Volumetric Element Research Articles

Non-Deterministic Exploration through Parametric Design

This paper explores non-deterministic parametric modelling as a design tool. Specifically, it addresses the application of parametric variables to the generation of a conceptual bridge design and the use of repeatable discrete components to the conceptual form. In order to control the generation of the bridge form, a set of design variables based on the concept of a law curve have been developed. These design variables are applied and tested through interactive modelling and variation, driven by manipulating the law curve. Combining this process with the application and control of a repeatable element, known as a Representative Volumetric Element (RVE), allows for the development and exploration of a design solution that could not be achieved through the use of conventional computer modelling. The competition brief for the Australian Institute of Architects (AIA) ‘Dialectical Bridge’ has been used as a case study to demonstrate the use of non-deterministic parametric modelling as a design tool. The results of the experimentation with parametric variables, the law curve and representative volumetric elements (RVE) are presented in the paper.

Cohesive modeling of delamination in Z-pin reinforced composite laminates

The mode I interlaminar fracture in Z-pin reinforced composite laminates is modeled using a cohesive volumetric finite element (CVFE) scheme. The test configuration used in this study is a Z-pin reinforced double cantilever beam specimen. A bilinear rate-independent but damage-dependent cohesive traction–separation law is adopted to model the fracture of the unreinforced composite and discrete nonlinear spring elements to represent the effect of the Z-pins. The delamination toughness and failure strength of the Z-pin reinforced composites are determined by a detailed comparison study of the numerical modeling results with experimental data. To further reduce the computational effort, we introduce an equivalent distributed cohesive model as a substitute for the discrete nonlinear spring representation of the Z-pins. The cohesive model is implemented on various test problems with varying failure parameters and for varying spatial Z-pin reinforcement configurations showing good agreement with the experimental results.

Heterogeneous meshing and biomechanical modeling of human spine

We aim to develop a patient-specific biomechanical model of human spine for the purpose of surgical training and planning. In this paper, we describe the development of a finite-element model of the spine from the VHD™ Male Data. The finite-element spine model comprises volumetric elements suitable for deformation and other finite-element analysis using ABAQUS. The mesh generation solution accepts segmented radiological slices as input, and outputs three-dimensional (3D) volumetric finite element meshes that are ABAQUS compliant. The proposed mesh generation method first uses a grid plane to divide the contours of the anatomical boundaries and its inclusions into discrete meshes. A grid frame is then built to connect the grid planes between any two adjacent planes using a novel scheme. The meshes produced consist of brick elements in the interior of the contours and with tetrahedral and wedge elements at the boundaries. The nodal points are classified according to their materials and hence, elements can be assigned different properties. The resultant spine model comprises a detailed model of the 7 cervical vertebrae, 12 thoracic vertebrae, 5 lumbar vertebrae, and S1. Each of the vertebrae and intervertebral disc has between 1200 and 6000 elements, and approximately 1200 elements, respectively. The accuracy of the resultant VHD™ finite element spine model was good based on visual comparison of volume-rendered images of the original CT data, and has been used in a computational analysis involving needle insertion and static deformation. We also compared the mesh generated using our method against two automatically generated models; one consists of purely tetrahedral elements and the other hexahedral elements.

A new method for connate water saturation calculation using time-lapse logging data

Connate water saturation is an important parameter from well logging evaluation. In order to accurately determine reservoir connate water saturation using the time-lapse logging data, on the basis of the study of the mud filtrate dynamic invasion process and the dynamic change laws of reservoir parameters around borehole, this study established a logging response equation according to the volumetric element integration method. In this paper, the exponential water saturation relationships between water saturation and invasion time as well as the calculation algorithm of connate water saturation using the new dynamic response equation have been given. The results of two case studies from QingHai Oilfield have shown that the connate water saturation derived from the exponential water saturation relationships and the calculation algorithm of connate water saturation presented in this paper is in great agreement with the results from the field testing and results from mercury injection analysis.

