Abstract
A unified methodology to solve problems of frictionless unilateral contact as well as adhesive contact between linear elastic solids is presented. This methodology is based on energetic principles and is casted to a minimization problem of the total potential energy. Appropriate boundary integral forms of the energy are defined and the quadratic problem form of the contact problem is proposed. The problem is solved by the collocation boundary element method (BEM). To solve the quadratic problem two algorithms are developed, both being variants of the well-known conjugate gradient algorithm. The difference between them is given by an explicit construction or not of the quadratic-problem matrix. This matrix has the same physical meaning as the stiffness matrix commonly used in the context of the finite element method (FEM). Both symmetric and non-symmetric formulations of this matrix are presented and discussed, showing that the non-symmetric one provides more accurate results. The present procedure, in addition to its interest by itself, can also be extended to problems where dissipative phenomena take place such as friction, damage and plasticity. Elements of the numerical implementation are briefly presented and the numerical solution of some standard problems of frictionless contact are given and compared to those obtained by other well-known BEM and FEM procedures for contact problems.
Highlights
Contact problems (Johnson, 1985), often present in engineering applications, represent one of the most important and interesting topics of mechanics
Unilateral frictionless contact problems for deformable bodies are usually numerically solved by the finite element method (FEM) or boundary element method (BEM)
The results obtained by this code are compared with the results obtained by 2D BEM codes developed previously by Blázquez et al (1998a,b, 2006), and Graciani et al (2005) in which standard techniques of BEM for contact problems essentially based on the so-called displacement and load scaling techniques (París and Blázquez, 1994) are deployed, as well as by the commercial FEM code ANSYS
Summary
Contact problems (Johnson, 1985), often present in engineering applications, represent one of the most important and interesting topics of mechanics. For crack onset and growth modeling (see Panagiotopoulos et al, 2013; Roubícek et al, 2013), the first two authors with coworkers developed an energy based procedure implemented by BEM In these applications, contact between crack faces should be considered, it is important to present in detail the theoretical background as well as details of the numerical procedure for problems of unilateral (i.e., Signorini) and adhesive frictionless contact. Contact between crack faces should be considered, it is important to present in detail the theoretical background as well as details of the numerical procedure for problems of unilateral (i.e., Signorini) and adhesive frictionless contact Hereinafter, this framework is referred to as Energetic approach for the solution of elastic Contact problems by BEM (EC-BEM).
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