Inverse finite element analysis for an axisymmetric model of vertical tooth extraction.

BACKGROUND AND OBJECTIVE: Tooth extraction is a common clinical procedure with biomechanical factors that can directly influence patient outcomes. Recent development in atraumatic extraction techniques have endeavoured to improve treatment outcomes, but the characterization of extraction biomechanics is sparse. An axisymmetric inverse finite element (FE) approach is presented to represent the biomechanics of vertical atraumatic tooth extraction in an ex-vivo swine model. METHODS: Geometry and boundary conditions from the model are determined to match the extraction of swine incisors in a self-aligning ex vivo extraction experiment. Material parameters for the periodontal ligament (PDL) model are determined by solving an inverse FE problem using clusters of data obtained from 10 highly-controlled mechanical experiments. A seven-parameter visco-hyperelastic damage model, based on an Arruda-Boyce framework, is used for curve fitting. Three loading schemes were fit to obtain a common set of material parameters. RESULTS: The inverse FE results demonstrate good predictions for overall force-time curve shape, peak force, and time to peak force. The fit model parameters are sufficiently consistent across all three cases that a coefficient-averaged model was taken that compares well to all three cases. Notably, the initial modulus ,u, converged across trials to an average value of 0.472 MPa with an average viscoelastic constant g of 0.561. CONCLUSIONS: The presented model is found to have consistent parameters across loading cases. The capability of this model to represent the fundamental mechanical characteristics of the dental complex during vertical extraction loading is a significant advancement in the modelling of extraction procedures. Future work will focus on verifying the model as a predictive design tool for assessing new loading schemes in addition to investigating its applications to subject-specific problems.

Towards the biomechanical modelling of the behaviour of ex-vivo porcine perineal tissues.

The perineum is a layered soft tissue structure with mechanical properties that maintain the integrity of the pelvic floor. During childbirth, the perineum undergoes significant deformation that often results in tears of various degrees of severity. To better understand the mechanisms underlying perineal tears, it is crucial to consider the mechanical properties of the different tissues that make up the perineum. Unfortunately, there is a lack of data on the mechanical properties of the perineum in the literature. The objective of this study is to partly fill these gaps. Hence sow perineums were dissected and the five perineal tissues involved in tears were characterized by uniaxial tension tests: Skin, Vagina, External Anal Sphincter, Internal Anal Sphincter and Anal Mucosa. From our knowledge, this study is the first to investigate all these tissues and to design a testing protocol to characterize their material properties. Six material models were used to fit the experimental data and the correlation between experimental and predicted data was evaluated for comparison. As a result, even if the tissues are of different nature, the best correlation was obtained with the Yeoh and Martins material models for all tissues. Moreover, these preliminary results show the difference in stiffness between the tissues which indicates that they might have different roles in the structure. These obtained results will serve as a basis to design an improved experimental protocol for a more robust structural model of the porcine perineum that can be used for the human perineum to predict perineal tears.

The origin of intraluminal pressure waves in gastrointestinal tract.

The gastrointestinal (GI) peristalsis is an involuntary wave-like contraction of the GI wall that helps to propagate food along the tract. Many GI diseases, e.g., gastroparesis, are known to cause motility disorders in which the physiological contractile patterns of the wall get disrupted. Therefore, to understand the pathophysiology of these diseases, it is necessary to understand the mechanism of GI motility. We present a coupled electromechanical model to describe the mechanism of GI motility and the transduction pathway of cellular electrical activities into mechanical deformation and the generation of intraluminal pressure (IP) waves in the GI tract. The proposed model consolidates a smooth muscle cell (SMC) model, an actin-myosin interaction model, a hyperelastic constitutive model, and a Windkessel model to construct a coupled model that can describe the origin of peristaltic contractions in the intestine. The key input to the model is external electrical stimuli, which are converted into mechanical contractile waves in the wall. The model recreated experimental observations efficiently and was able to establish a relationship between change in luminal volume and pressure with the compliance of the GI wall and the peripheral resistance to bolus flow. The proposed model will help us understand the GI tract's function in physiological and pathophysiological conditions.

Identification of constitutive materials of bi-layer soft tissues from multimodal indentations.

