This work utilizes mean-field self-consistent and full-field fast Fourier transform-based homogenizations to study the effective elastic behavior of several steels: three dual-phase (DP), DP 590, DP 980, and DP 1180, ...
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This work utilizes mean-field self-consistent and full-field fast Fourier transform-based homogenizations to study the effective elastic behavior of several steels: three dual-phase (DP), DP 590, DP 980, and DP 1180, and one martensitic (MS), MS 1700. Crystallographic textures and phase fractions of these steels are characterized using electron microscopy along with electron-backscattered diffraction to initialize the models. A comprehensive set of Young's modulus and Poisson's ratio data, measured at the ambient temperature as a function of orientation with respect to the rolling direction for each steel sheet, is used to calibrate and validate the models. The calibration of the models enabled us to estimate the single crystal elastic constants for both the martensitic phase and ferrite, while calculating the orientation dependent effective properties. Half of the data was used in the calibration. Subsequent predictions of the orientation dependent effective elastic properties for the remaining data verified that the estimated single crystal properties are reliable. As the steels exhibit a different level of anisotropy in their effective behavior, good predictions allowed us to discuss the role of texture, grain structure, phase fraction and distribution on the effective properties. The results of this work represent a significant incentive to introduce elastic anisotropy in numerical tools for simulating metal forming processes of dual-phase steels, in particular those processes involving springback, using the texture informed crystal mechanics-based models to more accurately estimate the effective elastic properties required by such simulations.
The static stress field in the vicinity of a rough crack in mode III is studied via a conformal mapping technique. This purely geometrical method (friction effects are not studied) proves a direct and efficient way of...
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The static stress field in the vicinity of a rough crack in mode III is studied via a conformal mapping technique. This purely geometrical method (friction effects are not studied) proves a direct and efficient way of solving the displacement field numerically for any prescribed geometry. It also leads to an analytical framework which is suited to a perturbation expansion for a small roughness amplitude. It is shown that the local stress intensity factor (SIF) at the crack tip differs from the ''far field'' SIF by a correction term which depends quadratically on the roughness amplitude. The Leading correction term, which is derived analytically, consists of two parts: (i) a local systematic term, which decreases the local SIF, is directly related to the orientation of the crack tip compared to its mean orientation;(ii) a second contribution which is non-local. In the case of a self-affine geometry, the second term has a non-zero average that also contributes to decrease the local SIF. Hence the mean local SIF is smaller than the far-field value, which induces a ''strengthening'' effect. The fluctuation amplitude due to both terms has the same dependence as the mean systematic decrease. Both effects are controlled by the lower scale cut-off of the self-affine regime. (C) 1997 Elsevier Science Ltd.
This paper is dedicated to establishing a thermodynamically compatible Eulerian theoretical framework for elastoplastic anisotropically damaging materials, that is applicable to high strain rate and strongly compressi...
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This paper is dedicated to establishing a thermodynamically compatible Eulerian theoretical framework for elastoplastic anisotropically damaging materials, that is applicable to high strain rate and strongly compressible problems. The proposed model comprises a system of thermodynamically compatible balance laws based upon hyperelastic-inelastic theory: the mechanical conservation laws are supplemented by kinematic evolution equations for material deformation gradients, which can be written in conservative form. The formulation is rotationally invariant and hyperbolic, with a determinable characteristic structure. An operator split approach is proposed for integrating the governing constitutive models for three-dimensional Cauchy problems, in conjunction with a ghost material numerical method to resolve internal Dirichlet boundaries. Such methods naturally allow the generation of new internal boundaries making them ideal for simulating fragmenting materials and macroscale fracture. A remarkable feature of the proposed approach is that the overall complexity compares favourably with that of the model for elastoplastic deformations only. The simulation of expanding ring and flyer plate experiments are chosen to demonstrate the effectiveness of the proposed approach. Crown Copyright (C) 2016 Published by Elsevier Ltd. All rights reserved.
QUATERNION algebra has found a number of applications for engineering and scientific problems, including fluid mechanics [1], quantum mechanics [2,3], robotics [4,5], and spacecraft attitude control [5,6]. Unfortunate...
