Shigenobu Okazawa

Recursive bifurcation of tensile steel specimens

Failure modes of steel specimens subjected to uniaxial tension are investigated. These modes are well known to display complex geometrical characteristics of deformation accompanied by the plastic instability behavior. As an underlying mechanism of such complexity, we here focus on the recursive occurrence of bifurcations. In the theory, the rule of recursive bifurcation of a rectangular parallelepiped domain is obtained by the group-theoretic bifurcation theory so as to exhaust all the mathematically possible courses of bifurcation. In the experiment, we examine the representative failure modes with reference to the rules to identify actual courses of recursive bifurcation. Three-dimensional finite element analysis of a thin specimen is conducted to observe the recursive bifurcation, in which diffuse necking is formed by the direct bifurcation and the single shear band by the secondary bifurcation. The recursive bifurcation has thus been identified as the mechanism to create the complex failure modes.

Imperfection sensitivity and probabilistic variation of tensile strength of steel members

Elastic stability theory is applied to description of tensile strength variation in steel members due to variation of initial imperfections, despite criticism on the occurrence of unloading due to plastic instability. In numerical simulation of such members, the maximum load is attained at a limit point or a hilltop bifurcation point. This load is not much different for either type of point; hence, little attention has been paid to the type of points up to now. Yet it is noteworthy that these two types of points follow different imperfection sensitivity laws within the framework of elastic stability theory. Numerical experiments on steel members undergoing plastic deformation are conducted to ensure that empirical imperfection sensitivities for these members agree well with those sensitivity laws. This assesses applicability of elastic stability theory to description of plastic instability behaviors of steel members. Moreover, empirical histograms of steel members obtained through Monte-Carlo simulations are compared with theoretical probabilities of maximum loads, which are a normal distribution for the limit point and a Weibull-like one for the hilltop point. Therefore, elastic stability theory is useful to describe tensile strength variation of steel members.

EULERIAN FINITE COVER METHOD FOR SOLID DYNAMICS

In order to deal with the kinematic and dynamic boundary conditions in the Eulerian framework, we develop an Eulerian finite cover method (FCM) for large deformation solid dynamics by incorporating the approximation strategy of the FCM into the existing Eulerian explicit finite element method. The operator split method is employed to solve Eulerian solid dynamics problems, and the resulting numerical algorithm consists of two steps. One is the nonadvective step, in which the standard Lagrangian FC analysis is carried out with the explicit time integration scheme, and the other is the advective step, in which the CIVA method is applied to project the solution obtained in the nonadvective step to the Eulerian mesh. Two representative numerical examples are presented to validate the proposed Eulerian FCM and demonstrate its capability especially in appropriately treating the kinematic and dynamic boundary conditions.

Simulations of Needle Insertion by Using a Eulerian Hydrocode FEM and the Experimental Validations

In this paper, simulations for needle insertion were performed by using a novel Eulerian hydrocode FEM, which was adaptive for large deformation and tissue fracture. We also performed experiments for the same needle insertion with silicon rubbers and needles, which had conical tips of different angles in order to investigate the accuracy of the simulations. The resistance forces in the simulations accurately followed those in the experiments until the conical portion of the needle was inside the rubbers, and the validation of the Eulerian hydrocode was revealed. However, the present simulation showed that after the conical portion was inside the tissue, the simulated resistance forces became lower than the experimental ones. The proportional increase of the friction forces and the roughly flatness of the tip force along the time were simulated. It was predicted that the tightening force along the needle side was underestimated.

New Material Model for Describing Large Deformation of Pressure Sensitive Adhesive

A material model to describe large deformation of pressure sensitive adhesive (PSA) is presented. A relationship between stress and strain of PSA includes viscoelasticity and rubber-elasticity. Therefore, we propose the material model for describing viscoelasticity and rubber-elasticity and formulate the presented material model for finite element analysis. And we validate the present formulation by using one axis tensile calculation.

Eulerian-Lagrangian Coupling in Finite Element Calculations With Applications to Machining

Multi-material Eulerian finite element methods are attractive for problems in solid mechanics where new free surfaces are created, e.g., the formation of chips in machining. One weakness associated with the Eulerian finite element formulation, however, is the interaction of materials at the contact interface. The standard mixture theories effectively bond the materials together, and prohibit the relative slip between the materials that is crucial for an accurate machining simulation. In this paper, we compare the results of a machining calculation performed using an Eulerian formulation with a contact mixture theory and a coupled Eulerian-Lagrangian calculation, where the workpiece is Eulerian, and the tool is Lagrangian.Copyright

Finite Element Seismic Response Analysis of a Reinforced Concrete Pier with a Fractured Fine Tetrahedron Mesh

A seismic response analysis of a reinforced concrete (RC) pier has been undertaken using seismic waves recorded at the Takatori station during the southern Hyogo perfecture earthquake in 1995 in Japan. Distinguishing characteristics of this analysis are as follows. First, the RC pier has been modeled using the finite element method with a solid mesh. The analysis model has been generated using tetrahedral elements with node connectivity, not only in the concrete but also in the reinforcement steel. Also, an analysis has been undertaken on fracture treatments in the concrete. Using PDS-FEM, a system of suitable fractures in the concrete resulting from the seismic event can be simulated. Ultimately, a finite element model is established with a fine tetrahedron mesh with about 20 million elements. We calculate a seismic response analysis using the K computer at the RIKEN Advanced Institute for Computational Science, and compare that result with a seismic experiment in E-Defense to confirm the computational approach.

Contact Algorithm for Eulerian Finite Element Method

The Euelrian finite element method fixes computational meshes and materials flow through the fixed meshes, and allows arbitrary large deformations and new free surfaces. A special algorithm, however, is indispensable for contact mechanics in Eulerian formulation. This study applies a simple contact algorithm for Eulerian finite element method to plastic working simulation.

Simulations of High‐Speed Machining Using a Multi‐Material Finite Element Formulation

Machining is a manufacturing process that is difficult to simulate because the generation of new free surfaces is difficult to model in a computational setting. Other processes which deform material but don’t alter its topology, such as stamping and forging, are routinely modeled with commercial software on a production basis in industry. While many research challenges remain in modeling them, they are mature areas relative to machining. Previous efforts have primarily focused on extending Lagrangian finite element methods, which have well‐developed algorithms for contact, to permit new free surfaces. The approach taken here is to extend an Eulerian finite element formulation, which has a well‐developed algorithm for generating new free surfaces, to model contact.