Improved Form of a Fracture Mechanics Based Failure Probability Model for Brittle Materials

Improved Form of a Fracture Mechanics Based Failure Probability Model for Brittle Materials

Cohesive modeling of dynamic fracture in functionally graded materials

The dynamic fracture of functionally graded materials (FGMs) is modeled using an explicit cohesive volumetric finite element scheme that incorporates spatially varying constitutive and failure properties. The cohesive element response is described by a rate-independent bilinear cohesive failure model between the cohesive traction acting along the cohesive zone and the associated crack opening displacement. A detailed convergence analysis is conducted to quantify the effect of the material gradient on the ability of the numerical scheme to capture elastodynamic wave propagation. To validate the numerical scheme, we simulate dynamic fracture experiments performed on model FGM compact tension specimens made of a polyester resin with varying amounts of plasticizer. The cohesive finite element scheme is then used in a parametric study of mode I dynamic failure of a Ti/TiB FGM, with special emphasis on the effect of the material gradient on the initiation, propagation and arrest of the crack.

COLLISION HANDLING OF FABRIC YARNS IN WOVEN STRUCTURES

The paper deals with the modelling of the physical behaviour of woven structures imitating the textile fabrics. The model is based on a combined approach which presents longitudinal elastic properties of each yarn by a system of non-volumetric structural elements (springs), while the collision search and response algorithm works in a 3D space based on tight-fitting of the yarns by using oriented bounding boxes (OBB). The separation axis theorem (SAT) for collision detection between OBBs is performed. Collision response is performed by applying collision impulses to colliding nodes thus avoiding interpenetrations of the yarns. A simplified approach is applied in order to take into account the deformation of the cross-section of a yarn. It is assumed that the cross-sectional area remains constant all the time while its shape is elliptic with changing lengths of axes. Numerical examples of simulation of tension, warp and shooting-through the fabric are presented. 1. Indroduction The problematic of the computational models for simulation of the textile structures is defined mainly by the necessity to present the behaviour of the material in two different length scales. At the macro- scale one is inclined to regard a fabric as a continuous membrane. At the same time a textile fabric is not a continuum as at the micro-level its behaviour is de- fined by the contact interactions of the yarns in the woven structure. The dimension of this micro-struc- tural level is finite and may be very complex depend- ing upon the properties of the yarn and of the weave. The continua based approximations of the fabric beha- viour are always only rough approximations of the real fabric. Moreover, different continua-based models for modelling different situations (extension, warping, failure, etc.) may be necessary. Therefore the model- ling of the fabric by directly including the weave geometry and physical behaviour into the model is preferable. Implementations of the woven structure models can be performed by using the finite element method (FEM) computational environments such as LSDYNA, ABAQUS Explicit, DYTRAN, etc. The dimensionality of the obtained models is huge as each yarn has to be presented as the volumetric finite element structure. Moreover, in applications focused on the problem-specific area of the simulation of the physical behaviour of a fabric, significant model im- plementation efforts are necessary. Therefore the development of more efficient physically-based approximate models of a yarn structure is an important issue at the present time.

A hybrid condensed finite element model with GPU acceleration for interactive 3D soft tissue cutting

AbstractTo meet the requirement of computer‐aided medical operations, apart from the real‐time deformation, it is also necessary in the design to simulate the tissue cutting and suturing in a surgery simulation. In this paper, we present a model on topology change and deformation of soft tissue, referred to as the hybrid condensed finite element model, based on the volumetric finite element method. The most important advantage of our model is its ability to achieve an interactive frame rate for the topology change in surgical simulation on standard PC platform. This is achieved through two innovations. One is to apply the condensation technique, by fully calculating the volumetric deformation in the operation part while only calculating the surface nodes in the non‐operation part. Secondly, the major calculation work in the Conjugate Gradient solver for cutting and deformation is migrated from the CPU to the contemporary GPU to promote the calculation. Test examples have been given to show the feasibility and efficiency of the model. Copyright © 2004 John Wiley & Sons, Ltd.

On the predictability of tissue changes for osteotomy planning in maxillofacial surgery: a comparison with postoperative results

A clinical case in maxillofacial surgery is presented, where a congenital hypoplasia of the midface with apparent dental malocclusion was to be treated. A 3D osteotomy planning on a polygonal skull model has been performed for different types of osteotomies, followed by a maxillary advancement under consideration of the implications on the facial soft tissue deformation, using a volumetric finite element approach. The simulation results of isotropic, homogeneous as well as inhomogeneous tissue models using a linear elastic modeling approach are quantitatively evaluated with the help of postoperative CT data.

