Phase-field models based on the variational formulation for brittle fracture have recently been shown capable of accurately and robustly predicting complex crack behavior. Their numerical ...implementation requires costly operations at the quadrature point level, which may include finding eigenvalues and forming tensor projection operators. We explore the application of isogeometric collocation methods for the discretization of second-order and fourth-order phase-field fracture models. We show that a switch from isogeometric Galerkin to isogeometric collocation methods has the potential to significantly speed up phase-field fracture computations due to a reduction of point evaluations. We advocate a hybrid collocation–Galerkin formulation that provides a consistent way of weakly enforcing Neumann boundary conditions and multi-patch interface constraints, is able to handle the multiple boundary integral terms that arise from the weighted residual formulation, and offers the flexibility to adaptively improve the crack resolution in the fracture zone. We present numerical examples in one and two dimensions that illustrate the advantages of our approach.
•Isogeometric collocation can significantly speed up phase-field fracture computations.•We advocate a hybrid collocation–Galerkin formulation.•It handles Neumann boundary and multi-patch conditions, and higher-order boundary terms.•The adaptive Galerkin resolution of the fracture zone is crucial for accuracy and efficiency.
A two-dimensional problem of multiple interacting circular nano-inhomogeneities or/and nano-pores is considered. The analysis is based on the Gurtin and Murdoch model Gurtin, M.E., Murdoch, A.I., ...1975. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323. in which the interfaces between the nano-inhomogeneities and the matrix are regarded as material surfaces that possess their own mechanical properties and surface tension. The precise component forms of Gurtin and Murdoch's three-dimensional equations are derived for interfaces of arbitrary shape to provide a basis for critical review of various modifications used in the literature. The two-dimensional specification of these equations is considered and their representation in terms of complex variables is provided. A semi-analytical method is proposed to solve the problem. Solutions to several example problems are presented to: (i) examine the difference between the results obtained with the original and modified Gurtin and Murdoch's equations, (ii) compare the results obtained using Gurtin and Murdoch's model and those for a problem of nano-inhomogeneities with thin membrane-type interphase layers, and (iii) demonstrate the effectiveness of the approach in solving problems with multiple nano-inhomogeneities.
In this article, we explore an embedded shell finite element method for the unfitted discretization of solid–shell interaction problems. Its core component is a variationally consistent approach that ...couples a shell discretization on the surface of an embedded solid domain to its unfitted discretization with hexahedral solid elements. Derived via an augmented Lagrangian formulation and the formal elimination of interface Lagrange multipliers, our method depends only on displacement variables, facilitated by a shift of the displacement-dependent traction vector entirely to the solid structure. We demonstrate that the weighted least squares term required for stability of the formulation triggers severe surface locking due to a mismatch in the polynomial spaces of the shell element and the embedding solid element. We show that reduced quadrature of the stabilization term that evaluates the kinematic constraint at the nodes of the embedded shell elements completely mitigates surface locking. For coarse discretizations, our variationally consistent method achieves superior accuracy with respect to a locking-free nodal penalty method. We illustrate the versatility of embedded shell finite elements for image-based analysis, including patient-specific stress prediction in a vertebra and local rind buckling in a plant structure.
•We couple a shell mesh on the surface of an embedded solid domain to its unfitted volumetric mesh.•The variationally consistent formulation depends only on displacement variables.•Its stabilization term triggers surface locking due to a polynomial mismatch between shell and solid elements.•Reduced quadrature of the stabilization term mitigates surface locking.•We present two use cases: patient-specific stress prediction in a vertebra and local rind buckling in a plant structure.
A new technique is presented for evaluating the effective properties of linearly elastic, multi-phase unidirectional composites. Various effects on the fiber/matrix interfaces (perfect bond, ...homogeneously imperfect interfaces, uniform interphase layers) are allowed. The analysis of nano-composite materials based on the Gurtin and Murdoch model of material surface is also included. The basic idea of the approach is to construct a circular inhomogeneity in an infinite plane whose effects on the displacements and stresses at distant points are the same as those of a finite cluster of inhomogeneities (fibers of circular cross-section) arranged in a pattern representative of the composite material in question. The elastic properties of the equivalent inhomogeneity then define the effective elastic properties of the material. The volume ratio of the composite material is found after the size of the equivalent circular inhomogeneity is defined in the course of the solution procedure. This procedure is based on a semi-analytical solution of a problem of an infinite plane containing a cluster of non-overlapping circular inhomogeneities subjected to loading at infinity. The method works equally well for periodic and random composites and – importantly – eliminates the necessity for averaging either stresses or strains. New results for nano-composite materials are presented.
