Inverse Finite Element Analysis Research Articles

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

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.

Determining the Young's Modulus of the Bacterial Cell Envelope.

Bacteria experience substantial physical forces in their natural environment, including forces caused by osmotic pressure, growth in constrained spaces, and fluid shear. The cell envelope is the primary load-carrying structure of bacteria, but the mechanical properties of the cell envelope are poorly understood; reports of Young's modulus of the cell envelope of Escherichia coli range from 2 to 18 MPa. We developed a microfluidic system to apply mechanical loads to hundreds of bacteria at once and demonstrated the utility of the approach for evaluating whole-cell stiffness. Here, we extend this technique to determine Young's modulus of the cell envelope of E. coli and of the pathogens Vibrio cholerae and Staphylococcus aureus. An optimization-based inverse finite element analysis was used to determine the cell envelope Young's modulus from observed deformations. The Young's modulus values of the cell envelope were 2.06 ± 0.04 MPa for E. coli, 0.84 ± 0.02 MPa for E. coli treated with a chemical (A22) known to reduce cell stiffness, 0.12 ± 0.03 MPa for V. cholerae, and 1.52 ± 0.06 MPa for S. aureus (mean ± SD). The microfluidic approach allows examination of hundreds of cells at once and is readily applied to Gram-negative and Gram-positive organisms as well as rod-shaped and cocci cells, allowing further examination of the structural causes behind differences in cell envelope Young's modulus among bacterial species and strains.

Identification of material parameters at high strain rates using ballistic impact tests and inverse finite element analysis

Identification of material parameters at high strain rates using ballistic impact tests and inverse finite element analysis

An estimation of the biomechanical properties of the continent and incontinent woman bladder via inverse finite element analysis.

Stress urinary incontinence often results from pelvic support structures' weakening or damage. This dysfunction is related to direct injury of the pelvic organ's muscular, ligamentous or connective tissue structures due to aging, vaginal delivery or increase of the intra-abdominal pressure, for example, defecation or due to obesity. Mechanical changes alter the soft tissues' microstructural composition and therefore may affect their biomechanical properties. This study focuses on adapting an inverse finite element analysis to estimate the in vivo bladder's biomechanical properties of two groups of women (continent group (G1) and incontinent group (G2)). These properties were estimated based on MRI, by comparing measurement of the bladder neck's displacements during dynamic MRI acquired in Valsalva maneuver with the results from inverse analysis. For G2, the intra-abdominal pressure was adjusted after applying a 95% impairment to the supporting structures. The material parameters were estimated for the two groups using the Ogden hyperelastic constitutive model. Finite element analysis results showed that the bladder tissue of women with stress urinary incontinence have the highest stiffness (α1 = 0.202 MPa and µ1 = 7.720 MPa) approximately 47% higher when compared to continent women. According to the bladder neck's supero-inferior displacement measured in the MRI, the intra-abdominal pressure values were adjusted for the G2, presenting a difference of 20% (4.0 kPa for G1 and 5.0 kPa for G2). The knowledge of the pelvic structures' biomechanical properties, through this non-invasive methodology, can be crucial in the choice of the synthetic mesh to treat dysfunction when considering personalized options.

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

Analysis of transverse thermal conductivity for mesophase pitch-based carbon fibers and the through-thickness heat conduction of their composites

A quantitative analysis method for the transverse thermal conductivity (TC) of carbon fiber is developed, which consists of three steps including TC and morphology characterization of unidirectional composite laminate, fiber contour extraction, and finite element inverse analysis. Two different pitch-based carbon fibers with folded-radial and onion-skin microstructure are characterized, and the influences of fiber volume fraction and microstructure on the heat conduction of their composites are investigated. The equivalent transverse TCs of TC–HC–800 and PCF-1 carbon fibers are measured to be 9.27 and 2.87 W m−1 K−1, respectively. The through-thickness TC of unidirectional composite exhibits rapid growth with the increase in fiber volume fraction. The finite element analysis reveals that more continuous heat conduction paths are formed with the increase in fiber volume fraction. Benefited from the bigger graphitization degree, larger cross-sectional area, and bigger aspect ratio, TC–HC–800 unidirectional composite shows higher through-thickness TC than PCF-1 composite at the same fiber volume fraction.

