A novel approach to modelling and simulating the contact behaviour between a human hand model and a deformable object

A deeper understanding of biomechanical behaviour of human hands becomes fundamental for any human hand-operated Q2 activities. The integration of biomechanical knowledge of human hands into product design process starts to play an increasingly important role in developing an ergonomic product-to-user interface for products and systems requiring high level of comfortable and responsive interactions. Generation of such precise and dynamic models can provide scientific evaluation tools to support product and system development through simulation. This type of support is urgently required in many applications such as hand skill training for surgical operations, ergonomic study of a product or system developed and so forth. The aim of this work is to study the contact behaviour between the operators’ hand and a hand-held tool or other similar contacts, by developing a novel and precise nonlinear 3D finite element model of the hand and by investigating the contact behaviour through simulation. The contact behaviour is externalised by solving the problem using the bi-potential method. The human body’s biomechanical characteristics, such as hand deformity and structural behaviour, have been fully modelled by implementing anisotropic hyperelastic laws. A case study is given to illustrate the effectiveness of the approac

Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions

We analytically and numerically analyze groundwater flow in a homogeneous soil described by the Richards equation, coupled to surface water represented by a set of ordinary differential equations (ODE's) on parts of the domain boundary, and with nonlinear outflow conditions of Signorini's type. The coupling of the partial differential equation (PDE) and the ODE's is given by nonlinear Robin boundary conditions. This article provides two major new contributions regarding these infiltration conditions. First, an existence result for the continuous coupled problem is established with the help of a regularization technique. Second, we analyze and validate a solver-friendly discretization of the coupled problem based on an implicit-explicit time discretization and on finite elements in space. The discretized PDE leads to convex spatial minimization problems which can be solved efficiently by monotone multigrid. Numerical experiments are provided using the DUNE numerics framework.Comment: 34 pages, 5 figure

Space-time adaptive finite elements for nonlocal parabolic variational inequalities

This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic variational inequalities associated to the fractional Laplacian we obtain a priori and a posteriori error estimates and study the resulting space-time adaptive mesh-refinement procedures. Particular emphasis is placed on mixed formulations, which include the contact forces as a Lagrange multiplier. Corresponding results are presented for elliptic problems. Our numerical experiments for $2$-dimensional model problems confirm the theoretical results: They indicate the efficiency of the a posteriori error estimates and illustrate the convergence properties of space-time adaptive, as well as uniform and graded discretizations.Comment: 47 pages, 20 figure

Boundary Integral Formulation of Frictionless Contact Problems Based on an Energetic Approach and Its Numerical Implementation by the Collocation BEM

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 the 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. Essential steps of the numerical implementation are briefly presented and the numerical solutions of some standard problemsof frictionless contact are given and compared to those obtained by other well-known BEM and FEM procedures for contact problems.Junta de Andalucía TEP-4051European Social Fund TEP-4051Spanish Ministry of Science and Innovation MAT2009-14022Spanish Ministry of Economy and Competitiveness MAT2012-37387 MAT2015-71036-PEuropean Regional Development Fund MAT2012-37387 MAT2015-71036-PSpanish Ministry of Education AP2009-3968Stavros Niarchos Foundatio

A CutFEM method for Stefan-Signorini problems with application in pulsed laser ablation

In this article, we develop a cut finite element method for one-phase Stefan problems, with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the melting/vaporisation temperature is represented by a fictitious gas phase. The moving interface between the workpiece and the fictitious gas phase may cut arbitrarily through the elements of the finite element mesh, which remains fixed throughout the simulation, thereby circumventing the need for cumbersome re-meshing operations. The primal/dual formulation of the linear one-phase Stefan problem is recast into a primal non-linear formulation using a Nitsche-type approach, which avoids the difficulty of constructing inf-sup stable primal/dual pairs. Through the careful derivation of stabilisation terms, we show that the proposed Stefan-Signorini-Nitsche CutFEM method remains stable independently of the cut location. In addition, we obtain optimal convergence with respect to space and time refinement. Several 2D and 3D examples are proposed, highlighting the robustness and flexibility of the algorithm, together with its relevance to the field of micro-manufacturing

Error estimates for Stokes problem with Tresca friction condition

In this work we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type non-linear boundary conditions. Two Lagrange multipliers are used to enforce div(u)=0 constraint and to regularize the energy functional. The resulting problem is discretised using "P1 bubble/P1-P1" finite elements. Error estimates are derived and several numerical studies are achieved