scholarly journals Understanding the deformation gradient in Abaqus and key guidelines for anisotropic hyperelastic user material subroutines (UMATs)

2019 ◽  
Author(s):  
David Nolan ◽  
Caitriona Lally ◽  
Patrick McGarry
Keyword(s):  
Local Coordinate System ◽  
Deformation Gradient ◽  
Worked Examples ◽  
Local Deformation ◽  
Cauchy Stress ◽  
Precise Understanding ◽  
Key Issues ◽  
Key Steps ◽  
Orientation Systems ◽  
Global And Local

This tutorial paper provides a step-by-step guide to developing a comprehensive understanding of the different forms of the deformation gradient used in Abaqus, and outlines a number of key issues that must be considered when developing an Abaqus user defined material subroutine (UMAT) in which the Cauchy stress is computed from the deformation gradient. Firstly, we examine the "classical" forms of global and local deformation gradients. We then show that Abaqus/Standard does not use the classical form of the local deformation gradient when continuum elements are used, and we highlight the important implications for UMAT development. We outline the key steps that must be implemented in developing an anisotropic fibre-reinforced hyperelastic UMAT for use with continuum elements and local orientation systems. We also demonstrate that a classical local deformation gradient is provided by Abaqus/Standard if structural (shell and membrane) elements are used, and by Abaqus/Explicit for all element types. We emphasise, however, that the majority of biomechanical simulations rely on the use of continuum elements with a local coordinate system in Abaqus/Standard, and therefore the development of a hyperelastic UMAT requires an in-depth and precise understanding of the form of the non-classical deformation gradient provided as input by Abaqus. Several worked examples and case studies are provided for each section, so that the details and implications of the form of the deformation gradient can be fully understood. For each worked example in this tutorial paper the source files and code (Abaqus input files, UMATs, and Matlab script files) are provided, allowing the reader to efficiently explore the implications of the form of the deformation gradient in the development of a UMAT.

Nonuniform Stress Field Determination Based on Deformation Measurement

2021 ◽  
pp. 1-26
Author(s):  
Cheng Liu
Keyword(s):  
Principal Stress ◽  
Deformation Gradient ◽  
Deformation Measurement ◽  
Cauchy Stress ◽  
Kirchhoff Stress ◽  
Nonuniform Deformation ◽  
Principal Stretch ◽  
Stress Orientation ◽  
Lagrangian Strain ◽  
Stretch Orientation

Abstract We demonstrate a technique that, under certain circumstances, will determine stresses associated with a nonuniform deformation field without knowing the detailed constitutive behavior of the deforming material. This technique is based on (1) a detailed deformation measurement of a domain and (2) the observation that for isotropic materials, the strain and the stress, which form the so-called work-conjugate pair, are co-axial, or their eigenvectors share the same direction. The particular measures for strain and stress considered are the Lagrangian strain and the second Piola-Kirchhoff stress. The deformation measurement provides the field of the principal stretch orientation θλ and since the Lagrangian strain and the second Piola-Kirchhoff stress are co-axial, the principal stress orientation θs of the second Piola-Kirchhoff stress is determined. The Cauchy stress is related to the second Piola-Kirchhoff stress through the deformation gradient tensor, which can be measured experimentally. We then show that the principal stress orientation θσ of the Cauchy stress is the sum of the principal stretch orientation θλ and the local rigid-body rotation θq, which is determinable by the deformation gradient through polar decomposition. With the principal stress orientation θσ known, the equation of equilibrium, now in terms of the two principal stresses σ1 and σ2, and θσ, can be solved numerically with appropriate traction boundary conditions. The technique is then applied to the experimental case of nonuniform deformation of a PVC sheet with a circular hole and subject to tension. Limitations and restrictions of the technique and possible extensions will be discussed.

scholarly journals Influencing factors of global and local deformation in hot compression

