# Computational Solid Mechanics

## Top PDF Computational Solid Mechanics:

### Variational time integrators in computational solid mechanics

AVIs sidestep these diﬃculties by allowing each element or region of space to advance at their own intrinsic pace. There are, in addition, several other application areas that badly need AVI-like al- gorithms, most notably with the fast development of complex multiscale material models. In this context, the core of the computational cost for ﬁnite element simulations has shifted from assembling forces and computing displacements to the elemental computations, which usually involve the use of elaborate material constitutive models. In addition to the thermoelastic problem, other physical processes are often considered as well, such as plastic deformation, chemical reactions and phase transitions. Highly spatially localized timescales can be induced by any or all of these processes. For instance, the propagation of a detonation wave in a thermoelastic material induces the usually faster timescale of the chemical reaction in the region surrounding the detonation front. Not only do we need spatially resolved meshes to accurately capture the detonation front, but the use of AVIs becomes essential if any meaningful time is to be reached by the simulation. We note additionally that despite the growing computational power provided by highly parallel machines, solutions are still obtained by advancing forward in time, which makes AVIs even more fundamental for large-scale simulations in the near future.

### Guide for Verification and Validation in Computational Solid Mechanics

The goal of a validation experiment is to be a physical realization of an initial boundary value problem, since an initial boundary value problem is what the computational model was developed to solve. Most existing experiments do not meet the requirements of a validation experiment, as they were typically performed for purposes other than validation. Certainly appropriate existing experimental data should be used in the validation process, but the resulting confidence in the model’s ability to make predictions, based on these experimental results, is diminished, relative to validation experiments. The reduced confidence arises from the necessity of an analyst needing to select physical and numerical parameters required for the model that were left undefined in the experiment. As an example, an experiment may report that a steel plate was tested and the steel used was designated A36 steel, indicating the manufacture’s minimum specification for a yield strength of 36,000 psi. In fact the yield strength of the specimen tested could be significant greater than that minimum.

### On the validation of solid mechanics models using optical measurements and data decomposition

Optical measurement technologies have reached a readiness level, due to recent developments, that enable displacement or strain data over large areas, or even the entire structure, to be reliably captured during an experimental test and thereafter visualized and analyzed. For example, Digital Image Correlation (DIC), Digital Speckle Pattern Interferometry (DSPI) and shearography are steadily replacing conventional measurement techniques such as strain gauges and extensometers [4]. Such developments provide the background for a more comprehensive approach to model validation, which could lead to optimized and less conservative designs. Although many companies have developed internal procedures for comparing simulation results to experimental data, there are no standard procedures for the validation of computational solid mechanics models used in engineering design. In the EU research project ADVISE [5], a methodology for validation of computational solid mechanics models based on full field data comparisons was developed [6]. In a subsequent European Union supporting action project VANESSA [7], the appropriateness of this validation procedure as part of a regulatory process for validation of computational solid mechanics models was examined.

### A Computational Mechanics Model for the Delamination and Buckling of Paper during the Creping Process.

More results in crack propagation of bi-material were demonstrated, such as the transonic delamination of bi-material interface, shock waves emanated from the crack contact zone. Parallel computational and experimental researches in this area were carried out. Those dynamic features were previously believed not feasible in physics, but was challenged by Liu et al. (1993) and Lambros and Rosakis (1994) in their experiments. Encouraged by the results above, Yu and Yang (1995) investigated the dynamic debonding by in-plane deformation including stress and strain. Nearly at the same time, Lambros and Rosakis (1995) also conducted and analyzed these transonic crack growths in their further experiment and showed impressive phenomena. Huang et al. (1998) generalized the intersonic propagation of interfacial crack tip from without crack face contact to with crack face contact, validating the experimental results. And in experiment Rosakis (1998) observed the two traveling shock waves from the intersonically moving crack tip and crack contact end predicted theoretically.

### An unstructured immersed finite element method for nonlinear solid mechanics

representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolation. For discretisation structured and unstructured background meshes with Lagrange basis functions are considered. We show numerically and analytically that the introduced cut-element stabilisation technique provides an eﬀective bound on the size of the Nitsche parameters and, in turn, leads to well-conditioned system matrices. In addition, we introduce a novel approach for representing and analysing geometries with sharp features (edges and corners) using an implicit geometry representation. This allows the computation of typical engineering parts composed of solid primitives without the need of boundary-ﬁtted meshes.