The personalisation of finite element models is an important problem in the biomechanical fields where subject-specific analyses are fundamental, particularly in studying soft tissue mechanics. The personalisation includes the choice of the constitutive law of the model's material, as well as the choice of the material parameters. In vivo identification of the material properties of soft tissues is challenging considering the complex behaviour of soft tissues that are, among other things, non-linear hyperelastic and heterogeneous. Hybrid experimental-numerical methods combining in vivo indentations and inverse finite element analyses are common to identify these material parameters. Yet, the uniqueness and the uncertainty of the multi-material hyperelastic model have not been evaluated. This study presents a sensitivity analysis performed on synthetic indentation data to investigate the identification uncertainties of the material parameters in a bi-material thigh phantom. Synthetic numerical data, used to replace experimental measurements, considered several measurement modalities: indenter force and displacement, stereo-camera 3D digital image correlation of the indented surface, and ultrasound B-mode images. A finite element model of the indentation was designed with either Ogden-Moerman or Mooney-Rivlin constitutive laws for both materials. The parameters' identifiability (i.e. the possibility of converging to a unique parameter set within an acceptable margin of error) was assessed with various cost functions formulated using the different synthetic data sets. The results underline the need for multiple experimental modalities to reduce the uncertainty of the identified parameters. Additionally, the experimental error can impede the identification of a unique parameter set, and the cost function depends on the constitutive law. This study highlights the need for sensitivity analyses before the design of the experimental protocol. Such studies can also be used to define the acceptable range of errors in the experimental measurement. Eventually, the impact of the evaluated uncertainty of the identified parameters should be further investigated according to the purpose of the finite element modelling.

Modeling the Effect of Annulus Fibrosus Stiffness on the Stressed State of a Vertebral L1 Body and Nucleus Pulposus.

The investigation examines the transference of stiffness from intervertebral discs (IVDs) to the lumbar body of the L1 vertebra and the interactions among adjacent tissues. A computational model of the vertebra was developed, considering parameters such as cortical bone thickness, trabecular bone elasticity, and the nonlinear response of the nucleus pulposus to external loading. A nonlinear dynamic analysis was performed, revealing certain trends: a heightened stiffness of the annulus fibrosus correlates with a significant reduction in the vertebral body's ability to withstand external loading. At a supplied displacement of 6 mm, the vertebra with a degenerative disc reached its yielding point, whereas the vertebrae with a healthy annulus fibrosus exhibited a strength capacity exceeding 20%. The obtained findings and proposed methodology are potentially useful for biomedical engineers and clinical specialists in evaluating the condition of the annulus fibrosus and predicting its influence on the bone components of the spinal system.

Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue.

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

Identification of Apple Fruit-Skin Constitutive Laws by Full-Field Methods Using Uniaxial Tensile Loading.

The protective and preservative role of apple skin in maintaining the integrity of the fruit is well-known, with its mechanical behaviour playing a pivotal role in determining fruit storage capacity. This study employs a combination of experimental and numerical methodologies, specifically utilising the digital image correlation (DIC) technique. A specially devised inverse strategy is applied to evaluate the mechanical behaviour of apple skin under uniaxial tensile loading. Three apple cultivars were tested in this work: Malus domestica Starking Delicious, Malus pumila Rennet, and Malus domestica Golden Delicious. Stress-strain curves were reconstructed, revealing distinct variations in the mechanical responses among these cultivars. Yeoh's hyperelastic model was fitted to the experimental data to identify the coefficients capable of reproducing the non-linear deformation. The results suggest that apple skin varies significantly in composition and structure among the tested cultivars, as evidenced by differences in elastic properties and non-linear behaviour. These differences can significantly affect how fruit is handled, stored, and transported. Thus, the insights resulting from this research enable the development of mathematical models based on the mechanical behaviour of apple tissue, constituting important data for improvements in the economics of the agri-food industry.

Shape-Programming in Hyperelasticity Through Differential Growth.

This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation on a hyperelastic body reaching a given target shape. We consider the two cases of globally compatible growth, where the growth tensor is a deformation gradient over the undeformed domain, and the incompatible one, which discards such hypothesis. We formulate the problem within the framework of optimal control theory in hyperelasticity. The Hausdorff distance is used to quantify dissimilarities between shapes; the complexity of the actuation is incorporated in the cost functional as well. Boundary conditions and external loads are allowed in the state law, thus extending previous works where the stress-free hypothesis turns out to be essential. A rigorous mathematical analysis is then carried out to prove the well-posedness of the problem. The numerical approximation is performed using gradient-based optimisation algorithms. Our main goal in this part is to show the possibility to apply inverse techniques for the numerical approximation of this problem, which allows us to address more generic situations than those covered by analytical approaches. Several numerical experiments for beam-like and shell-type geometries illustrate the performance of the proposed numerical scheme.

Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers.

The formulation of the entropic statistical theory and the related neo-Hookean model has been a major advance in the modeling of rubber-like materials, but the failure to explain some experimental observations such as the slope in Mooney plots resulted in hundreds of micromechanical and phenomenological models. The origin of the difficulties, the reason for the apparent need for the second invariant, and the reason for the relative success of models based on the Valanis-Landel decomposition have been recently explained. From that insight, a new micro-macro chain stretch connection using the stretch tensor (instead of the right Cauchy-Green deformation tensor) has been proposed and supported both theoretically and from experimental data. A simple three-parameter model using this connection has been suggested. The purpose of this work is to provide further insight into the model, to provide an analytical expression for the Gaussian contribution, and to provide a simple procedure to obtain the parameters from a tensile test using the Mooney space or the Mooney-Rivlin constants. From different papers, a wide variety of experimental tests on different materials and loading conditions have been selected to demonstrate that the simple model calibrated only from a tensile test provides accurate predictions for a wide variety of elastomers under different deformation levels and multiaxial patterns.

Modelling the rate-dependent mechanical behaviour of the brain tissue.

A new modelling approach is employed in this work for application to the rate-dependent mechanical behaviour of the brain tissue, as an incompressible isotropic material. Extant datasets encompassing single- and multi-mode compression, tension and simple shear deformation(s) are considered, across a wide range of deformation rates from quasi-static to rates akin to blast loading conditions, in the order of 1000 s-1 . With a simple functional form and a reduced number of parameters, the model is shown to capture the considered rate-dependent behaviours favourably, including in both single- and multi-mode deformation fits, and over all range of deformation rates. The provided modelling results here are obtained from either first fitting the model to the quasi-static data, or/and predicting the behaviour at a different rate than those used for calibrating the model parameters. Given its simplicity, versatility, predictive capability and accuracy, the application of the utilised modelling framework in this work to the rate-dependent mechanical behaviour of the brain tissue is proposed.

[Characterization of rabbit corneal biomechanical properties after corneal refractive surgery based on rapid loading-unloading uniaxial tensile test].

In order to understand how the biomechanical properties of rabbit cornea change over time after corneal ablation, 21 healthy adult rabbits were used in this study, with the left eye as experimental side and the right eye as the control side. Firstly, a lamellar knife was used to remove a portion of the anterior corneal surface tissue (30%~50% of the original corneal thickness) from the left eye of each rabbit, as an animal model simulating corneal refractive surgery. Secondly, postoperative experimental rabbits were kept for one, three, or six months until being euthanized. Strip specimens were produced using their corneas in vitro to perform a uniaxial tensile test with an average loading-unloading rate of approximately 0.16 mm/s. Finally, the visco-hyperelastic material constitutive model was used to fit the data. The results showed that there was a significant difference in the viscoelastic parameters of the corneas between the experimental and the control eyes at the first and third postoperative months. There was a difference in tangential modulus between the experimental and the control eyes at strain levels of 0.02 and 0.05 at the third postoperative month. There was no significant difference in biomechanical parameters between the experimental and the control eyes at the sixth postoperative month. These results indicate that compared with the control eyes, the biomechanical properties of the experimental eyes vary over postoperative time. At the third postoperative month, the ratio of corneal tangential modulus between the experimental and the control eyes significantly increased, and then decreased. This work lays a preliminary foundation for understanding the biomechanical properties of the cornea after corneal refractive surgery based on rapid testing data obtained clinically.

Unified three-dimensional finite elements for large strain analysis of compressible and nearly incompressible solids.