Material properties in regenerating axolotl limbs using inverse finite element analysis

BackgroundThe extracellular mechanical environment plays an important role in the skeletal development process. Characterization of the material properties of regenerating tissues that recapitulate development, provides insights into the mechanical environment experienced by the cells and the maturation of the matrix. In this study, we estimated the viscoelastic material properties of regenerating forelimbs in the axolotl (Ambystoma mexicanum) at three different regeneration stages: 27 days post-amputation (mid-late bud) and 41 days post-amputation (palette stage), and fully-grown time points. A stress-relaxation indentation test followed by two-term Prony series viscoelastic inverse finite element analysis was used to obtain material parameters. Glycosaminoglycan (GAG) content was estimated using a 1,9- dimethyl methylene blue assay. ResultsThe instantaneous and equilibrium shear moduli significantly increased with regeneration while the short-term stress relaxation time significantly decreased with limb regeneration. The long-term stress relaxation time in the fully-grown time point was significantly lower than 27 and 41 DPA groups. The GAG content was not significantly different between 27 and 41 DPA but the GAG content of cartilage in the fully-grown group was significantly greater than in 27 and 41 DPA. ConclusionsThe mechanical environment of the proliferating cells changes drastically during limb regeneration. Understanding how the tissue's mechanical properties change during limb regeneration is critical for linking molecular-level matrix production of the cells to tissue-level behavior and mechanical signals.

Characterizing atherosclerotic tissues: in silico analysis of mechanical properties using intravascular ultrasound and inverse finite element methods.

Atherosclerosis is a prevalent cause of acute coronary syndromes that consists of lipid deposition inside the artery wall, creating an atherosclerotic plaque. Early detection may prevent the risk of plaque rupture. Nowadays, intravascular ultrasound (IVUS) is the most common medical imaging technology for atherosclerotic plaque detection. It provides an image of the section of the coronary wall and, in combination with new techniques, can estimate the displacement or strain fields. From these magnitudes and by inverse analysis, it is possible to estimate the mechanical properties of the plaque tissues and their stress distribution. In this paper, we presented a methodology based on two approaches to characterize the mechanical properties of atherosclerotic tissues. The first approach estimated the linear behavior under particular pressure. In contrast, the second technique yielded the non-linear hyperelastic material curves for the fibrotic tissues across the complete physiological pressure range. To establish and validate this method, the theoretical framework employed in silico models to simulate atherosclerotic plaques and their IVUS data. We analyzed different materials and real geometries with finite element (FE) models. After the segmentation of the fibrotic, calcification, and lipid tissues, an inverse FE analysis was performed to estimate the mechanical response of the tissues. Both approaches employed an optimization process to obtain the mechanical properties by minimizing the error between the radial strains obtained from the simulated IVUS and those achieved in each iteration. The second methodology was successfully applied to five distinct real geometries and four different fibrotic tissues, getting median R 2 of 0.97 and 0.92, respectively, when comparing the real and estimated behavior curves. In addition, the last technique reduced errors in the estimated plaque strain field by more than 20% during the optimization process, compared to the former approach. The findings enabled the estimation of the stress field over the hyperelastic plaque tissues, providing valuable insights into its risk of rupture.