### Integrating planar polarity and tissue mechanics in computational models of epithelial morphogenesis

12, 56011 447 •• This computational study couples a model of polarisation of Rho-kinase, myosin 448 and Bazooka with a vertex model to understand the interplay between planar polarity 44[r]

### p-Version Direct Time Integration Method and Adaptive Procedure for Structure Dynamic Analysis

In recent years, error estimation and adaptive techniques have been emphasized in research on computational mechanics. The ultimate goal is to make the numerical solutions reliable in an efficient and economical manner. For structural dynamic problems, discretization errors that contain both spatial and temporal discretization errors can not be avoided. But these errors can be reduced. For the spatial discretization error, many techniques [1-4] have already been presented, such as h-refinement, p-refinement, and a combination of h- and p-refinement. Some of them are being incorporated into commercially available finite element codes. However, adaptive techniques for temporal discretization errors are just beginning to emerge. Zienkiewicz et al. [5] and Zienkiewicz together with Shiomi [6] introduced a simple expression as an indicator of the local error. Zienkiewicz and Xie [7] proposed another local error estimator by comparing the Newmark solutions with the exact solutions expanded in the Taylor series. Zeng et al. [8] obtained the same result in a more simple and intuitive way. Wiberg and Li [9] developed a more precise error estimator that can evaluate both displacement errors and velocity errors. Choi and Chung [10] presented global and local error estimates for various time integration methods. All of these efforts seek to find a reasonable step size so that the temporal discretization error is within the prescribed tolerance, which can be classified as the h-version method in the time domain.

### Computational Platform for Safety and Life-cycle Assessment of RC/PC Shells

Chemo-physical and mechanical modeling of concrete with greatly different scales of geometry was presented, and synthesized on a unified computational platform which may bring about quantitative assessment of structural concrete performances. The safety assessment method was extended to the life-cycle issue with multi-scaled information on microclimate states of cementitious composites. Currently granted is a great deal of knowledge earned by the past development. At the same time, we face a difficulty to quantitatively extract consequential figures from them. The authors expect that the systematic framework on the knowledge-based technology will be extended efficiently and can be steadily taken over by engineers in charge. This study was financially supported by JSPS Grant-in-aid for scientific research 14205065 and 14655160.

### Use of Polynomial Shape Function in Shear Deformation Theory for Thick Plate Analysis

Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory.. Applied and Computational Mechanics 6, pp.[r]

### Analysis of the Casing Collapse in Terms of Geomechanical Parameters and Solid Mechanics

Casing Collapse is one of the major problems in upstream oil industries. Millions of dollars are annually spent on repairing, rehabilitation and re-drilling wells due to the casing collapse in oil wells worldwide. Casing collapse occurs due to a variety of factors, including soft rock creep such as salt and shale, and the creation of a point load on the casing due to the lack of good cementation behind the casing, sliding motion of the soft layer that is mechanically located between the two harder layers, reservoir subsidence due to excessive harvest or other factors such as casing production and so on. Fig. 1 shows the classification of the causes of the casing collapse in terms of geomechanical parameters (of formations) and solid mechanics.

### US Office of Naval Research, Solid Mechanics Program Review

Understanding the mechanical and physical behaviour of layered orthotropic material is an essential key step in performance assessment of composite structures and sandwich structures. At the University of Southampton, UK, work has been conducted in analytical, numerical and experimental techniques for damage assessment of composite materials and structures. Data-rich experimental mechanics techniques have been developed to assess damage using thermoelastic stress analysis (TSA) [1], vibration-based approaches [2-4] and acoustic emission. Alongside this advanced signal processing procedures have been devised to parameterise the data. Work has also concentrated on extracting the stresses and their distributions from complex structures to establish the failure mechanisms and make predictions of the component life [5-8], in particular adhesive joints, e.g. [9]. A range of composite materials have been studied but the main thrust is in applications relating to the marine industry and therefore the work described in this extended abstract will focus on glass reinforced polymer composites; although some recent work on full scale tests in carbon fibre Nomex honeycomb sandwich structure is also detailed. Multi-scale evaluations are described from the fibre matrix interaction to assessment of full scale structure. A key part of the work has been in devising measurement approaches that permit detailed information to be extracted from experimental data to allow comprehensive assessment of structures and materials: some key examples of this are provided. The work covers examples of experimental stress analysis and its use as a validation tool, fatigue damage assessments and applications to NDE. In evaluating performance a key consideration is the manufacturing process and parts of the extended abstract are devoted to the discussion on the effects of manufacturing and concurrent engineering. Finally some insight into through life assessments is provided. The extended abstract concludes with an overview of what the Southampton team regard as technical and scientific challenges facing the marine industry in the future.