This work proposes a displacement-based finite element model for large strain analysis of isotropic compressible and nearly-incompressible hyperelastic materials. Constitutive law is written in terms of invariants of the right Cauchy-Green tensor; coupled and decoupled formulations of strain energy functions are presented, whereas a penalty function is used to impose an incompressibility constraint. Based on a total Lagrangian formulation, the nonlinear governing equations are thus obtained by employing the principle of virtual displacements. Analytic expression of both internal forces vector and tangent matrix of linear and high-order hexahedral finite elements are derived by adopting a three-dimensional formalism based on the Carrera Unified Formulation. Popular benchmark problems in hyperelasticity are analyzed to establish the capabilities of the present implementation of fully-nonlinear solid elements in the case of compressible and nearly-incompressible beams, cylindrical shells, and curved structures.

Nonlocal damage evaluation of a sigmoid-based damage model for fibrous biological soft tissues.

The comprehension and modeling of the mechanical behavior of soft biological tissues are essential due to their clinical applications. This knowledge is essential for predicting tissue responses accurately and enhancing our ability to compute the behavior of biological structures and bio-prosthetic devices under specific loading conditions. The current research is centered on modeling the initiation and progression of soft tissues damage, which typically exhibit intricate anisotropic and nonlinear elastic characteristics. For this purpose, the following study presents a comparative analysis of the computational performance of two distinct damage modeling techniques. The first technique employs a well-established damage model, based on a piece-wise exponential damage function as proposed by Calvo et al. (Int J Numer Methods Eng 69:2036-2057, 2007. https://doi.org/10.1002/nme.1825 ). The second approach adopts a sigmoid function, as proposed by López-Campos et al. (Comput Methods Biomech Biomed Eng 23(6):213-223. https://doi.org/10.1080/10255842.2019.1710742 ). The aim of this study is to verify the validity of the López-Campos sigmoid-based damage model to be used in finite element simulation, the implementation of which is unknown. For this proposal, both models were implemented within a commercial Finite Element software package, and their responses to local and non-local damage algorithms were assessed in depth through two standard benchmark tests: a plate with a hole and a ball burst. The results of this study indicate that, for a wide range of cases, such as in-plane stresses, out-plane stresses, stress concentration and contact, all over large displacement conditions, the López-Campos damage model shows a good response to non-local algorithms achieving mesh independence and convergence in all these cases. The results obtained are in line with those obtained for the Calvo's damage model, showing, in addition, larger deformations under in-plane stress and stress concentration conditions and a lower number of iterations under out-plane stress and contact conditions. Consequently, the López-Campos' damage model emerges as a valuable and useful tool in the field of mechanical damage research in biological systems.

Investigation of the ultrasound-induced collapse of air bubbles near soft materials.

A numerical investigation into the ultrasound-induced collapse of air bubbles near soft materials, utilizing a novel multi-material diffuse interface method (DIM) model with block-structured adaptive mesh refinement is presented. The present work expands from a previous five-equation DIM by incorporating Eulerian hyperelasticity. The model is applicable to any arbitrary number of interacting fluid and solid material. A single conservation law for the elastic stretch tensor enables tracking the deformations for all the solid materials. A series of benchmark cases are conducted, and the solution is found to be in excellent agreement against theoretical data. Subsequently, the ultrasound-induced bubble-tissue flow interactions are examined. The bubble radius was found to play a crucial role in dictating the stresses experienced by the tissue, underscoring its significance in medical applications. The results reveal that soft tissues primarily experience tensile forces during these interactions, suggesting potential tensile-driven injuries that may occur in relevant treatments. Moreover, regions of maximal tensile forces align with tissue elongation areas. It is documented that while early bubble dynamics remain relatively unaffected by changes in shear modulus, at later stages of the penetration processes and the deformation shapes, exhibit notable variations. Lastly, it is demonstrated that decreasing standoff distances enhances the interaction between bubbles and tissue, thereby increasing the stress levels in the tissue, although the behavior of the bubble dynamics remains largely unchanged.

A Novel Equivalent Method for Computing Mechanical Properties of Random and Ordered Hyperelastic Cellular Materials.

Simulating the mechanical behavior of cellular materials stands as a pivotal step in their practical application. Nonetheless, the substantial multitude of unit cells within these materials necessitates a considerable finite element mesh, thereby leading to elevated computational expenses and requisites for formidable computer configurations. In order to surmount this predicament, a novel and straightforward equivalent calculation method is proposed for the computation of mechanical properties concerning both random and ordered hyper-elastic cellular materials. By amalgamating the classical finite element approach with the distribution attributes of cells, the proposed equivalent calculation method adeptly captures the deformation modes and force-displacement responses exhibited by cell materials under tensile and shear loads, as predicted through direct numerical simulation. This approach reflects the deformation characteristics induced by micro-unit cells, elucidates an equivalent principle bridging cellular materials and equivalent materials, and substantially curtails exhaustive computational burdens. Ultimately, this method furnishes an equivalent computational strategy tailored for the engineering applications of cellular materials.

