Yuki Yamakawa

Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain

Abstract We introduce the notion of two-scale kinematics and the procedure of two-scale linearization , which are indispensable to the simultaneous two-scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain. These are accomplished by formulating the two-scale boundary value problem in both material and spatial descriptions with reference to the two-scale modeling strategy developed in [Comput. Methods Appl. Mech. Engrg. 190 (40–41) (2001) 5427] that utilized the convergence results of mathematical homogenization. The formulation brings the intimate relationship between micro- and macro-scale kinematics in describing the micro–macro coupling behavior inherent in heterogeneous media. It is also shown that the two-scale linearization necessitates the strict consistency with the micro-scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions. Several numerical examples of simultaneous two-scale computations are presented to illustrate the two-scale nature of the deformation of a heterogeneous solid at finite strain.

Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids

The diffuse mode bifurcation of elastoplastic solids at finite strain is investigated. The multiplicative decomposition of deformation gradient and the hyperelasto-plastic constitutive relationship are adapted to the numerical bifurcation analysis of the elastoplastic solids. First, bifurcation analyses of rectangular plane strain specimens subjected to uniaxial compression are conducted. The onset of the diffuse mode bifurcations from a homogeneous state is detected; moreover, the post-bifurcation states for these modes are traced to arrive at localization to narrow band zones, which look like shear bands. The occurrence of diffuse mode bifurcation, followed by localization, is advanced as a possible mechanism to create complex deformation and localization patterns, such as shear bands. These computational diffuse modes and localization zones are shown to be in good agreement with the associated experimental ones observed for sand specimens to ensure the validity of this mechanism. Next, the degradation of horizontal sway stiffness of a rectangular specimen due to plane strain uniaxial compression is pointed out as a cause of the bifurcation of the first antisymmetric diffuse mode, which triggers the tilting of the specimen. Last, circular and punching failures of a footing on a foundation are simulated.

Introduction to Finite Strain Theory for Continuum Elasto-Plasticity: Hashiguchi/Introduction to Finite Strain Theory for Continuum Elasto-Plasticity

Elasto-plastic deformation is frequently observed in machines and structures, hence its prediction is an important consideration at the design stage. Elasto-plasticity theories will be increasingly required in the future in response to the development of new and improved industrial technologies. Although various books for elasto-plasticity have been published to date, they focus on infi nitesimal elasto-plastic deformation theory. However, modern computational techniques employ an advanced approach to solve problems in this fi eld and much research has taken place in recent years into fi nite strain elasto-plasticity. This book describes this approach and aims to improve mechanical design techniques in mechanical, civil, structural and aeronautical engineering through the accurate analysis of fi nite elasto-plastic deformation.

Mode switching and recursive bifurcation in granular materials

Abstract The existence of the “mode switching” and “recursive bifurcation” behavior in granular materials (sand triaxial-compression-test specimens) under shearing is revealed. Group-theoretic bifurcation theory is employed to categorize bifurcation modes through the observation of deformation patterns of these materials, and hence to detect the occurrence of recursive bifurcation. A bifurcation point search technique is developed and applied to a strain versus stress curve of a specimen to identify the presence of a series of bifurcation points associated with the recursive bifurcation. In addition, an imperfection sensitivity law is employed to testify the occurrence of mode switching between two dominant bifurcation modes. Curves of strain versus stress undergoing mode switching and recursive bifurcation are simulated well by the bifurcation equation. The predominant role of mode switching and recursive bifurcation in shearing behavior of the granular materials is clearly demonstrated and fully described with the use of the bifurcation theory.

Biological-data-based finite-element stress analysis of mandibular bone with implant-supported overdenture

BACKGROUND This study aimed to evaluate the stress distribution in a mandibular bone with an implant-supported overdenture by a biological-data-based finite element analysis (FEA) utilizing personal CT images and in vivo loading data, and to evaluate the influence of the number and alignment of implants and bone conditions on the stress in peri-implant bone. METHODS FEA models of a mandible were constructed for two types of overdentures: 4 implants supported overdenture (4-OD) and 2 implants supported overdenture (2-OD). The geometry of these models was constructed from CT images of a subject, who wore an implant-supported overdenture. The magnitude and direction of the loads on the implants for two types of overdentures during the maximal voluntary clenching were measured with 3D force transducers. FEA using these loads was carried out to observe stress distributions in peri-implant bone. RESULTS Higher stress was observed in cortical bone around the implant neck. Stress in peri-implant bone for 4-OD was reduced in comparison with those for the 2-OD. For the 4-OD, notwithstanding such reduction of the stress, the stress concentrated at the cortical bone around the implant aligned with large deviation from load direction. CONCLUSIONS In this study, biological data from a certain subject was successfully duplicated to the FEA models. The results demonstrate the mechanical prominence of using more implants. Even in 4 implants model, high stress was found around an implant with a large inclination and with thin cortical bone. This suffices to demonstrate the capability and usefulness of the biological-data-based FEA.

Stress distribution in the peri-implant bone with splinted and non-splinted implants by in vivo loading data-based finite element analysis.

The aim of this study was to evaluate stress distribution in peri-implant bone and to investigate the influence of splinting implants by finite element analysis (FEA) with in vivo loading data. The magnitude and direction of the force exerted on implants during maximal voluntary clenching of a subject were recorded with 3-D piezoelectric force transducers. FEA using in vivo loading data was conducted on splinted and non-splinted models with two implants. Overall, the splinted model reduced stress in peri-implant bone in comparison with the non-splinted model.

Finite Strain Elastoplastic Constitutive Equation Based on Subloading Surface Model

The finite elastoplastic constitutive equation incorporating the initial subloading surface model and the explicit constitutive equation of metal are formulated by the authors. In this article, the formulation of the finite elastoplastic constitutive equation incorporating the extended subloading surface model is attempted, in which the formulation for evolution rule of the similarity-center of the subloading and the normal-yield surfaces is required. The evolution rule of the similarity-center is proposed for metals with von Mises yield condition.