Panayiotis Papadopoulos

Automotive disc brake squeal

Disc brake squeal remains an elusive problem in the automotive industry. Since the early 20th century, many investigators have examined the problem with experimental, analytical, and computational techniques, but there is as yet no method to completely suppress disc brake squeal. This paper provides a comprehensive review and bibliography of works on disc brake squeal. In an effort to make this review accessible to a large audience, background sections on vibrations, contact and disc brake systems are also included.

A mixed formulation for the finite element solution of contact problems

Abstract In this paper we present a finite element algorithm for the static solution of two-dimensional frictionless contact problems involving bodies undergoing arbitrarily large motions and deformations. A mixed penalty formulation is employed in approximating the resulting variational inequalities. The algorithm is applied to quadratic elements along with a rational scheme for determining the contacting regions. Several numerical simulations illustrate the applicability and accuracy of the proposed solution procedure.

An experimental study of the superelastic effect in a shape-memory Nitinol alloy under biaxial loading

Abstract Constitutive laws for shape-memory alloys subjected to multiaxial loading, which are based on direct experimental observations, are generally not available in the literature. Accordingly, in the present work, tension–torsion tests are conducted on thin-walled tubes (thickness/radius ratio of 1:10) of the polycrystalline superelastic/shape-memory alloy Nitinol using various loading/unloading paths under isothermal conditions. The experimental results show significant variations in the mechanical response along the two loading axes. These are attributed to changes in the martensitic variants nucleated in response to the directionality of the applied loading, as well as to microstructural texture present in the parent material. Numerical simulations suggest that the characterization and modeling of the microstructure is of paramount importance in understanding the phenomenology of shape-memory alloys.

Plate bending elements with discrete constraints: New triangular elements

Abstract In recent years a series of elements based on Reissner-Mindlin assumptions and using discrete (collocation type) constraints has been introduced. These elements have proved to be very effective, however their relation to straightforward mixed approximations has not been clear. In this paper this relationship is discussed and the reasons for their success explained. This allows new and effective triangular elements to be developed. The presentation shows the close relationships with the DKT (Discrete Kirchhoff Theory) element previously available only for thin plates and allows extension of their applications

Ultrascalable Implicit Finite Element Analyses in Solid Mechanics with over a Half a Billion Degrees of Freedom

The solution of elliptic diffusion operators is the computational bottleneck in many simulations in a wide range of engineering and scientific disciplines. We present a truly scalable-ultrascalable-algebraic multigrid (AMG) linear solver for the diffusion operator in unstructured elasticity problems. Scalability is demonstrated with speedup studies of a non-linear micro-finite element analyses of a human vertebral body with over a half of a billion degrees of freedom on up to 4088 processors on the ACSI White machine. This work is significant because in the domain of unstructured implicit finite element analysis in solid mechanics with complex geometry, this is the first demonstration of a highly parallel and efficient application of a mathematically optimal linear solution method on a common large scale computing platform — the IBM SP Power3.

On the formulation and numerical solution of problems in anisotropic finite plasticity

Abstract This article discusses an extension of the Green–Naghdi finite plasticity theory to explicitly include anisotropic effects in the stress response, yield condition, flow rule and hardening rule. Constitutive models are developed within the context of the extended theory and used in formulating implicit integration algorithms which inherit the characteristics of the classical return-mapping scheme of isotropic plasticity. Representative numerical simulations demonstrate the applicability and predictive capacity of the proposed model in the presence of large plastic deformations.

A general framework for the numerical solution of problems in finite elasto-plasticity

This article discusses a general framework for the analysis of initial/boundary-value problems of rate-independent finite elasto-plasticity based on the theory of Green and Naghdi. A constitutive model is developed within the context of the above theory employing generalized measures of Lagrangian strain and work-conjugate measures of stress. Computational implications of the proposed formulation are discussed in conjunction with an implicit time integrator for the differential/algebraic equations of plastic flow. Representative numerical simulations demonstrate the applicability and predictive capacity of the model in the presence of large plastic deformations.

A simple algorithm for three-dimensional finite element analysis of contact problems

Abstract This paper addresses the numerical solution of three-dimensional frictionless contact problems by a finite element method. The two-body contact problem is considered in the context of fully non-linear kinematics. The impenetrability constraint is satisfied via a classical penalty formulation. The contacting surfaces are discretized by means of projections of the interacting element faces onto suitably chosen flat surfaces. Attention is focused on the efficiency of the overall algorithm. Numerical simulations are conducted for a series of test problems to assess the performance of the proposed methodology.

A Lagrange multiplier method for the finite element solution of frictionless contact problems

This article proposes a novel Lagrange multiplier-based formulation for the finite element solution of the quasi-static two-body contact problem in the presence of finite motions and deformations. The main idea rests in the interpretation of the two-body contact as a composition of two simultaneous Signorini-like problems, which naturally yield geometrically unbiased approximations of the kinematics and kinetics of frictionless contact. A two-dimensional finite element is introduced that exactly satisfies the impenetrability constraint and allows for the direct computation of consistent pressure distributions on the interacting surfaces.

Numerical Modeling of Stress in Stenotic Arteries With Microcalcifications: A Micromechanical Approximation

Most finite element models of atherosclerotic arteries do not account for the heterogeneity of the plaque constituents at the microscale. Failure of plaque lesions has been shown to be a local event, linked to stress concentrations caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. There is growing evidence that microcalcifications exist in the fibrous cap of plaque lesions. However, their role is not yet fully understood. The goal of the present work is to investigate the effects of localized regions of microcalcifications on the stress field of atherosclerotic plaque caps in a section of carotid artery. This is achieved by performing finite element simulations of three-dimensional fluid-structure interaction models. The material response in the region of microcalcification is modeled using a combination of finite elements, homogenization theory, and a stress concentration function that approximates the average local stresses in the fibrous tissue and microcalcification phases. The results indicate that the circumferential stress in the fibrous tissue phase increases as the volume fraction of microcalcifications is increased, and that the stress exceeds a critical threshold when the fibrous cap thickness is decreased. Furthermore, the presence of the microcalcifications significantly influences the distribution of stress by shifting the maximum circumferential stress away from the cap shoulders, where failure is most common when the effective region of microcalcification is located at the center of the cap. This is a possible explanation of why 40% of plaque ruptures occur away from the shoulder region of the cap.