The effects of surface elasticity and surface tension on the transverse overall behavior of unidirectional nano-scale fiber-reinforced composites are studied. The interfaces between the nano-fibers ...and the matrix are regarded as material surfaces described by the Gurtin and Murdoch model. The analysis is based on the equivalent inhomogeneity technique. In this technique, the effective elastic properties of the material are deduced from the analysis of a small cluster of fibers embedded into an infinite plane. All interactions between the inhomogeneities in the cluster are precisely accounted for. The results related to the effects of surface elasticity are compared with those provided by the modified generalized self-consistent method, which only indirectly accounts for the interactions between the inhomogeneities. New results related to the effects of surface tension are presented. Although the approach employed is applicable to all transversely isotropic composites, in this paper we consider only a hexagonal arrangement of circular cylindrical fibers.
The concept of Maxwell's equivalent inhomogeneity is re-evaluated in the context of the effective elastic properties of unidirectional multi-phase composite materials with the fibers of circular ...cross-section. The following key questions are addressed in this paper. Is the concept of equivalent inhomogeneity valid only for the materials with low volume fractions, as originally suggested by Maxwell? When do the interactions among the fibers matter? Could Maxwell's concept be generalized to allow for accurate estimates of the effective properties? The approach advocated in the paper provides an unique opportunity to study, in the framework of one model, the effects of the interactions among fibers on the effective transversely isotropic elastic properties of multi-phase composite materials.
A complete solution has been obtained for the problem of multiple interacting spherical inhomogeneities with a Gurtin–Murdoch interface model that includes both surface tension and surface stiffness ...effects. For this purpose, a vectorial spherical harmonics-based analytical technique is developed. This technique enables solution of a wide class of elasticity problems in domains with spherical boundaries/interfaces and makes fulfilling the vectorial boundary or interface conditions a routine procedure. A general displacement solution of the single-inhomogeneity problem is sought in a form of a series of the vectorial solutions of the Lame equation. This solution is valid for any non-uniform far-field load and it has a closed form for polynomial loads. The superposition principle and re-expansion formulas for the vectorial solutions of the Lame equation extend this theory to problems involving multiple inhomogeneities. The developed semi-analytical technique precisely accounts for the interactions between the nanoinhomogeneities and constitutes an efficient computational tool for modeling nanocomposites. Numerical results demonstrate the accuracy and numerical efficiency of the approach and show the nature and extent to which the elastic interactions between the nanoinhomogeneities with interface stress affect the elastic fields around them.
► Interacting spherical nanoinhomogeneities with Gurtin–Murdoch interface are studied. ► The vector spherical harmonics-based analytical technique of solution is developed. ► The technique precisely accounts for the interactions between the inhomogeneities. ► Numerical results demonstrate an accuracy and numerical efficiency of the approach. ► Interface stress greatly affects the elastic fields around the nanoinhomogeneities.
A multiphysics model of the Pacinian corpuscle Quindlen, Julia C; Stolarski, Henryk K; Johnson, Matthew D ...
Integrative biology (Cambridge),
11/2016, Letnik:
8, Številka:
11
Journal Article
Recenzirano
The Pacinian corpuscle (PC) is a dermal mechanoreceptor that responds to high-frequency (20-1000 Hz) vibrations. The PC's structure allows transmission of vibrations through its layers (lamellae) to ...the centrally-located nerve fiber (neurite). This work combines mechanical models of the PC with an electrochemical model of peripheral nerves to simulate the tactile response of the entire system. A three-stage model of response to a vibratory input was developed, consisting of (1) outer core mechanics, (2) inner core mechanics, and (3) neurite electrochemistry. The model correctly predicts the band-pass nature of the PC's frequency response, showing that the PC structure can amplify oscillatory strains within its target frequency band. Specifically, strain induced by a vibratory stimulus is amplified by a factor of 8-12 from the PC surface to the neurite. Our results also support the hypothesis that PC rapid adaptation is affected by the lamellar structures without requiring neuronal adaptivity. Simulated different-sized PCs showed a shift in frequency response, suggesting that clusters of different-sized PCs could enable more nuanced tactile encoding than uniform clusters. By modeling the PC's mechano-to-neural transduction, we can begin to characterize the mechanosensation of other receptors to understand how multiple receptors interact to create our sensation of touch.
This study integrates mechanics and neuroscience to model the mechanoelectrochemical transduction of vibrations into neural signals in the Pacinian corpuscle.
Nonlinear three-dimensional finite element modeling of precast, prestressed concrete spandrel beams is a challenging task and requires exploration of the effects of material parameters and modeling ...assumptions. To this end, the numerical results obtained using the commercial software ABAQUS/Standard were compared with existing experimental data. The sensitivity of the spandrel beam response to various parameters such as finite element type, dilation angle, fracture energy, tension stiffening, bearing stress distribution and support representation was investigated. The behavior of precast, prestressed concrete spandrels under vertical loading was found to be sensitive to the type of element, the dilation angle for the concrete, bearing stress distribution at the supports, and deck-tie stiffness. Many of the findings reported are believed to be applicable to other types of reinforced concrete structures.
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