Simulating and Predicting the Mechanical Behavior of Electrospun Scaffolds for Cardiac Patches Fabrication.

Fabricating helical scaffolds using electrospinning is a common approach for cardiac implantation, aiming to achieve properties similar to native tissue. However, this process requires multiple experimental attempts to select suitable electrospun properties and validate resulting mechanical responses. To overcome the time and cost constraints associated with this iterative procedure, Finite Element Analysis (FEA) can be applied using stable hyperelastic and viscoelastic models that describe the response of electrospun scaffolds under different conditions. In this study, we aim to create accurate simulations of the viscoelastic behavior of electrospun helical scaffolds. We fabricated helical fibers from Poly (3-caprolactone) (PCL) using the electrospinning process to achieve this. The electrospun samples were subjected to uniaxial deformation, and their response was modelled using existing hyperelastic and stress relaxation models. The simulations were built on experimental data for specific deformation speed and maximum strain conditions. The FEM results were evaluated by accounting for the stress-softening phenomenon, which significantly impacted the models. The electrospun scaffolds' predictions were performed in other than the initial experimental conditions to verify our simulations' accuracy and reliability.

Inverse identification of region-specific hyperelastic material parameters for human brain tissue.

The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson's ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson's ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.

Simulation Analysis of Equibiaxial Tension Tests for Rubber-like Materials.

For rubber-like materials, there are three popular methods of equibiaxial tension available: inflation tension, equibiaxial planar tension, and radial tension. However, no studies have addressed the accuracy and comparability of these tests. In this work, we model the tension tests for a hyperelastic electroactive polymer (EAP) membrane material using finite element method (FEM) and investigate their experimental accuracy. This study also analyzes the impact of apparatus structure parameters and specimen dimensions on experimental performances. Additionally, a tensile efficiency is proposed to assess non-uniform deformation in equibiaxial planar tension and radial tension tests. The sample points for calculating deformation in inflation tensions should be taken near the top of the inflated balloon to obtain a more accurate characteristic curve; the deformation simulation range will be constrained by the material model and its parameters within a specific limit (λ ≈ 1.9); if the inflation hole size is halved, the required air pressure must be doubled to maintain equivalent stress and strain values, resulting in a reduction in half in inflation height and decreased accuracy. The equibiaxial planar tension test can enhance uniform deformation and reduce stress errors to as low as 2.1% (at λ = 4) with single-corner-point tension. For circular diaphragm specimens in radial tension tests, increasing the number of cuts and using larger punched holes results in more uniform deformation and less stress error, with a minimum value of 3.83% achieved for a specimen with 24 cuts and a 5 mm punched hole. In terms of tensile efficiency, increasing the number of tensile points in the equibiaxial planar tension test can improve it; under radial tension, increasing the number of cuts and decreasing the diameter of the punched hole on the specimen has a hedging effect. The findings of this study are valuable for accurately evaluating various equibiaxial tension methods and analyzing their precision, as well as providing sound guidance for the effective design of testing apparatus and test plans.

An Unusual Case of Ehlers-Danlos Syndrome Presenting as Proptosis.

Ehlers-Danlos syndrome (EDS) is a rare, heterogeneous group of genetic connective tissue disorders that affect collagen proteins. Currently, they are classified into 13 subtypes, many of which share general characteristics such as thin, hyperextensible skin and joint hypermobility. Vascular Ehlers-Danlos syndrome (vEDS) is characterized by tissue fragility, which predisposes individuals to premature arterial, uterine, or intestinal rupture. In this case, a young female presented with proptosis, skin hyperelasticity, and multiple joint dislocations. On computed tomography angiography (CTA), a direct caroticocavernous fistula, along with multiple segments of narrowing and ectasia in the internal carotid arteries and vertebral arteries, were detected, leading to a diagnosis of vEDS. This case report highlights the importance of clinical evaluation and the role of imaging in detecting this rare condition.

Automated model discovery for muscle using constitutive recurrent neural networks.

The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney-Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.