Fracture toughness evaluation of a nuclear graphite with non-linear elastic properties by 3D imaging and inverse finite element analysis

Effective small specimen tests are needed to obtain fracture toughness and elastic properties as the limited availability of irradiated graphite restricts the quantity and dimensions of test specimens. Both properties have evaluated simultaneously in a crack propagation test with the double cleavage drilled compression (DCDC) specimen geometry of a fine-grained graphite (SNG742) that has non-linear elastic properties in the unirradiated condition. Three-dimensional displacement fields were obtained by digital volume correlation of in situ laboratory X-ray computed tomographs, and the 3D crack geometry (crack tip position, crack opening displacements and angle) was determined objectively by a wavelet variance method. The tensile softening of the Young modulus was determined by inverse analysis of the strain field using the finite element model updating (FEMU) method. The strain energy release rate of the quasi-static propagating crack was calculated using the contour integral method in a finite element model with the derived non-linear elastic properties and the measured displacements as boundary conditions. The critical strain energy release rate was constant with crack length (118 ± 14 J m−2) and equivalent to a fracture toughness of 1.13 ± 0.07 MPa m1/2.

Biomechanical Characterisation of Thoracic Ascending Aorta with Preserved Pre-Stresses.

Mechanical properties of an aneurysmatic thoracic aorta are potential markers of future growth and remodelling and can help to estimate the risk of rupture. Aortic geometries obtained from routine medical imaging do not display wall stress distribution and mechanical properties. Mechanical properties for a given vessel may be determined from medical images at different physiological pressures using inverse finite element analysis. However, without considering pre-stresses, the estimation of mechanical properties will lack accuracy. In the present paper, we propose and evaluate a mechanical parameter identification technique, which recovers pre-stresses by determining the zero-pressure configuration of the aortic geometry. We first validated the method on a cylindrical geometry and subsequently applied it to a realistic aortic geometry. The verification of the assessed parameters was performed using synthetically generated reference data for both geometries. The method was able to estimate the true mechanical properties with an accuracy ranging from 98% to 99%.

Assessment of residual stresses in welded T-joints using contour method

Welded T-joints are commonly used in manufacturing of stiffened panels or crossbeams. However, welding of web-to-flange joint induces residual stresses and distortions resulting in significant challenges during both manufacturing and service. These issues can ultimately impact the structural performance, including fatigue and stability, and lifetime of the weldment. The purpose of current paper is determining the distribution and magnitude of manufacturing-induced longitudinal residual stresses in welded T-joints. Influence of hot rolling, thermal cutting, prestressing, welding, etc. are all included using the so-called contour method. Deformed surfaces are measured using coordinate measuring machine after wire electrical discharge machining of specimens. An inverse linear elastic finite element analysis is carried out for assessing residual stresses after data smoothing. Two-dimensional longitudinal residual stress patterns are evaluated in representative cross-sections clearly indicating high stress peaks near the welds, even exceeding yield strength of the base material. In addition, longitudinal membrane residual stresses are determined based on through-thickness stresses. In addition, a simplified residual stress model, satisfying the requirement for equilibrium of internal forces and bending moments, is developed for welded T-joints with double-sided fillet welds based on contour method results.

Viscoelastic properties of porcine lenses using optical coherence elastography and inverse finite element analysis

The mechanical properties of the crystalline lens are crucial in determining the changes in lens shape that occur during the accommodation process and are also a major factor in the development of the two most prevalent age-related diseases of the lens, presbyopia and cataracts. However, a comprehensive understanding of these properties is currently lacking. Previous methods for characterizing the mechanical properties of the lens have been limited by the amount of data that could be collected during each test and the lack of complex material modeling. These limitations were mainly caused by the lack of imaging techniques that can provide data for the entire crystalline lens and the need for more complex models to describe the non-linear behavior of the lens. To address these issues, we characterized the mechanical properties of 13 porcine lenses during an ex vivo micro-controlled-displacement compression experiment using optical coherence elastography (OCE) and inverse finite element analysis (iFEA). OCE allowed us to quantify the internal strain distribution of the lens and differentiate between the different parts of the lens, while iFEA enabled us to implement an advanced material model to characterize the viscoelasticity of the lens nucleus and the relative stiffness gradient in the lens. Our findings revealed a pronounced and rapid viscoelastic behavior in the lens nucleus (g1 = 0.39 ± 0.13, τ1 = 5.01 ± 2.31 s) and identified the lens nucleus as the stiffest region, with a stiffness 4.42 ± 1.20 times greater than the anterior cortex and 3.47 ± 0.82 times greater than the posterior cortex. However, due to the complex nature of lens properties, it may be necessary to employ multiple tests simultaneously for a more comprehensive understanding of the crystalline lens.

