Vratislav Kafka

Surface fissures in articular cartilage: new concepts, hypotheses and modeling

OBJECTIVE Clarification and mesomechanical modeling of the inception of fissures at the surface of articular cartilage. DESIGN Articular cartilage is described as a macroscopically heterogeneous medium consisting of zones - layers - with different orientation of collagen fibers. BACKGROUND Degradation of mechanical properties of cartilage is a serious, still not fully clarified problem that deserves attention. METHODS Theoretical analysis based on a survey of known experimental findings related to the subject. The general authors mesomechanical concept of modeling heterogeneous media is applied to the elucidation and description of the formation of fissures at the surface of articular cartilage. RESULTS Our model clarifies how the high tensile stresses in the collagen fibers of the superficial tangential zone depend on the rate of loading. CONCLUSIONS The superficial cracks are caused predominantly by a very quick loading. This explains among others the high incidence of post-traumatic osteoarthritis of the lower extremity after accidents and injuries in sports. RELEVANCE Superficial fissures in articular cartilage are observed in joints with primary osteoarthritis. The current study specifies the kinds of loading that lead to their inception.

On the mechanical function of tendon

A mesoscopic approach is followed for mathematical modelling of the specific deformation properties of tendon. The approach starts from our general concept of modelling mechanical behaviour of heterogeneous media and assumes that the structure of tendon is optimized in such a way that it enables its adjacent muscle to work with a constant performance in the course of increasing loading (acting like a gearbox in a car). The model based on this assumption gives results that are in a very good accordance with observed properties of tendons. Clinical experience reveals that if this function of tendon is violated pathological changes appear in the respective muscle. RELEVANCE: Clarification and mathematical modelling of the mechanical function of tendon is of intellectual interest in its own right, but it is important also for cautioning surgeons against unnecessary violation of this function, and for tissue engineering aspects if tendon must be replaced.

Necking and softening as a consequence of latent continuum damage

Abstract Necking and softening in ductile polycrystalline metals are modeled as consequences of continuum damage (CD) that consists in braking through of barriers resisting plastic deformation. Our model describes these materials as two-phase continua consisting of microdomains with easy glide and barriers with decreasing continuity in the course of deformation. Macroscopic homogeneity and increase of macroscopic stress with increasing deformation are conditioned by sufficient continuity of these barriers. Our model describes the whole course of engineering stress–strain diagrams up to rupture and the differences in the diagrams for test specimens of different length. The model is compared to experimental data measured on two materials − sorbitic steel and an AlMg3 alloy.

An Overview of Applications of the Mesomechanical Approach to Shape Memory Phenomena - Completed by a New Application to Two-way Shape Memory

An overview of the wide possibilities of applications of the authors mesomechanical concept to shape memory (SM) phenomena is presented, and a new application worked out for modeling the two-way SM is framed in this concept. Explanation of the common background of the different methods of training the two-way SM is presented. It is demonstrated, how and why, specific kinds of deformation lead to improvement or impairment of the two-way SM.

A MESOMECHANICAL CONSTITUTIVE MODELING APPLIED TO CUMULATIVE DAMAGE AND NECKING

Mesomechanical constitutive modeling is applied to modeling cumulative damage and necking. The model is applied to the description of necking in specimens under uniaxial tension, and compared with experimental results received with specimens of pure iron and Fe-2.75wt%Si alloy. The process is modeled as a change in the structure; i.e. as a successive loss of continuity of the substructure of barriers resisting plastic deformation. It is shown that this model can be used for the evaluation of continuum damage, and of the description of: (i) the stress-strain diagrams up to rupture, (ii) the effect of the length of the specimen, (iii) the development of the form of the neck and its final form at rupture, (iv) the creation of internal residual energy.

