Numer Methods Eng 50(8): 1777–1799, 2001) with artificial neural networks is formulated. Here, all four models are calibrated with simulation data of the homogenization of two cubic lattice metamaterials at finite deformations. The data-driven models are able to reproduce the calibration data very well and reproduce the manifestation of lattice instabilities. Furthermore, they achieve superior accuracy over the analytical model also in additional test scenarios. The introduced hyperelastic models are formulated as general as possible, such that they can not only be used for lattice structures, but for any anisotropic hyperelastic material. Further, access to the complete simulation data is provided through the public repository https://github.com/CPShub/sim-data.

A Novel Anisotropic Failure Criterion With Dispersed Fiber Orientations for Aortic Tissues.

Accurate failure criteria play a fundamental role in biomechanical analyses of aortic wall rupture and dissection. Experimental investigations have demonstrated a significant difference of aortic wall strengths in the circumferential and axial directions. Therefore, the isotropic von Mises stress and maximum principal stress, commonly used in computational analysis of the aortic wall, are inadequate for modeling of anisotropic failure properties. In this study, we propose a novel stress-based anisotropic failure criterion with dispersed fiber orientations. In the new failure criterion, the overall failure metric is computed by using angular integration (AI) of failure metrics in all directions. Affine rotations of fiber orientations due to finite deformation are taken into account in an anisotropic hyperelastic constitutive model. To examine fitting capability of the failure criterion, a set of off-axis uniaxial tension tests were performed on aortic tissues of four porcine individuals and 18 human ascending thoracic aortic aneurysm (ATAA) patients. The dispersed fiber failure criterion demonstrates a good fitting capability with the off-axis testing data. Under simulated biaxial stress conditions, the dispersed fiber failure criterion predicts a smaller failure envelope comparing to those predicted by the traditional anisotropic criteria without fiber dispersion, which highlights the potentially important role of fiber dispersion in the failure of the aortic wall. Our results suggest that the deformation-dependent fiber orientations need to be considered when wall strength determined from uniaxial tests are used for in vivo biomechanical analysis. More investigations are needed to determine biaxial failure properties of the aortic wall.

A new anisotropic soft tissue model for elimination of unphysical auxetic behaviour

Auxetic behaviour, the unphysical transverse expansion during uniaxial tension, is a common and undesirable feature of classical anisotropic hyperelastic constitutive models for soft tissue. In this study we uncover the underlying mechanism of such behaviour; high levels of in-plane compaction occurs due to increasing tension in strain-stiffening fibres, leading to unphysical out-of-plane expansion. We demonstrate that auxetic behaviour is primarily influenced by the ratio of fibre to matrix stiffness, and is accentuated by strain-stiffening fibres in a constant stiffness matrix (e.g., the widely used neo-Hookean matrix with exponentially stiffening fibres). We propose a new bilinear strain stiffening fibre and matrix (BLFM) model which allows close control of the fibre-matrix stiffness ratio, thereby robustly eliminating auxetic behaviour. We demonstrate that our model provides accurate prediction of experimentally observed out-of-plane compaction, in addition to stress-stretch anisotropy, for arterial tissue subjected to uniaxial tension testing.

An Anisotropic Hyperelastic Constitutive Model with Bending Stiffness Interaction for Cord-Rubber Composites: Comparison of Simulation Results with Experimental Data

Based on the invariant theory of continuum mechanics by Spencer, the strain energy depends on deformation, fiber direction, and the gradients of the fiber direction in the deformed configuration. The resulting extended theory is very complicated and brings a nonsymmetric stress and couple stress. By introducing the gradient of fiber vector in the current configuration, the strain energy function can be decomposed into volumetric, isochoric, anisotropic, and bending deformation energy. Due to the particularity of bending deformation, the reinforced material has tensile deformation and compression deformation. The bending stiffness should be taken into consideration, and it is further verified by the bending simulation.

Some unexpected predictions from strongly anisotropic hyperelastic constitutive models of soft tissue

It is shown that a widely used class of constitutive models for the mechanical response of elastic arteries, which includes the so-called HGO model, responds as if it were inextensible in simple tension in the zero limit of a non-dimensional ratio of material parameters. A significant auxetic response is predicted for an incompressible hyperelastic elastic sheet reinforced with inextensible cords. Thus, a significant lateral deformation of arterial specimens modelled by this class of materials should be observed in simple tension for small values of the non-dimensional parameter. However, such a response has not been observed experimentally. The analysis therefore suggests that predictions for this class of strongly anisotropic constitutive models for arteries should be treated with caution.

Macro- and mesoscopic mechanical properties of complex fabric rubber composite under different temperatures

In this paper, the mechanical properties of complex fabric rubber composite under different temperatures are studied based on the macro- and mesoscopic structural characterization. First, the normal stresses of the inner reticulated fabric rubber composite are determined based on the anisotropic hyperelastic constitutive model and the corresponding hyperelastic material parameters under different temperatures are obtained using the normal stress equations to fit the experimental results. Second, the representative volume element of surface fabric rubber composite is established and the corresponding homogenization anisotropic constitutive parameters are obtained numerically under different temperatures. Finally, the mechanical properties of complex fabric rubber composite under different temperatures are characterized by means of numerical simulation and experiment. This paper provides an effective method to analyze the mechanical properties of complex fabric rubber composite under different temperatures, which has important guiding significance for the design of advanced fabric rubber composite.