2018 ◽  
Vol 15 ◽  
pp. 381-387
Author(s):  
Baohui Tian ◽  
Siegfried Kleber ◽  
Silvia Schneller ◽  
Peter Markiewicz
Keyword(s):  
Influencing Factors ◽  
Local Deformation ◽  
Hot Compression ◽  
Global And Local

scholarly journals A novel thermo-mechanical coupling approach for thermal fracturing of rocks in the three-dimensional FDEM

2020 ◽  
Vol 7 (5) ◽  
pp. 935-946 ◽  
Author(s):  
Clément Joulin ◽  
Jiansheng Xiang ◽  
John-Paul Latham
Keyword(s):  
Thermal Expansion ◽  
Deformation Gradient ◽  
Linear Thermal Expansion ◽  
Three Dimensional ◽  
Cauchy Stress ◽  
Reinforced Concrete Structure ◽  
Expansion Formula ◽  
Mechanical Coupling ◽  
Coupling Approach ◽  
Thermal Fracturing

Abstract This paper presents a new three-dimensional thermo-mechanical (TM) coupling approach for thermal fracturing of rocks in the finite–discrete element method (FDEM). The linear thermal expansion formula is implemented in the context of FDEM according to the concept of the multiplicative split of the deformation gradient. The presented TM formulation is derived in the geo-mechanical solver, enabling thermal expansion and thermally induced fracturing. This TM approach is validated against analytical solutions of the Cauchy stress, thermal expansion and stress distribution. Additionally, the thermal load on the previously validated configurations is increased and the resulting fracture initiation and propagation are observed. Finally, simulation results of the cracking of a reinforced concrete structure under thermal stress are compared to experimental results. Results are in excellent agreement.

scholarly journals Skeleton-Based Gesture Recognition Using Several Fully Connected Layers with Path Signature Features and Temporal Transformer Module

2019 ◽  
Vol 33 ◽  
pp. 8585-8593 ◽  
Author(s):  
Chenyang Li ◽  
Xin Zhang ◽  
Lufan Liao ◽  
Lianwen Jin ◽  
Weixin Yang
Keyword(s):  
Gesture Recognition ◽  
Network Architecture ◽  
Temporal Dynamics ◽  
Classification Model ◽  
Feature Descriptor ◽  
Temporal Features ◽  
Key Issues ◽  
Motion Characteristics ◽  
Fully Connected ◽  
Global And Local

The skeleton based gesture recognition is gaining more popularity due to its wide possible applications. The key issues are how to extract discriminative features and how to design the classification model. In this paper, we first leverage a robust feature descriptor, path signature (PS), and propose three PS features to explicitly represent the spatial and temporal motion characteristics, i.e., spatial PS (S PS), temporal PS (T PS) and temporal spatial PS (T S PS). Considering the significance of fine hand movements in the gesture, we propose an ”attention on hand” (AOH) principle to define joint pairs for the S PS and select single joint for the T PS. In addition, the dyadic method is employed to extract the T PS and T S PS features that encode global and local temporal dynamics in the motion. Secondly, without the recurrent strategy, the classification model still faces challenges on temporal variation among different sequences. We propose a new temporal transformer module (TTM) that can match the sequence key frames by learning the temporal shifting parameter for each input. This is a learning-based module that can be included into standard neural network architecture. Finally, we design a multi-stream fully connected layer based network to treat spatial and temporal features separately and fused them together for the final result. We have tested our method on three benchmark gesture datasets, i.e., ChaLearn 2016, ChaLearn 2013 and MSRC-12. Experimental results demonstrate that we achieve the state-of-the-art performance on skeleton-based gesture recognition with high computational efficiency.