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QUATERNION algebra has found a number of applications for engineering and scientific problems, including fluid mechanics [1], quantum mechanics [2,3], robotics [4,5], and spacecraft attitude control [5,6]. Unfortunately, the literature available for supporting engineering applications is diffuse for matrix applications.
A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width ref...
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A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conducted in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift. (c) 2005 Elsevier Inc. All rights reserved.
Since its advent in the 1960s, elastoplastic micromechanics has been confronted by continuous challenges, as the classical incremental elastoplastic tangents are known to deliver unrealistically stiff material respons...
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Since its advent in the 1960s, elastoplastic micromechanics has been confronted by continuous challenges, as the classical incremental elastoplastic tangents are known to deliver unrealistically stiff material responses. As a complement to the various "secant" approximations targeting this challenge, we here develop a theoretical framework based on an extension of Dvorak's transformation field analysis, comprising the derivation of concentration and influence tensors. We thereby overcome the problem of actually non homogeneous stress distributions across finite (often spherical) material phases, through consideration of infinitely many (non-spherical) solid phases oriented in all space directions, arriving at a micro-elastoplasticity theory of porous polycrystals. The resulting governing equations are discretized in time and space, and then solved in the framework of a new return mapping algorithm, the realization of which we exemplify by means of Mohr-Coulomb plasticity at the solid phase level. The corresponding homogenized material law is finally shown to satisfactorily represent the behavior of the porous hydroxyapatite polycrystals making up the so-called cement lines in osteonal bone. This is experimentally validated through strength and ultrasonic tests on hydroxyapatite, as well as through mass density, light microscopy, chemical composition, and osteon pushout tests on bone. (C) 2017 Elsevier Ltd. All rights reserved.
The adaptive cubic regularization algorithm described in Cartis et al. (2009, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program....
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The adaptive cubic regularization algorithm described in Cartis et al. (2009, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program., 127, 245-295;2010, Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity [online]. Math. Program., DOI: 10.1007/s10107-009-0337-y) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over a convex domain. Convergence to first-order critical points is shown under standard assumptions, without any Lipschitz continuity requirement on the objective's Hessian. A worst-case complexity analysis in terms of evaluations of the problem's function and derivatives is also presented for the Lipschitz continuous case and for a variant of the resulting algorithm. This analysis extends the best-known bound for general unconstrained problems to nonlinear problems with convex constraints.
In this paper we suggest a new phenomenological material model for shape memory alloys. In contrast to many earlier concepts of this kind the present approach includes arbitrarily large deformations. The work is motiv...
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In this paper we suggest a new phenomenological material model for shape memory alloys. In contrast to many earlier concepts of this kind the present approach includes arbitrarily large deformations. The work is motivated by the requirement, also expressed by regulatory agencies, to carry out finite element simulations of NiTi stents. Depending on the quality of the numerical results it is possible to circumvent, at least partially, expensive experimental investigations. Stent structures are usually designed to significantly reduce their diameter during the insertion into a catheter. Thereby large rotations combined with moderate and large strains occur. In this process an agreement of numerical and experimental results is often hard to achieve. One of the reasons for this discrepancy is the use of unrealistic material models which mostly rely on the assumption of small strains. In the present paper we derive a new constitutive model which is no longer limited in this way. Further its efficient implementation into a finite element formulation is shown. One of the key issues in this regard is to fulfil "inelastic" incompressibility in each time increment. Here we suggest a new kind of exponential map where the exponential function is suitably computed by means of the spectral decomposition. A series expansion is completely avoided. Finite element simulations of stent structures show that the new concept is well appropriate to demanding finite element analyses as they occur in practically relevant problems. (C) 2007 Elsevier Ltd. All rights reserved.
This paper describes a controller for automatic attitude maneuvers of reaction-control-jet-equipped spacecraft. It is based on a new, real-time algorithm for solution of fuel-optimal maneuvers, assuming on-off control...
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This paper describes a controller for automatic attitude maneuvers of reaction-control-jet-equipped spacecraft. It is based on a new, real-time algorithm for solution of fuel-optimal maneuvers, assuming on-off control and linearized dynamics. These solutions provide efficient model trajectories that are easily tracked using a feed-forward, feedback controller structure. This approach was developed as a software upgrade to the Space Shuttle Orbiter on-orbit autopilot, for which it shows a very substantial performance benefit in a wide range of simulated maneuver tasks.
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