Influence of tension–shear coupling on draping of plain weave fabrics

Although tension–shear coupling of weave fabrics in large deformation has been observed in experiments, most constitutive models for weave fabrics often ignore this coupling effect for simplicity. In this paper, a nonlinear anisotropic hyperelastic constitutive model is proposed to consider this tension–shear coupling effect. Draping experiments of a plain weave fabric over a tetrahedron mold are carried out to validate the proposed coupling constitutive model. Subsequently, the influences of tension–shear coupling on draping processes are investigated. Numerical simulation results indicate that the tension–shear coupling effect significantly changes fiber reorientation during draping process, which makes shear deformation tend to be uniform and reduces the local shear deformation concentration and should not be neglected in woven fabric stamping with salient double curvatures.

Large-Strain Hyperelastic Constitutive Model of Envelope Material under Biaxial Tension with Different Stress Ratios.

This paper reports the biaxial tensile mechanical properties of the envelope material through experimental and constitutive models. First, the biaxial tensile failure tests of the envelope material with different stress ratio in warp and weft directions are carried out. Then, based on fiber-reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model on envelope material with different stress ratio is developed. A strain energy function that characterizes the anisotropic behavior of the envelope material is decomposed into three parts: fiber, matrix and fiber–fiber interaction. The fiber–matrix interaction is eliminated in this model. A new simple model for fiber–fiber interaction with different stress ratio is developed. Finally, the results show that the constitutive model has a good agreement with the experiment results. The results can be used to provide a reference for structural design of envelope material.

Micropatterned cell sheets as structural building blocks for biomimetic vascular patches

To successfully develop a functional tissue-engineered vascular patch, recapitulating the hierarchical structure of vessel is critical to mimic mechanical properties. Here, we use a cell sheet engineering strategy with micropatterning technique to control structural organization of bovine aortic vascular smooth muscle cell (VSMC) sheets. Actin filament staining and image analysis showed clear cellular alignment of VSMC sheets cultured on patterned substrates. Viability of harvested VSMC sheets was confirmed by Live/Dead® cell viability assay after 24 and 48 h of transfer. VSMC sheets stacked to generate bilayer VSMC patches exhibited strong inter-layer bonding as shown by lap shear test. Uniaxial tensile testing of monolayer VSMC sheets and bilayer VSMC patches displayed nonlinear, anisotropic stress-stretch response similar to the biomechanical characteristic of a native arterial wall. Collagen content and structure were characterized to determine the effects of patterning and stacking on extracellular matrix of VSMC sheets. Using finite-element modeling to simulate uniaxial tensile testing of bilayer VSMC patches, we found the stress-stretch response of bilayer patterned VSMC patches under uniaxial tension to be predicted using an anisotropic hyperelastic constitutive model. Thus, our cell sheet harvesting system combined with biomechanical modeling is a promising approach to generate building blocks for tissue-engineered vascular patches with structure and mechanical behavior mimicking native tissue.

An anisotropic hyperelastic constitutive model for plain weave fabric considering biaxial tension coupling

A nonlinear anisotropic hyperelastic constitutive model is developed for plain weave fabrics by considering biaxial tensile coupling. The strain energy function is decomposed into two parts to represent tensile energy, including the biaxial tensile coupling effect from fiber elongation and shearing energy from relative rotation between warp and weft yarns. A simple and efficient material parameter identification method is proposed. The model is exemplified on a balanced plain weave glass fabric. Experimental data from the literature are used to identify material parameters in the constitutive model. Model validation is implemented by comparing numerical results with various experimental data, including biaxial tension tests under different stretch ratios and the picture frame shearing test. The developed constitutive model is applied to numerical simulation of a double-dome stamping of the plain weave fabric. The influences of binder force and initial fiber yarn orientation on forming are investigated. Numerical results demonstrated that the biaxial tensile coupling effect could not be neglected in forming simulation. The developed constitutive model is suitable to characterize the nonlinear behavior of plain weave fabrics under large deformation.

An Anisotropic Hyperelastic Constitutive Model with Tension–Shear Coupling for Woven Composite Reinforcements

An anisotropic hyperelastic constitutive model with tension–shear coupling was developed for woven composite reinforcements based on fiber reinforced continuum mechanics theory. The strain energy of the model was additively decomposed into two parts nominally representing the fiber stretches and fiber–fiber interaction considering shear–tension coupling, respectively. Experimental data were used to identify material parameters orderly and simply in the constitutive model for a specific balanced plain woven carbon fabric. The developed model was validated by comparing numerical results with picture-frame shear tests under different pre-stretch ratios, and was then applied to the simulation of a hemispherical stamping experiment, demonstrating that the developed constitutive model is highly suitable to characterize the nonlinear and anisotropic mechanical behaviors of woven composite reinforcements under large deformation. The proposed model establishes a theoretical foundation for more accurate forming simulation and processing optimization of woven fabric composites.