A mixing-length model for predicting vertical velocity distribution in flows through emergent vegetation

The vertical profiles of streamwise velocities are computed on flood plains vegetated with trees. The calculations were made based on a newly developed one-dimensional model, taking into account the relevant forces acting on the volumetric element surrounding the considered vegetation elements. A modified mixing length concept was used in the model. An important by-product of the model is the method for evaluating the friction velocities, and consequently bed shear stresses, in a vegetated channel. The model results were compared with the relevant experimental results obtained in a laboratory flume in which flood plains were covered by simulated vegetation.

A unit cell-based design support system for composite structures

A unit cell-based design support system (UCBDSS) for composite structural design is introduced. A unit cell is defined as the smallest representative volumetric element to carry the information of composite constituent materials, heterogeneous structures, homogenized mechanical properties, and appropriate manufacturing processes. The database of various composite unit cells is organized to form a unit cell library (UCL). The UCBDSS can intelligently use the information from the UCL to simplify and automate the composite design process, to increase the design efficiency, and to facilitate the tailored composite structure design. The framework of the UCBDSS, its modules, the development of the UCL, the blackboard architecture for design control, and the UCBDSS working environment for Internet-based design are presented.

Simulation of fiber debonding with friction in a model composite pushout test

Abstract The interface failure observed in quasi-static fiber pushout tests performed on a model fiber-reinforced composite is simulated using a cohesive volumetric finite element scheme. The numerical analysis is conducted under axisymmetric condition. The debonding process is captured with the aid of intrinsic rate-independent cohesive elements. The augmented Lagrangian approach is used to solve the frictional contact between the crack faces. The numerical method is first applied to a model polyester/epoxy system, showing excellent agreement with the experimentally obtained load-deflection curve and with the observed evolution of the debonding length. The numerical scheme is then further applied in a parametric study of the effects of the friction coefficient, the interfacial bond strength and the process-induced residual stresses on the fiber–matrix interface failure process.

The evaluation of the Biot–Savart integral

A computational method is described for evaluating the Biot–Savart integral. The approach emphasizes the transformation of the involved integrand into suitable forms, from which integral theorems can be used to reduce the volume integral into line integrals. This method is applied to the case where the density of vorticity (current) distributed over a volumetric element bounded by planar surfaces (straight lines in two-dimensional) is constant and/or linear. The resulting expressions for the volume integral involve closed-form expressions for line integrals along the edges of the element. The evaluation of the line integrals is treated independently for each of the edges as opposed to direct numerical integration. The closed-form formulas are expressed in terms of geometric parameters of the element edges. The versatility of the proposed scheme is demonstrated by applying it to two examples: (i) two-dimensional lid-driven cavity flows; (ii) a magnetic field induced by a toroidal tokamak coil. A systematic extension to the general cases where the vorticity distribution is of higher-order polynomial form is also presented.

Real‐time Volumetric Deformable Models for Surgery Simulation using Finite Elements and Condensation

AbstractThis paper discusses the application of 3D solid volumetric Finite Element models to surgery simulation. In particular it introduces three new ideas for solving the problem of achieving real‐time performance for these models. The simulation system we have developed is described and we demonstrate real‐time deformation using the methods developed in the paper.

4771242 In-vivo spatially encoded magnetic resonance spectroscopy with solvent suppression

A binomial pulse generator (32) selectively generates binomial radio frequency excitation pulses (60) which induce magnetic resonance only in selected hydrogen dipoles and suppresses resonance in others. An inversion pulse generator (34) generates a first inversion pulse (70) in the presence of a first magnetic field gradient (72) generated by a gradient control (22). The inversion pulse only inverts the magnetization of resonating nuclei in a first plane defined by the first magnetic field gradient. A second inversion pulse (74) applied in the presence of a second magnetic field gradient (76) inverts the magnetization of resonating nuclei in a second planar region defined by the second magnetic field gradient. A third inversion pulse (78) applied concurrently with a third magnetic field gradient (80) inverts the magnetization of resonating nuclei in a third planar region defined by the third magnetic field gradient. Only resonating nuclei in a volumetric element defined at the intersection of the first, second, and third planes are inverted all three times. The magnetization of other dipoles will have dephased differently from the dipoles in the volumetric element. In this manner, only the dipoles in the volumetric element contribute to a spin echo (82) which follows the third inversion pulse. Data acquired during the third spin echo may be spectrographically analyzed to determine the chemical composition within the volumetric element. Alternately, a phase encoding gradient (90) and a read gradient (92) may be applied as part of the sequence to provide the appropriate phase encoding to the acquired data such that the acquired data can be reconstructed into an image representation.