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Register a new userQuasi-Static Anti-Plane Shear Crack Propagation in a New Class of Nonlinear Strain-Limiting Elastic Solids using Phase-Field Regularization
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Mallikarjunaiah Muddamallppa
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We present a novel constitutive model using the framework of strain-limiting theories of elasticity for an evolution of quasi-static anti-plane fracture. The classical linear elastic fracture mechanics (LEFM), with conventional linear relationship between stress and strain, has a well documented inconsistency through which it predicts a singular cracktip strain. This clearly violates the basic tenant of the theory which is a first order approximation to finite elasticity. To overcome the issue, we investigate a new class of material models which predicts uniform and bounded strain throughout the body. The nonlinear model allows the strain value to remain small even if the stress value tends to infinity, which is achieved by an implicit relationship between stress and strain. A major objective of this paper is to couple a nonlinear bulk energy with diffusive crack employing the phase-field approach. Towards that end, an iterative L-scheme is employed and the numerical model is augmented with a penalization technique to accommodate irreversibility of crack. Several numerical experiments are presented to illustrate the capability and the performance of the proposed framework We observe the naturally bounded strain in the neighborhood of the crack-tip, leading to different bulk and crack energies for fracture propagation.
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Variational phase-field methods have been shown powerful for the modeling of complex crack propagation without a priori knowledge of the crack path or ad hoc criteria. However, phase-field models suffer from their energy functional being non-linear and non-convex, while requiring a very fine mesh to capture the damage gradient. This implies a high computational cost, limiting concrete engineering applications of the method. In this work, we propose an efficient and robust fully monolithic solver for phase-field fracture using a modified Newton method with inertia correction and an energy line-search. To illustrate the gains in efficiency obtained with our approach, we compare it to two popular methods for phase-field fracture, namely the alternating minimization and the quasi-monolithic schemes. To facilitate the evaluation of the time step dependent quasi-monolithic scheme, we couple the latter with an extrapolation correction loop controlled by a damage-based criteria. Finally, we show through four benchmark tests that the modified Newton method we propose is straightforward, robust, and leads to identical solutions, while offering a reduction in computation time by factors of up to 12 and 6 when compared to the alternating minimization and quasi-monolithic schemes.
Material surface may have a remarkable effect on the mechanical behavior of magneto-electro-elastic (or multiferroic) structures at nano-scale. In this paper, a surface magneto-electro-elasticity theory (or effective boundary condition formulation), which governs the motion of the material surface of magneto-electro-elastic nano-plates, is established by employing the state-space formalism. The properties of anti-plane shear (SH) waves propagating in a transversely isotropic magneto-electro-elastic plate with nano-thickness are investigated by taking surface effects into account. The size-dependent dispersion relations of both antisymmetric and symmetric SH waves are presented. The thickness-shear frequencies and the asymptotic characteristics of the dispersion relations considering surface effects are determined analytically as well. Numerical results show that surface effects play a very pronounced role in elastic wave propagation in magneto-electro-elastic nano-plates, and the dispersion properties depend strongly on the chosen surface material parameters of magneto-electro-elastic nano-plates. As a consequence, it is possible to modulate the waves in magneto-electro-elastic nano-plates through surface engineering.
We study a 2D quasi-static discrete {it crack} anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transfered to all elements through elastic forces. This model can be considered as belonging to the class of self-organized models which may exhibit spontaneous criticality, with four additional ingredients compared to sandpile models, namely quenched disorder, boundary driving, long range forces and fast time crack rules. In this crack model, as in the dislocation version previously studied, we find that the occurrence of repeated earthquakes organizes the activity on well-defined fault-like structures. In contrast with the dislocation model, after a transient, the time evolution becomes periodic with run-aways ending each cycle. This stems from the crack stress transfer rule preventing criticality to organize in favor of cyclic behavior. For sufficiently large disorder and weak stress drop, these large events are preceded by a complex space-time history of foreshock activity, characterized by a Gutenberg-Richter power law distribution with universal exponent $B=1 pm 0.05$. This is similar to a power law distribution of small nucleating droplets before the nucleation of the macroscopic phase in a first-order phase transition. For large disorder and large stress drop, and for certain specific initial disorder configurations, the stress field becomes frustrated in fast time : out-of-plane deformations (thrust and normal faulting) and/or a genuine dynamics must be introduced to resolve this frustration.
MiniBooNE anti-neutrino charged-current quasi-elastic (CCQE) data is compared to model predictions. The main background of neutrino-induced events is examined first, where three independent techniques are employed. Results indicate the neutrino flux is consistent with a uniform reduction of $sim$ 20% relative to the largely uncertain prediction. After background subtraction, the $Q^{2}$ shape of $ umub$ CCQE events is consistent with the model parameter $M_{A}$ = 1.35 GeV determined from MiniBooNE $ umu$ CCQE data, while the normalization is $sim$ 20% high compared to the same prediction.
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation gradient $mathbf{F}$ and initial stress $boldsymbol tau$, i.e. $W:= W(mathbf F, boldsymbol tau)$. The restriction is a consequence of energy conservation and ensures that the predicted stress and strain energy do not depend upon an arbitrary choice of reference configuration. We call this restriction: initial stress reference independence (ISRI). It transpires that almost all strain energy functions found in the literature do not satisfy ISRI, and may therefore lead to unphysical behaviour, which we illustrate via a simple example. To remedy this shortcoming we derive three strain energy functions that do satisfy the restriction. We also show that using initial strain (often from a virtual configuration) to model initial stress leads to strain energy functions that automatically satisfy ISRI. Finally, we reach the following important result: ISRI reduces the number of unknowns of the linear stress tensor of initially stressed solids. This new way of reducing the linear stress may open new pathways for the non-destructive determination of initial stresses via ultrasonic experiments, among others.
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