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Mechanics are increasingly recognized to play an important role in modulating brain form and function. Computational simulations are a powerful tool to predict the mechanical behavior ...of the human brain in health and disease. The success of these simulations depends critically on the underlying constitutive model and on the reliable identification of its material parameters. Thus, there is an urgent need to thoroughly characterize the mechanical behavior of brain tissue and to identify mathematical models that capture the tissue response under arbitrary loading conditions. However, most constitutive models have only been calibrated for a single loading mode. Here, we perform a sequence of multiple loading modes on the same human brain specimen – simple shear in two orthogonal directions, compression, and tension – and characterize the loading-mode specific regional and directional behavior. We complement these three individual tests by combined multiaxial compression/tension-shear tests and discuss effects of conditioning and hysteresis. To explore to which extent the macrostructural response is a result of the underlying microstructural architecture, we supplement our biomechanical tests with diffusion tensor imaging and histology. We show that the heterogeneous microstructure leads to a regional but not directional dependence of the mechanical properties. Our experiments confirm that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry. Using our measurements, we compare the performance of five common constitutive models, neo-Hookean, Mooney-Rivlin, Demiray, Gent, and Ogden, and show that only the isotropic modified one-term Ogden model is capable of representing the hyperelastic behavior under combined shear, compression, and tension loadings: with a shear modulus of 0.4–1.4kPa and a negative nonlinearity parameter it captures the compression-tension asymmetry and the increase in shear stress under superimposed compression but not tension. Our results demonstrate that material parameters identified for a single loading mode fail to predict the response under arbitrary loading conditions. Our systematic characterization of human brain tissue will lead to more accurate computational simulations, which will allow us to determine criteria for injury, to develop smart protection systems, and to predict brain development and disease progression.
There is a pressing need to characterize the mechanical behavior of human brain tissue under multiple loading conditions, and to identify constitutive models that are able to capture the tissue response under these conditions. We perform a sequence of experimental tests on the same brain specimen to characterize the regional and directional behavior, and we supplement our tests with DTI and histology to explore to which extent the macrostructural response is a result of the underlying microstructure. Results demonstrate that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry, and we show that the multiaxial data can best be captured by a modified version of the one-term Ogden model.
The objective of this contribution is to formulate a geometrically nonlinear theory of higher-gradient elasticity accounting for boundary (surface and curve) energies. Surfaces and curves can ...significantly influence the overall response of a solid body. Such influences are becoming increasingly important when modeling the response of structures at the nanoscale. The behavior of the boundaries is well described by continuum theories that endow the surface and curve with their own energetic structures. Such theories often allow the boundary energy density to depend only on the superficial boundary deformation gradient. From a physical point of view though, it seems necessary to define the boundary deformation gradient as the evaluation of the deformation gradient at the boundary rather than its projection. This controversial issue is carefully studied and several conclusions are extracted from the rigorous mathematical framework presented.
In this manuscript the internal energy density of the bulk is a function of the deformation gradient and its first and second derivatives. The internal energy density of the surface is, consequently, a function of the deformation gradient at the surface and its first derivative. The internal energy density of a curve is, consequently, a function of the deformation gradient at the curve.
It is shown that in order to have a surface energy depending on the total (surface) deformation gradient, the bulk energy needs to be a function of at least the first derivative of the deformation gradient. Furthermore, in order to have a curve energy depending on the total (curve) deformation gradient, the bulk energy needs to be a function of at least the second derivative of the deformation gradient. Clearly, the surface elasticity theory of Gurtin and Murdoch is intrinsically limited since it is associated with the classical (first-order) continuum theory of elasticity in the bulk. In this sense this contribution shall be also understood as a higher-gradient surface elasticity theory.
Computational homogenization in magneto-mechanics Javili, A.; Chatzigeorgiou, G.; Steinmann, P.
International journal of solids and structures,
December 2013, 2013-12-00, 20131201, 2013-12, Letnik:
50, Številka:
25-26
Journal Article
Recenzirano
Odprti dostop
This work presents a geometrically nonlinear homogenization framework for composites with magneto-mechanical behavior whereby the composite can be subject to large deformation processes. The ...magneto-mechanical governing equations in the material description for both the overall body and its microstructure are presented, and the connections between micro- and macro-scale field variables are identified. Considering periodic boundary conditions for the microscopic unit cell, a finite element framework for computing the macroscopic field variables and the effective tangent moduli is developed. The proposed methodology is utilized to study a variety of two- and three-dimensional numerical examples. In particular, the behavior of fiber and particle reinforced composites with magneto-mechanical constitutive laws are illustrated. Finally, a specific physically motivated problem of a magnetorheological elastomer, consisting of a polymer matrix and iron particles, under finite deformation and applied magnetic field is analyzed and the results are given for several combinations of deformation modes and applied magnetic fields.
The main objective of this contribution is to develop a novel continuum-kinematics-inspired approach for peridynamics (PD), and to revisit PD’s thermodynamic foundations. We distinguish between three ...types of interactions, namely, one-neighbour interactions, two-neighbour interactions and three-neighbour interactions. While one-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism, two- and three-neighbour interactions are fundamentally different to state-based interactions in that the basic elements of continuum kinematics are preserved exactly. In addition, we propose that an externally prescribed traction on the boundary of the continuum body emerges naturally and need not vanish. This is in contrast to, but does not necessarily violate, standard PD. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interactions accordingly. Furthermore, we elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically-consistent constitutive laws through a Coleman–Noll-like procedure.
Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. CPD can ...capture the Poisson effect exactly, unlike the original formulation of peridynamics (PD). Due to its geometrically exact nature, CPD does not suffer from zero-energy modes and displacement oscillations that may be observed in state-based PD formulations. For a two-dimensional analysis, CPD builds upon one-neighbor and two-neighbor interactions. The one-neighbor interactions of CPD are equivalent to the bond-based interactions of the original PD formalism. Two-neighbor interactions, however, are key in CPD since the basic notions of classical continuum kinematics, namely length and area, are preserved exactly. The isotropic two-dimensional CPD formulation of non-local elasticity therefore involves two material constants, namely C1 and C2, associated with length and area, respectively. This manuscript aims to establish relationships between the material parameters of CPD and isotropic linear elasticity for an affine deformation in a two-dimensional setting. It is shown that each of the CPD material parameters can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. Finally, we establish the admissible ranges for CPD material parameters.
Reducing rotator cuff failure after repair remains a challenge due to suboptimal tendon-to-bone healing. In this study we report a novel biomaterial with engineered tendon-fibrocartilage-bone ...composite (TFBC) and bone marrow-derived mesenchymal stem cell sheet (BMSCS); this construct was tested for augmentation of rotator cuff repair using a canine non-weight-bearing (NWB) model. A total of 42 mixed-breed dogs were randomly allocated to 3 groups (n = 14 each). Unilateral infraspinatus tendon underwent suture repair only (control); augmentation with engineered TFBC alone (TFBC), or augmentation with engineered TFBC and BMSCS (TFBC + BMSCS). Histomorphometric analysis and biomechanical testing were performed at 6 weeks after surgery. The TFBC + BMSCS augmented repairs demonstrated superior histological scores, greater new fibrocartilage formation and collagen fiber organization at the tendon-bone interface compared with the controls. The ultimate failure load and ultimate stress were 286.80 ± 45.02 N and 4.50 ± 1.11 MPa for TFBC + BMSCS group, 163.20 ± 61.21 N and 2.60 ± 0.97 MPa for control group (TFBC + BMSCS vs control, P = 1.12E-04 and 0.003, respectively), 206.10 ± 60.99 N and 3.20 ± 1.31 MPa for TFBC group (TFBC + BMSCS vs TFBC, P = 0.009 and 0.045, respectively). In conclusion, application of an engineered TFBC and BMSCS can enhance rotator cuff healing in terms of anatomic structure, collagen organization and biomechanical strength in a canine NWB model. Combined TFBC and BMSCS augmentation is a promising strategy for rotator cuff tears and has a high potential impact on clinical practice.
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Brain stiffness plays an important role in neuronal development and disease, but reported stiffness values vary significantly for different species, for different brains, and even for ...different regions within the same brain. Despite extensive research throughout the past decade, the mechanistic origin of these stiffness variations remains elusive. Here we show that brain tissue stiffness is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. In 116 indentation tests of six freshly harvested bovine brains, we found that the cerebral stiffnesses of 1.33±0.63kPa in white matter and 0.68±0.20kPa in gray matter were significantly different (p<0.01). Strikingly, while the inter-specimen variation was rather moderate, the minimum and maximum cerebral white matter stiffnesses of 0.59±0.19 kPa and 2.36±0.64kPa in each brain varied by a factor of four on average. To provide a mechanistic interpretation for this variation, we performed a histological characterization of the tested brain regions. We stained the samples with hematoxylin and eosin and luxol fast blue and quantified the local myelin content using image analysis. Interestingly, we found that the cerebral white matter stiffness increased with increasing myelin content, from 0.72kPa at a myelin content of 64–2.45kPa at a myelin content of 89%, with a Pearson correlation coefficient of ρ=0.91 (p<0.01). This direct correlation could have significant neurological implications. During development, our results could help explain why immature, incompletely myelinated brains are softer than mature, myelinated brains and more vulnerable to mechanical insult as evident, for example, in shaken baby syndrome. During demyelinating disease, our findings suggest to use stiffness alterations as clinical markers for demyelination to quantify the onset of disease progression, for example, in multiple sclerosis. Taken together, our study indicates that myelin might play a more important function than previously thought: It not only insulates signal propagation and improves electrical function of single axons, it also provides structural support and mechanical stiffness to the brain as a whole.
Increasing evidence suggests that the mechanical environment of the brain plays an important role in neuronal development and disease. Reported stiffness values vary significantly, but the origin of these variations remains unknown. Here we show that stiffness of our brain is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. Myelin has been discovered in 1854 as an insulating layer around nerve cells to improve electric signal propagation. Our study now shows that it also plays an important mechanical role: Using a combined mechanical characterization and histological characterization, we found that the white matter stiffness increases linearly with increasing myelin content, from 0.5kPa at a myelin content of 63–2.5kPa at 92%.
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