A dynamic contact problem with history-dependent operators

In this paper we present results on existence, uniqueness and convergence of solutions to the Cauchy problem for abstract first order evolutionary inclusion which contains two operators depending on the history of the solution. These results are applicable to a dynamic contact problem for viscoelastic materials with a normal compliance contact condition with memory and a friction law in which the friction bound depends on the magnitude of the tangential displacement. The proofs are based on recent results for hemivariational inequalities and a fixed point argument

Duality Arguments in the Analysis of a Viscoelastic Contact Problem

We consider a mathematical model which describes the quasistatic frictionless contact of a viscoelastic body with a rigid-plastic foundation. We describe the mechanical assumptions, list the hypotheses on the data and provide three different variational formulations of the model in which the unknowns are the displacement field, the stress field and the strain field, respectively. These formulations have a different structure. Nevertheless, we prove that they are pairwise dual of each other. Then, we deduce the unique weak solvability of the contact problem as well as the Lipschitz continuity of its weak solution with respect to the data. The proofs are based on recent results on history-dependent variational inequalities and inclusions. Finally, we present numerical simulations in the study of the contact problem, together with the corresponding mechanical interpretations.Comment: 25 pages, 4 figure

Modelling and well-posedness of evolutionary differential variational-hemivariational inequalities

In this paper, we study the well-posedness of a class of evolutionary variational-hemivariational inequalities coupled with a nonlinear ordinary differential equation in Banach spaces. The proof is based on an iterative approximation scheme showing that the problem has a unique mild solution. In addition, we established continuity of the flow map with respect to the initial data. Under the general framework, we consider two new applications for modelling of frictional contact with viscoelastic materials, where the friction coefficient $\mu$ depends on an external state variable $\alpha$ and the slip rate $|\dot{u}_\tau|$. In the first application, we consider Coulomb friction with normal compliance, and in the second, normal damped response. In both cases, we present a new first-order approximation of the Dieterich rate-and-state friction law

Implementation and validation of a cohesive fracture model through contact mechanics with application to cutting and needle insertion into human skin

Understanding the highly non-linear biomechanics of the complex structure of human skin would not only provide valuable information for the development of biological comparable products that could be used for the improvement, restoration or maintenance of the biological tissue or replacement of the whole organ, but would also support the development of an advanced computational model (e.g. finite element skin models) that do not differ (or do not differ very much!) from experimental data. This could be very useful for surgical training, planning and navigation. In particular, the major goal of this thesis was the development of robust and easy to use computational models of the cutting and tearing of soft materials, including large deformations, and the development of repeatable, reproducible and reliable physical skin models in comparison to in-ex vivo human skin samples. In combination with advanced computational/mechanical methods, these could offer many possibilities, such as optimised device design which would be used for effective and reproducible skin penetration in the clinical setting and for in vivo measurements. To be able to carry out experimental cutting tests, physical models of skin were manufactured in the laboratory using silicone rubber. The mechanical properties of the physical models were examined experimentally by applying tensile and indentation tests to the test models using the Zwick universal testing machine and the Digital Image Correlation (DIC) System. To estimate the mechanical properties of the physical models and calculate the quantities, Poisson’s ratio, Young’s modulus and shear modulus -which were used later in computational cutting models - and inverse analyses were performed for each example of manufactured silicone rubber in the laboratory using the analytical study on indentation method, the curve fitting technique and DIC measurements. Then, the results were compared to the mechanical properties of human skin experimentally obtained in vivo/ ex vivo (from published studies). A new large deformation cohesive zone formulation was implemented using contact mechanics, which allows easy definition of crack paths in conventional finite element models. This was implemented in the widely used open source FE package FEBio through modification of the classical contact model to provide a specific implementation of a mesh independent method for straightforward controlling of (non-linear) fracture mechanical processes using the Mixed Mode Cohesive-Zone method. Additionally, new models of friction and thermodynamically coupled friction were developed and implemented. The computational model for the simulation of the cutting process (the finite element (FE) model of cutting) was reduced to the simplified model for the sharp interaction (triangular prisms wedge cutting), where the Neo Hookean hyperelastic material model was chosen to represent the skin layers for the FEM analysis. Practical, analytical and experimental verification tests, alongside convergence analysis, were performed. Comparison of the computational results with the analytical and experimental results revealed that applying the modified contact algorithm to the fracture problem was effective in predicting and simulating the cutting processes

15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS

From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare