Analysis of wave-induced crack propagation through a coupling algorithm of the peridynamics and isogeometric analysis
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Peridynamics
Classification of discontinuities
Isogeometric analysis
Peridynamics (PD) is a widely used theory to simulate discontinuities, but its application in real-world structural problems is somewhat limited due to the relatively low-efficiency. The numerical substructure method (NSM) pr... | Find, read and cite all the research you need on Tech Science Press
Peridynamics
Substructure
Classification of discontinuities
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Peridynamics
Damage mechanics
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Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves conver- gence behavior. Finally, a novel approach for modeling ductile failure has been developed, moti- vated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software im- plementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.
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Peridynamics
Spurious relationship
Classification of discontinuities
Elasticity
Geomechanics
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Peridynamics (PD) is a non local continuum mechanics theory developed by Silling in 2000. The inception of peridynamics can be dated back to the works of Piola according to dell’Isola et al. [1]. Classical continuum theory (CCM) was there to study the materials response to deformation and loading conditions deformation response of materials and structures subjected to external loading conditions without taking into effect the atomistic structure. Classical continuum theory can be applied to various challenging problems but its governing equation have a limitation that it cannot be applied on any discontinuity such as a crack, as the partial derivatives with respect to space are not defined at a crack. To overcome this limitation , a new non local continuum approach i.e Peridynamics (PD) was developed.It was introduced as it governing equations donot contain any partial derivative with respect to space so it can be applied at cracks also. We can also think of Peridynamics as the continuum version of molecular dynamics. This behaviour of peridynamics makes it handy for multi-scale analysis of materials. Peridynamics finds it usefulness in other fields also such as moisture, thermal, fracture, aerospace etc., so that multiscale analysis can be done . The analysis of structure due to progressive failure is challenge. These challenges can be overcome by techniques such as using both nonlocal and classical (local) theories. But Peridynamic theory is computationally costly compared to the finite element method. While analyzing structures with compelxity , utilize structural idealizations is to be done to make computations feasible. Peridynamics has been catching the eyes of the researchers as its formulation include integral equations , unlike the partial differential equations in classical continuum theory. This method is still in early stages, a lot of research work is to be done to make it feasible for a large no. of problems.
Peridynamics
Continuum hypothesis
Timoshenko beam theory
Coalescence (physics)
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Peridynamics
Isogeometric analysis
Meshfree methods
Basis function
Representation
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Composites structural failure usually involves a complex interplay of intralaminar and interlaminar damage. In this paper, we investigate the development of a particle-based, Non-Ordinary State-Based (NOSB) formulation of Peridynamics to predict the failure mechanism of carbon fiber composite laminates subjected to high-velocity impacts. In NOSB-peridynamics, the bonding energy set between particles can be introduced as a fracture parameter associated with the energy release rate. The accuracy of the NOSB-Peridynamics was verified for a simply supported beam, It was shown that the stress-displacement curves of the Peridynamics and the commercial FEM software were consistent. Furthermore, a dynamic delamination calculation of a laminated structure was performed using the NOSB-Peridynamics. The elastic wave which can induce delamination were suppressed by the viscous damping introduced to stabilize the Peridynamics simulation. It was found that the coefficients of the NOSB Peridynamics should be chosen appropriately to simulate the phenomenon correctly.
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Delamination
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13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials (2014)
Peridynamics is a nonlocal reformulation of classical continuum mechanics. In contrast to classical models, governing equations in peridynamics are based on spatial integration, rather than spatial differentiation, of displacement fields. Therefore, peridynamics has been applied to the description of material failure and damage. As a nonlocal model, peridynamics is computationally more expensive than classical models; this motivates the development of concurrent multiscale methods, for which peridynamics is applied in regions where discontinuities appear or may be generated, whereas classical models are used elsewhere. A main challenge in concurrent multiscale modeling is how to couple different models without introducing spurious effects. We derive blending schemes to concurrently couple peridynamics and classical continuum mechanics, avoiding common artifacts present in these types of methods. We demonstrate the performance of the coupling schemes analytically and numerically.
Peridynamics
Classification of discontinuities
Spurious relationship
Multiscale Modeling
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Peridynamics is a particle method with an advantage in fracture simulation of solid bodies. In the fracture simulation, one can easily delete the bonding between the peridynamics particles to model the fracture if the bonding energy reaches a certain criterion such as a release energy rate. In this research, we have examined the applicability of the NOSB peridynamics in orthotropic elasto-plastic materials. The NOSB peridynamics is a variant of peridynamics which allows us to implement any kind of constitutive law to peridynamics framework. To model the plastic deformation, we implemented a return mapping method to our peridynamics code to find the yield surface. Thorough a unidirectional tensile simulation for a rectangular box, we checked peridynamics code can properly realize the constitutive law of an orthotropic elasto-plastic body: we compared the computational results obtained in peridynamics and FEM with different material directions.
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Orthotropic material
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