S5E7

Abstract

In this research webinar, a general higher-order theory for open and closed curved tubes using a novel curvilinear cylindrical coordinate system for the general hyperelastic material model will be presented. In contrast to the classical Cosserat rod theories, the impetus for this study comes from the need to study bulging and other deformation of tubes (such as arterial walls). First, a novel generalized curvilinear cylindrical coordinate system is introduced in the tube’s reference configuration. This coordinate system is based on a new generalized hybrid frame that contains the well-known orthonormal moving frames of Frenet and Bishop as special cases. Such a coordinate system provides a geometric mapping system to map very complex geometries of the curved tubes with a reference curve (including any general closed curves) having a continuous tangent. Hence, it can be used for analyzing any general pipe-like 3-D structures with a variable cross-section (e.g., artery or vein). The displacement field of the structure’s cross-section is approximated by general basis functions in the polar coordinates in the normal plane, enabling this tube theory to analyze the response to any general loading condition applied to the curved structure. The governing equation is obtained using the virtual work principle for a general hyperelastic material response. The governing equation is solved using a weak form finite element method. Furthermore, the potential application of this tube theory in the bio-mechanics problem, such as blood flow simulation in arteries with moving computational domain, will be discussed. Moreover, I will briefly discuss the general higher-order shell theory for hyperelastic material, highlighting the use of orthonormal (Cartan’s) moving frame in shell theory formulation. This shell theory can analyze large deformation of arbitrarily curved thin or thick, soft shell structures. In both the 1-D tube and shell theories, Cartan’s moving frame is used in contrast to the commonly used natural covariant frame, making the formulations and their numerical models computationally very efficient. Various numerical examples will be presented, illustrating the theories presented, followed by conclusions of the study.

Introduction of speaker

Dr. Archana Arbind is an assistant professor in the mechanical engineering department at the Indian Institute of Technology Kharagpur, India. Her research interest broadly includes applied continuum and computational mechanics and their various applications in modeling natural structures and phenomena. In her graduate research, she has proposed various general higher-order theories for beams, plates, rods, and shells in the classical and Cosserat continuum. Her recent work aims to develop an efficient software tool to solve biomechanics and soft material problems. She is a recipient of Aruna and J. N. Reddy Distinguished Fellow in Computational Mechanics from the Department of Mechanical Engineering, Texas A&M University, and various travel awards from the US national and world congress of computational mechanics. She holds MS and Ph.D. degrees from Texas A&M University, College Station, USA, and B. Tech. degree from IIT Guwahati, India. She worked as a post-doctoral research associate in the department of mechanical engineering at Texas A&M university before joining IIT Kharagpur.

Abstract

Magnesium alloys are promising candidates for replacing conventional alloys in aerospace and automotive applications. However, they are highly anisotropic due to their hexagonal-close-packed crystalline structure, but such anisotropy may be tailored to enhance the performance of advanced materials. Their anisotropy manifest at various scales as it results from low crystal symmetry, strong crystallographic texture, and deformation twinning leading to tension-compression asymmetry. Thus, the plastic flow response is dependent upon orientation and loading mode.

On the other hand, voids are observed to mediate failure in a variety of circumstances. A constitutive theory describing the damage accumulation to failure in ductile materials by void growth and coalescence is developed from the first principles. The interplay between void mediated failure and anisotropic plasticity is not well understood in Magnesium alloys. This is due in part to the lack of comprehensive constitutive formulations for plasticity coupled with damage in this class of materials. Here, progress on two distinct formulations are adopted to predict the ductility and/or strain to failure in magnesium alloys. The first development concerns a two-surface, pressure-insensitive plasticity model to describe the mechanical behavior of damage free materials. The two surfaces separately account for the primary deformation mechanisms of glide and twinning. The model captures the evolving plastic anisotropy

and the tension-compression asymmetry during straining. The second development concerns the effective behavior of porous plastic materials. Two or more surfaces account for one mode of homogeneous yielding (void growth in triaxial tension) and one or more modes of unhomogeneous yielding (void coalescence in triaxial tension and void distortion under severe shear). The model captures failure by internal necking or by void-sheet coalescence quite well. Implementing the new constitutive formulation promises a high-fidelity in high-throughput evaluations of anisotropy dependent failure loci for Mg alloys.

Introduction of speaker

Vignesh is a Ph.D. candidate in the Department of Aerospace Engineering, Texas A&M University. He obtained a master's in Aerospace Engineering from the Indian Institute of Technology, Kanpur. He specializes in Materials and Structures, and his research interests are in Structural mechanics, Finite element methods, Plasticity, and Ductile fracture. He has been working with Dr. Amine Benzerga for the past five years toward obtaining a Ph.D.