SUMMARYA generalized variational formulation, including quasi-convexification of energy wells for arbitrarily many martensitic variants in case of mono-crystals for linearized strains, was developed by Govindjee and Miehe (Comp. Meth. Appl. Mech. Eng. 2001; 191(3-5):215-238) and computationally extended by Stein and Zwickert (Comput. Mech. 2006; in press). This work is generalized here for finite strain kinematics with monotonous hyperelastic stress-strain functions in order to account for large transformation strains that can reach up to 15%.A major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation (PT) problems for multiple phase variants, n 2. The zigzag-type experimental stressstrain curve within PT at loading, called 'yield tooth', is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during PT.

The depth determination from the gravity data in frequency domain is carried out using the classical fast Fourier transform (FFT) method utilizing scaling properties of ensemble of anomalous source. The problem of calculating power spectrum from the FFT is well described in the literature. Here, the application of other high-resolution methods of power spectrum calculation, such as maximum entropy method (MEM) and multi-taper method (MTM) are explored to estimate depth to anomalous sources. At the outset, the FFT, the MEM and the MTM are tested on synthetic gravity data, generated for different types of synthetic models and then all these methods are applied to the field gravity data of the Bengal basin. The MTM with scaling is found to be superior for providing the detailed subsurface information rather than the MEM and the FFT methods in the case of synthetic as well as field examples.

Purpose-The purpose of this paper is to examine quadratic convergence of finite element analysis for hyperelastic material at finite strains via Abaqus-UMAT as well as classification of the rates of convergence for iterative solutions in regular cases. Design/methodology/approach-Different formulations for stiffness-Hessian form of the free energy functionals-are systematically given for getting the rate-independent analytical tangent and the numerical tangent as well as rate-dependent tangents using the objective Jaumann rate of Kirchoff stress tensor as used in Abaqus. The convergence rates for available element types in Abaqus are computed and compared for simple but significant nonlinear elastic problems, such as using the 8-node linear brick (B-bar) element-also with hybrid pressure formulation and with incompatible modesfurther the 20-node quadratic brick element with corresponding modifications as well as the 6-node linear triangular prism element and 4-node linear tetrahedral element with modifications. Findings-By using the Jaumann rate of Kirchoff stress tensor for both, rate dependent and rate independent problems, quadratic or nearly quadratic convergence is achieved for most of the used elements using Abaqus-UMAT interface. But in case of using rate independent analytical tangent for rate independent problems, even convergence at all is not assured for all elements and the considered problems. Originality/value-First time the convergence properties of 3D finite elements available in Abaqus sre systematically treated for elastic material at finite strain via Abaqus-UMAT.

It is widely known that filler-reinforced rubber material in tires shows a very complicated material behavior when subjected to cyclic loadings. One of the most interesting effects for rolling tires is the nonlinear rate-dependent behavior, which is implicitly linked to the amplitude dependency of dynamic stiffness (Payne effect) at a given frequency and temperature. This effect, however, cannot be described by a conventional linear viscoelastic constitutive law, e.g., the Prony series model. Several nonlinear viscoelastic material models have been proposed in the last decades. Among others, Lapczyk et al. (Lapczyk, I., Hurtado, J. A., and Govindarajan, S. M., “A Parallel Rheological Framework for Modeling Elastomers and Polymers,” 182nd Technical Meeting of the Rubber Division of the American Chemical Society, Cincinnati, Ohio, October 2012) recently proposed a quite general framework for the class of nonlinear viscoelasticity, called parallel rheological framework (PRF), which is followed by Abaqus. The model has an open option for different types of viscoelastic creep laws. In spite of the very attractive nonlinear rate-dependency, the identification of material parameters becomes a very challenging task, especially when a wide frequency and amplitude range is of interest. This contribution points out that the creep law is numerically sound if it can be degenerated to the linear viscoelastic model at a very small strain amplitude, which also significantly simplifies model calibration. More precisely, the ratio between viscoelastic stress and strain rate has to converge to a certain value, i.e., the viscosity in a linear viscoelastic case. The creep laws implemented in Abaqus are discussed in detail here, with a focus on their fitting capability. The conclusion of the investigation consequently gives us a guideline to develop a new creep law in PRF. Here, one creep law from Abaqus that meets the requirements of our guideline has been selected. A fairly good fit of the model is shown by the comparison of the simulated complex modulus in a wide frequency and amplitude range with experimental results.

