Heterogeneous Tissue Modulus Improved Prediction of Mechanical Behavior in Osteoporotic Vertebral Cancellous Bone

The structural integrity of cancellous bone, which is essential to skeletal load-bearing capacity, is governed chiefly by apparent density, trabecular architecture, and tissue material properties. Metabolic bone disorders such as osteoporosis can affect each of these factors separately, resulting in compromised load-bearing function. While the impact of apparent density and architecture on bone mechanical behavior has been well-documented, much less is known about the influence of tissue material properties, particularly in osteoporotic bone. The goal of the present study is to isolate the influence of tissue material properties on the pre-yield mechanical response of normal and osteoporotic cancellous bone to uniaxial compression using finite element (FE) models derived from 3D micro-computed tomography images. Both average tissue material properties and the degree of tissue material heterogeneity vary between individuals. Therefore, three sets of FE models were created to study the relative importance of these two factors: 1) models with material homogeneity within and between subjects, 2) models with material homogeneity within subjects only, and 3) models with material heterogeneity within and between subjects. The results of finite element analyses were compared to data gathered from physical testing with matched conditions. For normal bone, incorporating material heterogeneity within and between subjects had no significant effect on model performance. For osteoporotic bone, incorporating material heterogeneity within subjects did not affect model performance, but models that incorporated subject-specific average material properties were significantly more accurate in replicating the results of physical testing. We conclude that, while the influence of bone apparent density and trabecular architecture on apparent stiffness are dominant in healthy bone, average material properties also play a role in osteoporotic bone. Osteoporosis is diagnosed based on apparent density alone, so our findings suggest a need to consider other patient-specific differences that may affect average tissue material properties, such a bone remodeling rate, in clinical assessments of osteoporotic bone structural integrity.

Effect of Material Heterogeneity on Environmentally Assisted Cracking Growth Rate of Alloy 600 for Safe-End Welded Joints

Environmentally assisted cracking (EAC) is essential in predicting light water reactors’ structural integrity and service life. Alloy 600 (equivalent to Inconel 600) has excellent corrosion resistance and is often used as a welding material in welded joints, but material properties of the alloy are heterogeneous in the welded zone due to the complex welding process. To investigate the EAC crack growth behavior of Alloy 600 for safe-end welded joints, the method taken in this paper concerns the probability prediction of the EAC crack growth rate. It considers the material heterogeneity, combining the film slip-dissolution/oxidation model, and the elastic-plastic finite element method. The strain rate at the crack tip is a unique factor to describe the mechanical state. Still, it is challenging to accurately predict it because of the complicated and heterogeneous material microstructure. In this study, the effects of material heterogeneity on the EAC crack growth behavior are statistically analyzed. The results show that the material heterogeneity of Alloy 600 can not be ignored because it affects the prediction accuracy of the crack growth rate. The randomness of yield strength has the most influence on the EAC growth rate, while Poisson’s ratio has the smallest.

Geomechanical simulation of energy storage in salt formations

A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns. An elaborate sensitivity analysis of parameters involved with creep and damage constitutive laws is performed to understand the influence of creep and damage on deformation and stress evolution around the salt cavern configurations. The simulator developed in this work is publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/Salt_Cavern.

Calibration of a Heterogeneous Brain Model Using a Subject-Specific Inverse Finite Element Approach

Central to the investigation of the biomechanics of traumatic brain injury (TBI) and the assessment of injury risk from head impact are finite element (FE) models of the human brain. However, many existing FE human brain models have been developed with simplified representations of the parenchyma, which may limit their applicability as an injury prediction tool. Recent advances in neuroimaging techniques and brain biomechanics provide new and necessary experimental data that can improve the biofidelity of FE brain models. In this study, the CAB-20MSym template model was developed, calibrated, and extensively verified. To implement material heterogeneity, a magnetic resonance elastography (MRE) template image was leveraged to define the relative stiffness gradient of the brain model. A multi-stage inverse FE (iFE) approach was used to calibrate the material parameters that defined the underlying non-linear deviatoric response by minimizing the error between model-predicted brain displacements and experimental displacement data. This process involved calibrating the infinitesimal shear modulus of the material using low-severity, low-deformation impact cases and the material non-linearity using high-severity, high-deformation cases from a dataset of in situ brain displacements obtained from cadaveric specimens. To minimize the geometric discrepancy between the FE models used in the iFE calibration and the cadaveric specimens from which the experimental data were obtained, subject-specific models of these cadaveric brain specimens were developed and used in the calibration process. Finally, the calibrated material parameters were extensively verified using independent brain displacement data from 33 rotational head impacts, spanning multiple loading directions (sagittal, coronal, axial), magnitudes (20–40 rad/s), durations (30–60 ms), and severity. Overall, the heterogeneous CAB-20MSym template model demonstrated good biofidelity with a mean overall CORA score of 0.63 ± 0.06 when compared to in situ brain displacement data. Strains predicted by the calibrated model under non-injurious rotational impacts in human volunteers (N = 6) also demonstrated similar biofidelity compared to in vivo measurements obtained from tagged magnetic resonance imaging studies. In addition to serving as an anatomically accurate model for further investigations of TBI biomechanics, the MRE-based framework for implementing material heterogeneity could serve as a foundation for incorporating subject-specific material properties in future models.

Effect of material heterogeneity on the deformation behaviour of multidirectional (1D/2D/3D) functionally graded composite panels

Purpose The purpose of this study is the comprehensive numerical assessment of multidirectional (1D/2D/3D) functionally graded composite panel structures with different material gradation patterns and degrees of material heterogeneity. Here, deformation characteristics are obtained under different loading and support conditions. Design/methodology/approach The finite element solutions of multidirectional functionally graded composite panels subjected to uniform and sinusoidal transverse loads are presented under different support conditions. Here, different functionally graded composites, such as unidirectional (1D) and multidirectional (2D/3D), are considered by distributing constituent materials in one, two and three directions, respectively, using single and multivariable power-law functions. A constitutive model with fully spatial-dependent elastic stiffness is developed, whereas the kinematics of the present structure is defined using equivalent single-layer higher-order theory. The weak form, based on the principle of virtual work, is established and solved consequently using isoparametric finite element approximations via quadrilateral Lagrangian elements. Findings The appropriate mesh-refinement process is carried out to achieve the mesh convergence; whereas, the correctness of proposed heterogeneous model is confirmed through a verification test. The comprehensive numerical assessment of multidirectional functionally graded panels under various loading and support conditions depicts the importance of degree of material heterogeneity with different gradation patterns and volume-fraction exponents. Originality/value A comprehensive analysis on the deformation behaviour of 1D-functionally graded materials (FGMs) (X-FGM, Y-FGM and Z-FGM), 2D-FGMs (XY-FGM, YZ-FGM and XZ-FGM) and 3D-FGM composite panels FGM structures is presented. Multifaceted heterogeneous FGMs are modelled by varying constituent materials in one, two and three directions, using power-law functions. The constitutive model of multi-directional FGM is developed using fully spatial-dependent elastic matrix and higher-order kinematics. Isoparametric 2D finite element formulation is adopted using quadrilateral Lagrangian elements to model 1D/2D/3D-FGM structures and to obtain their deflection responses under different loading and support conditions.