Surface fissures in articular cartilage: effect of pathological changes in synovial fluid

OBJECTIVE A unified mathematical model of two different modes of inception of fissures at the surface of articular cartilage in healthy and pathological joints. DESIGN The superficial tangential zone of articular cartilage is modeled as a three-phase medium consisting of collagen fibers, matrix, and of infiltrated thin constituent of synovial fluid. BACKGROUND The authors general mesomechanical concept is applied to the analysis of deterioration of articular cartilage. METHODS Theoretical analysis based on the results of the authors preceding paper. RESULTS The presented analysis shows that superficial fissures in articular cartilage can also be caused by pathological thinning of synovial fluid. CONCLUSIONS Whereas in healthy joints the probable cause of creation of fissures at the surface of cartilage was shown to be fast impact loading, in joints with inflammatory synovial fluid the fissures can be caused by plain walking. RELEVANCE Appearance of surface fissures in articular cartilage is a serious, still not fully clarified problem that deserves attention.

Shape Memory Elements in Bending: Influence of the Shape of their Cross-Section

The effect of the shape of the cross-section of a bent prismatic bar on its shape memory recovery moment is investigated. The analysis is based on the mathematical model of the first author (Kafka, 1994a, 1994b, 2001). The area of the cross-section of the bar is assumed to be constant, the shape of the cross-section is varied. The investigated shapes are rectangles with various relations of their sides, and a circular cross-section. It is assumed that the rod is bent above elastic limit and unloaded at room temperature, which results in macroscopic residual stresses giving zero bending moment, and in residual internal variables descriptive of the change of the state of the material. Then, the resulting form is held fixed and temperature of the rod is raised. Due to the increase of temperature there arise recovery stresses resulting in recovery moments. These moments—depending on the shape of the cross-section—are calculated, and in this way the effectiveness of the shape of the cross-section is evaluated. In the case of a rectangular cross-section the effect of the relation of the sides is strongly non-linear, the effect of the circular cross-section is lower by 20% than that of a square cross-section.

Mathematical modelling of the incomplete transformations in pseudoelastic processes in binary alloys

In his two papers Kafka (1994,1994a) presented a new approach to explanation and to mathematical modelling of shape memory effect and of pseudoelasticity. This approach was based on his general concept of modelling inelastic processes in heterogeneous media (Kafka 1987) and it was shown that this concept can successfiilly be applied even in the case where the heterogeneity under study is on the atomic scale, i.e. in the case of binary alloys and their shape memory behaviour. In the second quoted paper (Kafka 1994a) quantitative comparisons with experimental data received with samples ofNiTi alloy were shown and it was demonstrated that the unified mathematical model is able to quantitatively describe the shape memory effect as well as the pseudoelastic processes under different temperatures.

Constitutive Equation of Concrete: Mesomechanical Isotropic Model

The general concept of mesomechanical constitutive modeling developed by the first author is applied to the description of inelastic mechanical behavior of concrete under very complex loading in three orthogonal directions. Concrete is modeled as an isotropic heterogeneous medium consisting of elastic inclusions that are embedded in a plastically deforming and fracturing matrix. The fracturing process of the matrix results in cumulative damage, in changes of elastic moduli, and in volumetric expansion. It was the confrontation with the complex experimental data presented in this study that led us to a new version of the hypotheses on which our special model for concrete is based. Three kinds of deformation modes in different loading segments are differentiated: elastic‐plastic‐damaging deformation, elastic‐plastic deformation, and only elastic deformation. Criteria for distinguishing between these three kinds of deformation are newly formulated. The results of this isotropic mesoscale model are shown to a...

Shape Memory: Heterogeneity and Thermodynamics

Shape memory (SM) of some mechanical systems is a very useful and widely used property. In a broader sense, this term relates not only to the special ‘shape memory materials’, but also to all elastic bodies, springs, bi-metals, and generally to many mechanical actuators, such as thermostats and others. The aim of our contribution is to show that all these systems or materials have one common factor: at least one elastic or thermoelastic continuous substructure. Some of these systems are composed of only thermoelastic substructures, e.g. of two thermoelastic materials in the case of bi-metals. In such a case the system works without dissipation of mechanical energy. On the other hand, if taking into consideration the spongy bone, tendons or cartilage, the viscous constituent, that ensures very useful dissipation of energy in cases of dangerous impacts, is present in the material. But even here, the material contains the elastic substructures composed of collagen and elastin that ensure SM. Similar situation is found in some shock-absorbers.