A finite porous-viscoelastic model capturing mechanical behavior of human cervix under multi-step spherical indentation

The cervix is a soft tissue exhibiting time-dependent behavior under mechanical loads. The cervix is a vital mechanical barrier to protect the growing fetus. The remodeling of the cervical tissue, characterized by an increase in time-dependent material properties, is necessary for a safe parturition. The failure of its mechanical function and accelerated tissue remodeling is hypothesized to lead to preterm birth, which is birth before 37 weeks of gestation. To understand the mechanism of the time-dependent behavior of the cervix under compressive states, we employ a porous-viscoelastic material model to describe a set of spherical indentation tests performed on nonpregnant and term pregnant tissue. A genetic algorithm-based inverse finite element analysis is used to fit the force-relaxation data by optimizing the material parameters, and the statistical analysis of the optimized material parameters is conducted on different sample groups. The force response is captured well using the porous-viscoelastic model. The indentation force-relaxation of the cervix is explained by the porous effects and the intrinsic viscoelastic properties of the extracellular matrix (ECM) microstructure. The hydraulic permeability obtained from the inverse finite element analysis agrees with the trend of the value directly measured previously by our group. The nonpregnant samples are found significantly more permeable than the pregnant samples. Within nonpregnant samples, the posterior internal os is found significantly less permeable than the anterior and posterior external os. The proposed model exhibits the superior capability to capture the force-relaxation response of the cervix under indentation, as compared to the conventional quasi-linear viscoelastic framework (range of r2 of the porous-viscoelastic model 0.88–0.98 vs. quasi-linear model: 0.67–0.89). As a constitutive model with a relatively simple form, the porous-viscoelastic framework has the potential to be used to understand disease mechanisms of premature cervical remodeling, model contact of the cervix with biomedical devices, and interpret force readings from novel in-vivo measurement tools such as an aspiration device.

Additively manufactured polyethylene terephthalate scaffolds for scapholunate interosseous ligament reconstruction

The regeneration of the ruptured scapholunate interosseous ligament (SLIL) represents a clinical challenge. Here, we propose the use of a Bone-Ligament-Bone (BLB) 3D-printed polyethylene terephthalate (PET) scaffold for achieving mechanical stabilisation of the scaphoid and lunate following SLIL rupture. The BLB scaffold featured two bone compartments bridged by aligned fibres (ligament compartment) mimicking the architecture of the native tissue. The scaffold presented tensile stiffness in the range of 260 ± 38 N/mm and ultimate load of 113 ± 13 N, which would support physiological loading. A finite element analysis (FEA), using inverse finite element analysis (iFEA) for material property identification, showed an adequate fit between simulation and experimental data. The scaffold was then biofunctionalized using two different methods: injected with a Gelatin Methacryloyl solution containing human mesenchymal stem cell spheroids (hMSC) or seeded with tendon-derived stem cells (TDSC) and placed in a bioreactor to undergo cyclic deformation. The first approach demonstrated high cell viability, as cells migrated out of the spheroid and colonised the interstitial space of the scaffold. These cells adopted an elongated morphology suggesting the internal architecture of the scaffold exerted topographical guidance. The second method demonstrated the high resilience of the scaffold to cyclic deformation and the secretion of a fibroblastic related protein was enhanced by the mechanical stimulation. This process promoted the expression of relevant proteins, such as Tenomodulin (TNMD), indicating mechanical stimulation may enhance cell differentiation and be useful prior to surgical implantation. In conclusion, the PET scaffold presented several promising characteristics for the immediate mechanical stabilisation of disassociated scaphoid and lunate and, in the longer-term, the regeneration of the ruptured SLIL.