### Isotropic hyperelasticity in principal stretches : explicit elasticity tensors and numerical implementation

Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method. Hyperelastic constitutive models defined by this strain measure are known to accurately model the response of rubber, and similar materials. These models may not be available in the library of a Finite Element Analysis software, but a numerical implementation of the constitutive model may be provided by a programmed subroutine. The implementation proposed here is robust and accurate, with straightforward user input. It is presented in multiple configurations with novel features, including efficient definition of isochoric stress and elasticity coefficients, symmetric dyadic products of the principal directions, and development of a stable and accurate algorithm for equal and similar principal stretches. The proposed implementation is validated, for unique, equal and similar principal stretches. Further validation in the Finite Element Method demonstrates the developed implementation requires lower computational effort compared with an alternative, well-known implementation. Keywords Hyperelasticity · Principal stretches · Finite Element Method · Numerical implementation · Elasticity tensors

### An analog of Titchmarsh's theorem for the Bessel transform in the space $\mathrm{L}_{p,\alpha}(\mathbb{R}_{+})$

Integral transforms and their inverses (e.g., the Bessel transform) are widely used to solve various problems in calculus, mechanics, mathematical physics, and computational mathematics [r]

### Parallel Partitioned Simulations of Real World’s Coupled Problems

In the present one-way coupling analysis, the REVOCAP_Coupler (Yoshimura et al., 2008), which is a family of ADVENTURE_Coupler, was employed. Time dependent pressure fluctuations on the exterior surfaces of the vehicle are calculated by the flow solver, which simulates turbulent flow of air around the vehicle. These surface pressure fluctuation data on the mesh surfaces of the CFD analysis are mapped onto the mesh surfaces of the structural analysis. Appropriate mesh sizes for the flow solver are different from those for the structural solver. In our research, a kei-car in which interior and under- floor were simplified was employed to the wind tunnel tests as well as for the computational analyses. The wind tunnel tests were performed with the main stream velocity of 100km/h (Yamade et al., 2016; Iida et al., 2016).

### Computational Heterogeneous Electrochemistry – From Quantum Mechanics to Machine Learning

In electrochemistry, electrolytes are needed to transport charges between the cathode and the anode for conducting electricity. Since electrolytes are mobile ions in solution, heterogeneous catalysts in electrochemistry are typically in the solid phase. Solid catalysts can take many different forms, including perfect crystals, polycrystalline films or particles, and amorphous structures, with increasing complexity. Because chemical reactions take place at the interface between the heterogeneous catalysts and the reactants in the solution, the surface morphology directly determines the interfacial chemistry. However, because the complexities of the surface morphology differ in different categories of materials, the study of each type of catalysts require specific treatments. In this thesis, we employed quantum mechanical methods to study the three main categories of catalysts, as shown in Figure 1 below:

### Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

Tensor mathematics is focused on the creation of direct computational experiments in solving prac- tical problems of ﬂuid mechanics. The continual-corpuscular approach is based on the numerical scheme of the ﬁrst order with a consistent diﬀerence in the integration of the laws of motion of conju- gate phases of scalar argument, i.e., time. Division of the computing stages by the physical processes enables continuous monitoring and hybrid evolution of mathematical relationships according to as- sessment of the current state of the simulated continuous medium, taking into account the intensity of the physical interaction between adjacent corpuscles as virtual numeric objects. The canonical rep- resentation of the laws of ﬂuid mechanics allows strictly and unambiguously to associate numerical objects with arithmetic and logical operations and complex geometric algorithms, including the use of fast interpolation for unregularized grid spaces.

### General Nonlinear-Material Elasticity in Classical One-Dimensional Solid Mechanics

Walter Ramberg and William Osgood were working at the National Advisory Committee for Aeronautics in 1943. NACA was the precursor organization to the modern day National Aeronautics and Space Administration, which superceded its predecessor in 1958. They worked on various projects in experimental mechanics from the compressive and tensile strength of sheet metal, to dynamic testing of models and the strength of aircraft structures [26]. In the year prior to 1943, C. S. Aitchison and James A. Miller [27] had published results from mechanical tests on Aluminums Alloys, Carbon Steel, and Chromium Nickel steel. The data published by Aitchison and Miller described a highly nonlinear material which lacked a clear yield point unlike more common materials such as structural steel. Nonlinearity was not a new concept in materials science. Fewer than 20 years prior Heinrich Hencky [28] had independently rediscovered the von Mises yield criterion laid out by Richard Edler von Mises [29] in 1913.

### A Neuro-Finite Element Analysis of Partial Differential Equations of Solid Mechanics

In order to enhance the computational efficiency of FEM, artificial neural network are employed in this study. ANN can help in predicting displacement of finer mesh from coarse mesh which thereby overcomes the major difficulties of FEM like memory requirements and computational time. Since computation time is directly related to mesh size, the proposed approach is bound to reduce the computational time. In Fig. 1 (b) major computational steps of the proposed Neuro-FEM are shown. The results of coarse Finite Element Mesh is used for training of neural network. Successfully trained network can predict the field variable in the given domain.