Non-Rigid Liver Registration in Liver Computed Tomography Images Using Elastic Method with Global and Local Deformations

2021 ◽  
Vol 11 (3) ◽  
pp. 810-816
Author(s):  
Taeyong Park ◽  
Jeongjin Lee ◽  
Juneseuk Shin ◽  
Kyoung Won Kim ◽  
Ho Chul Kang
Keyword(s):  
Computed Tomography ◽  
Liver Cancer ◽  
Ct Images ◽  
Local Deformation ◽  
Rigid Registration ◽  
Liver Ct ◽  
Liver Surface ◽  
Global And Local ◽  
Local Deformations

The study of follow-up liver computed tomography (CT) images is required for the early diagnosis and treatment evaluation of liver cancer. Although this requirement has been manually performed by doctors, the demands on computer-aided diagnosis are dramatically growing according to the increased amount of medical image data by the recent development of CT. However, conventional image segmentation, registration, and skeletonization methods cannot be directly applied to clinical data due to the characteristics of liver CT images varying largely by patients and contrast agents. In this paper, we propose non-rigid liver segmentation using elastic method with global and local deformation for follow-up liver CT images. To manage intensity differences between two scans, we extract the liver vessel and parenchyma in each scan. And our method binarizes the segmented liver parenchyma and vessel, and performs the registration to minimize the intensity difference between these binarized images of follow-up CT images. The global movements between follow-up CT images are corrected by rigid registration based on liver surface. The local deformations between follow-up CT images are modeled by non-rigid registration, which aligns images using non-rigid transformation, based on locally deformable model. Our method can model the global and local deformation between follow-up liver CT scans by considering the deformation of both the liver surface and vessel. In experimental results using twenty clinical datasets, our method matches the liver effectively between follow-up portal phase CT images, enabling the accurate assessment of the volume change of the liver cancer. The proposed registration method can be applied to the follow-up study of various organ diseases, including cardiovascular diseases and lung cancer.

Global and local deformation behavior and mechanical properties of individual phases in a quenched and partitioned steel

2015 ◽  
Vol 630 ◽  
pp. 27-35 ◽  
Author(s):  
I. de Diego-Calderón ◽  
D. De Knijf ◽  
M.A. Monclús ◽  
J.M. Molina-Aldareguia ◽  
I. Sabirov ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Deformation Behavior ◽  
Local Deformation ◽  
Global And Local

A method to reconstruct myocardial sarcomere lengths and orientations at transmural sites in beating canine hearts

1992 ◽  
Vol 263 (1) ◽  
pp. H293-H306 ◽  
Author(s):  
E. K. Rodriguez ◽  
W. C. Hunter ◽  
M. J. Royce ◽  
M. K. Leppo ◽  
A. S. Douglas ◽  
...  
Keyword(s):  
Sarcomere Length ◽  
Deformation Gradient ◽  
Local Deformation ◽  
Left Ventricular ◽  
Reference State ◽  
Cellular Processes ◽  
Chamber Volume ◽  
Length Changes ◽  
Whole Heart ◽  
Cyclic Changes

The ability to measure cyclic changes in myocardial sarcomere lengths and orientations during cardiac ejection and filling would improve our understanding of how the cellular processes of contraction relate to the pumping of the whole heart. Previously, only postmortem sarcomere measurements were possible after arresting the heart in one state and fixing it for histology. By combining such histological measurements with direct observations of the deformation experienced by the same myocardial region while the heart was beating, we have developed a method to reconstruct sarcomere lengths and orientations throughout the cardiac cycle and at several transmural layers. A set of small (1 mm) radiopaque beads was implanted in approximately 1 cm3 of the left ventricular free wall. Using biplane cineradiography, we tracked the motion of these markers through various cardiac cycles. To quantify local myocardial deformation (as revealed by the relative motion of the markers), we calculated the local deformation gradient tensors. As the heart deforms, these describe how any short vectorial line segment alters its length and orientation relative to a reference state. Specifically, by choosing the reference state to be the arrested and fixed heart and by measuring the sarcomere vector in that state, we could then use the deformation gradient tensors to reconstruct the sarcomere vector that would exist in the beating heart. As ventricular chamber volume varied over its normal range of operation, the range of reconstructed sarcomere lengths (approximately 1.7-2.4 microns) was comparable to other histological studies and to measurements of sarcomere length in excised papillary muscles or trabeculae. The pattern of sarcomere length changes was markedly different, however, during ejection vs. filling.

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