Validating MRI-Derived Myocardial Stiffness Estimates Using In Vitro Synthetic Heart Models.

Impaired cardiac filling in response to increased passive myocardial stiffness contributes to the pathophysiology of heart failure. By leveraging cardiac MRI data and ventricular pressure measurements, we can estimate in vivo passive myocardial stiffness using personalized inverse finite element models. While it is well-known that this approach is subject to uncertainties, only few studies quantify the accuracy of these stiffness estimates. This lack of validation is, at least in part, due to the absence of ground truth in vivo passive myocardial stiffness values. Here, using 3D printing, we created soft, homogenous, isotropic, hyperelastic heart phantoms of varying geometry and stiffness and simulate diastolic filling by incorporating the phantoms into an MRI-compatible left ventricular inflation system. We estimate phantom stiffness from MRI and pressure data using inverse finite element analyses based on a Neo-Hookean model. We demonstrate that our identified softest and stiffest values of 215.7 and 512.3kPa agree well with the ground truth of 226.2 and 526.4kPa. Overall, our estimated stiffnesses revealed a good agreement with the ground truth ([Formula: see text] error) across all models. Our results suggest that MRI-driven computational constitutive modeling can accurately estimate synthetic heart material stiffnesses in the range of 200-500kPa.

Reduction of wrinkles: From a computational hypothesis to a clinical, instrumental, and biological proof.

Facial wrinkles are clear markers of the aging process, being chronological, photo-induced, or reflecting repetitive facial expressions. The aim of this study is to provide new insights into the biophysical and biological mechanisms involved in the formation, prevention, or elimination of the expression wrinkles. We use a computational model to get a better understanding of the wrinkle mechanical behavior and evolution after skin softening and suggesting a possible antiaging mechanism. Then, we provide a clinical demonstration of the anti-wrinkle effect of a long-term application of a 20% glycerol in a moisturizer formula (GBM) versus its vehicle on crow's feet. Skin hydration, elasticity, and wrinkles visibility were evaluated by a combination of clinical and instrumental in vivo data, inverse finite element analysis, and proteomic data. The computational model shows a predominantly compressive stress beneath the wrinkle and its significant decrease by the softening of stratum corneum. The associated clinical study confirmed a significant increase of skin hydration and elasticity as well as a decrease of wrinkle visibility after 2 and 4 months as application for both formulas; this effect being stronger for GBM. A softening effect on stratum corneum and dermis was also observed for the GBM. Furthermore, proteomic data revealed an effect of upregulation of four proteins associated with desquamation, cell-glycan extracellular interactions, and protein glycation/oxidation, functions related to the tissue mechanics and adhesion. We provide an in vivo demonstration of the anti-ageing benefit of glycerol at high dose (20%) reflected by a cumulative skin surface softening effect. The use of high moisturizing potent formulations should bring additional performance to other conventional moisturizing formulations.

Identifiability of soft tissue constitutive parameters from in-vivo macro-indentation

