This paper describes modern techniques used to solve contact problems within Computational Mechanics. On the basis of a continuum description of contact, the mathematical structure of the contact formulation for finite element methods is derived. Emphasis is also placed on the constitutive behavior at the contact interface for normal and tangential (frictional) contact. Furthermore, different discretization schemes currently applied to solve engineering problems are formulated for small and finite strain problems. These include isoparametric interpolations, node-to-segment discretizations and also mortar and Nitsche techniques. Furthermore, several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed. Here, especially the penalty and Lagrange multiplier schemes are considered and also SQP- and linear-programming methods are reviewed.


Keywords:

contact mechanics;
friction;
penalty method;
Lagrange multiplier method;
contact algorithms;
finite element method;
finite deformations;
discretization methods

Computational Contact Mechanics

Vibration based condition monitoring refers to the use of in situ non-destructive sensing and analysis of system characteristics –in the time, frequency or modal domains –for the purpose of detecting changes, which may indicate damage or degradation. In the field of civil engineering, monitoring systems have the potential to facilitate the more economical management and maintenance of modern infrastructure. This paper reviews the state of the art in vibration based condition monitoring with particular emphasis on structural engineering applications.

Vibration Based Condition Monitoring: A Review:

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

Multi-scale computational homogenization: Trends and challenges

1 Formulation of the equations of motion 2 Element energy functions 3 Introduction to the finite element displacement method 4 In-plane vibration of plates 5 Vibration of solids 6 Flexural vibration of plates 7 Vibration of stiffened plates and folded plate structures 8 Vibration of shells 9 Vibration of laminated plates and shells 10 Hierarchical finite element method 11 Analysis of free vibration 12 Forced response 13 Forced response II 14 Computer analysis technique

Introduction to finite element vibration analysis

Second-order computational homogenisation:scale transition and enforcement of RVE boundary conditions

There are many similarities and unifying aspects between the seemingly different discontinuous modelling frameworks and formulations (Discrete Element Method DEM, Combined DEM/FEM, MDEM Modified Distinct Element Method, Discontinuous Deformation Analysis DDA, Non Smooth Contact Dynamics NSCD, Stress Based DEM). This is reflected in the manner they deal with the characterisation of bodies geometry and the contact detection, with the imposition of contact constraints and boundary conditions, with the definition and description of bodies deformability, fracturing and fragmentation, the transition from continua to discontinua as well as the associated time stepping algorithms… Some modelling aspects and illustrative applications of three specific discontinuous computational frameworks will be considered—rigid body spring method (RBSM), discontinuous deformation analysis (DDA) and non-smooth contact dynamics (NSCD)—applicable for analyses of solids and structures with both existing and/or emerging dis...

Nenad Bićanić

Papers

Second-order computational homogenisation:scale transition and enforcement of RVE boundary conditions

Discontinuous modelling of cohesive-frictional blocky materials

A Numerical Model for Prediction of Spalling of Concrete Exposed to Elevated Temperatures

Modelling of Transport Processes in Concrete at Elevated Temperatures

Djelomično prevrtanje slobodno položenog blokovskog stupca pri dinamičkoj pobudi