It is known that signals (which could be functions of space or time) belonging to 𝕃2-space cannot be localized simultaneously in space/time and frequency domains. Alternatively, signals have a positive lower bound on the product of their effective spatial andeffective spectral widths, for simplicity, hereafter called the effective space-bandwidthproduct (ESBP). This is the classical uncertainty inequality (UI), attributed to many, but, from a signal processing perspective, to Gabor who, in his seminal paper, established the uncertainty relation and proposed a joint time-frequency representation in which the basis functions have minimal ESBP. It is found that the Gaussian function is the only signal that has the lowest ESBP. Since the Gaussian function is not bandlimited, no bandlimited signal can have the lowest ESBP. We deal with the problem of determining finite-energy, bandlimited signals which have the lowest ESBP. The main result is as follows. By choosing the convolution product of a Gaussian signal (with σ as the variance parameter) and a bandlimited filter with a continuous spectrum, we demonstrate that there exists a finite-energy, bandlimited signal whose ESBP can be made to be arbitrarily close (dependent on the choice of σ) to the optimal value specified by the UI

In this article new contributions to the theory and computation of cyclic martensitic phase transformations (PT) in monoand poly-crystalline metallic shape memory alloys are presented. The PT models of the non-convex variational problem are based on the Cauchy-Born hypothesis and Bain's principle. A quasi-convexified C 1 -continuous thermo-mechanical micromacro constitutive model for metallic monocrystals is developed which is represented together with the phase transformation constraints by a unified Lagrangian variational functional including phase evolution equations with mass conservation. The unified setting presented here includes poly-crystalline shape memory alloys whose microstructure is modeled using lattice variants. A pre-averaging scheme for randomly distributed poly-crystalline variants of transformation strains is used to transform them into those of a fictitious monocrystal. Thus, the incremental integration in process time and the spatial integration algorithms of the discrete variational problems for both mono-and poly-crystalline phase transformations can be implemented into a unified algorithm with branching for mono-and poly-crystalline phase transformations. Furthermore, an error-controlled adaptive 3D finite element method in space is presented for phase transformation problems using explicit error indicator with gradient smoothing and mesh refinements via new mesh generation in each adaptive step. Computations of informative examples with convergence studies, and comparisons with published experimental results are presented using 3D finite elements. Shape memory alloys: phenomenology, physical effects, and applicationsShape memory alloys (SMAs) have immense technological potential because of various aspects of their special thermomechanical behavior, such as shape memory effect (SME) in form of reversible quasiplastic (QP) deformation, superelasticity (SE), and bio-compatibility. Nowadays, it is widely used for biomedical systems e.g. endovascular stents, orthodontic arc wires; for controlling and activating mechanical systems such as actuators and connectors and also for structural systems e.g. vibration control devices.SMAs exhibit a strong nonlinear thermomechanical behavior associated with abrupt changes in their lattice structure called martensitic phase transformation (PT). They have intrinsic ability to transform between austenite (parent phase) and a number of symmetry-related martensitic variants (product phases). Those SMAs considered here are copper based alloy CuAlNi and nickel based alloy NiTi, which both can behave as QP and SE depending on the operating temperature.Martensitic PT is considered as a diffusionless first-order transformation between 'high' temperature, θ > A s , austenite and 'low' temperature martensitic phases, θ < M s , Fig. 1. A s and M s are the so-called austenite and martensite start temperatures. Other critical temperatures are austenite and martensite finish temperatures which are denoted by A f and M f , respectively. SMAs exhibit a specific feature...

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