Reliable identification of soft tissue material parameters is frequently required in a variety of applications, particularly for biomechanical simulations using finite element analysis (FEA). However, determining representative constitutive laws and material parameters is challenging and often comprises a bottleneck that hinders the successful implementation of FEA. Soft tissues exhibit a nonlinear response and are commonly modeled using hyperelastic constitutive laws. In-vivo material parameter identification, for which standard mechanical tests (e.g., uniaxial tension and compression) are inapplicable, is commonly achieved using finite macro-indentation test. Due to the lack of analytical solutions, the parameters are commonly identified using inverse FEA (iFEA), in which simulated results and experimental data are iteratively compared. However, determining what data must be collected to accurately identify a unique parameter set remains unclear. This work investigates the sensitivities of two types of measurements: indentation force-depth data (e.g., measured using an instrumented indenter) and full-field surface displacements (e.g., using digital image correlation). To eliminate model fidelity and measurement-related errors, we employed an axisymmetric indentation FE model to produce synthetic data for four 2-parameter hyperelastic constitutive laws: compressible Neo-Hookean, and nearly incompressible Mooney-Rivlin, Ogden, and Ogden-Moerman models. For each constitutive law, we computed the objective functions representing the discrepancies in the reaction force, the surface displacement, and their combination, and visualized them for hundreds of parameter sets, spanning a representative range as found in the literature for the bulk soft tissue complex in human lower limbs. Moreover, we quantified three identifiability metrics, which provided insights into the uniqueness (or lack thereof) and the sensitivities. This approach provides a clear and systematic evaluation of the parameter identifiability, which is independent of the selection of the optimization algorithm and initial guesses required in iFEA. Our analysis indicated that the indenter’s force-depth data, despite being commonly used for parameter identification, was insufficient for reliably and accurately identifying both parameters for all the investigated material models and that the surface displacement data improved the parameter identifiability in all cases, although the Mooney-Rivlin parameters remained poorly identifiable. Informed by the results, we then discuss several identification strategies for each constitutive model. Finally, we openly provide the codes used in this study, to allow others to further investigate the indentation problem according to their specifications (e.g., by modifying the geometries, dimensions, mesh, material models, boundary conditions, contact parameters, or objective functions).

Response of thin walled transversely stiffened clamped circular plates under uniform impulsive loads

Paper presents numerical models based on detailed characterization of various uncoupled damage models in a finite element analysis (FEA) setup to assess large deformations and observed ductile fracture failure modes of fully clamped circular plates as well as transversely stiffened circular plates in cross stiffened configurations under uniform impulsive loads. The numerical schemes have been based on a detailed definition of the constitutive properties based on inverse FEA simulations of the uniaxial tension test for the calibration of material and failure parameters. Experiments have been conducted using two types of freshly prepared mild steel uniaxial tension test specimens covering the envisaged range of stress tri-axialities to establish the steel plate material and fracture characteristics necessary for the calibration of the presented phenomenological damage models. Published results based on extensive experimental works by various authors on response of thin walled clamped circular plates under transversely applied uniform air blast loads, manifesting in large plastic deformations, thinning and tearing under various ductile fracture modes, have been used in the performance assessment of presented numerical models and procedure, which incorporate different damage models including temperature effects due to plastic dissipation. Based on evaluated performance of the discussed failure models within the FEA setup, a hybrid damage model with a tri-axiality based two part ductile fracture locus has been proposed, which shows very good correlation with the published experimental results, presented in terms of non-dimensional parameters over a wide range of impulsive loading. The validated numerical setup using the proposed hybrid damage model has also been used to predict the effect of transverse cross stiffened configurations of flat bar stiffeners on large deformations and ductile fracture of clamped circular plates under transverse uniform impulsive blast loads, along with some key insights in the evolution of plastic zones and damage progression.

Constitutive parameter identification of transtibial residual limb soft tissue using ultrasound indentation and shear wave elastography

Finite element analysis (FEA) can be used to evaluate applied interface pressures and internal tissue strains for computational prosthetic socket design. This type of framework requires realistic patient-specific limb geometry and constitutive properties. In recent studies, indentations and inverse FEA with MRI-derived 3D patient geometries were used for constitutive parameter identification. However, long computational times and use of specialized equipment presents challenges for clinical, deployment. In this study, we present a novel approach for constitutive parameter identification using a combination of FEA, ultrasound indentation, and shear wave elastography. Local shear modulus measurement using elastography during an ultrasound indentation experiment has particular significance for biomechanical modeling of the residual limb since there are known regional dependencies of soft tissue properties such as varying levels of scarring and atrophy. Beyond prosthesis design, this work has broader implications to the fields of muscle health and monitoring of disease progression.