A novel model for one-dimensional morphoelasticity. Part I - Theoretical foundations

While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previously-derived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.\ud \ud In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on one-dimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a three-dimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop one-dimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblast-populated collagen lattice, which we further investigate in Part II

Verification of a mathematical model for layered T-beams

CER73-74MLK-MEC-JRG-JB-EGT-MDV28.March 1974.Includes bibliographical references.An experimental program and the verification of a mathematical model for layered T-beams, developed assuming small deflection theory and including effects of interlayer slip, are described in this report. This research is a part of an overall program to develop a verified analysis procedure for wood joist floor systems. After a description of the construction and load-testing of 14 two-and three-layered T-beams, a brief discussion on the mechanical properties of the materials used is given. The deflections observed in the loading tests are then compared with the predicted deflections given by the mathematical model, which used a finite element solution technique. These comparisons for the fourteen T-beams, including two and three-layered systems, formed the primary basis for the verification of the mathematical model. Test results provided by a manufacturer of joist systems were also compared to the mathematical model. Good agreement between the observed and theoretical values were obtained for all tests. These favorable results show the validity of this general layered beam theory

An Alternative Framework for Developing Material Models for Finite-Strain Elastoplasticity

Contemporary plasticity theories and their related material models for finite deformations are either based on additive decomposition of a strain-rate tensor or on multiplicative decomposition of a deformation gradient tensor into an elastic part and a plastic part. From the standpoint of the nonlinear continuum mechanics, the former theories, which are used to model hypoelastic-plastic materials, are rather incomplete theories, while the latter theories, which are used to model hyperelastic-plastic materials, are not even continuum-based theories, while none of their related material models are thermodynamically consistent. Recently, a nonlinear continuum theory for finite deformations of elastoplastic media was proposed, which allows for the development of objective and thermodynamically consistent material models. Therefore, the analysis results of the models are independent of the description and the particularities of their mathematical formulation. Here by the description we mean total or updated Lagrangian description and by the particularities of formulation, the ability to describe the model in various stress spaces using internal mechanical power conjugate stress measures and strain rates. In this chapter, an alternative framework for developing objective and thermodynamically consistent hypoelastic-plastic- and hyperelastic-plastic-based material models is presented using the first nonlinear continuum theory of finite deformations of elastoplastic media

Physical theory of the twentieth century and contemporary philosophy

It has been shown that the criticism of Pauli as well as of Susskind and Glogover may be avoided if the standard quantum-mechanical mathematical model has been suitably extended. There is not more any reason for Einstein's citicism, either, if in addition to some new results concerning Bell's inequalities and Belifante's argument are taken into account. The ensemble interpretation of quantum mechanics (or the hidden-variable theory) should be preferred, which is also supported by the already published results of experiments with three polarizers. Greater space in the text has been devoted also to the discussion of epistemological problems and some philosophical consequences.Comment: 12 page

Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives

Mechanics of fluid membranes may be described in terms of the concepts of mechanical deformations and stresses, or in terms of mechanical free-energy functions. In this paper, each of the two descriptions is developed by viewing a membrane from two perspectives: a microscopic perspective, in which the membrane appears as a thin layer of finite thickness and with highly inhomogeneous material and force distributions in its transverse direction, and an effective, two-dimensional perspective, in which the membrane is treated as an infinitely thin surface, with effective material and mechanical properties. A connection between these two perspectives is then established. Moreover, the functional dependence of the variation in the mechanical free energy of the membrane on its mechanical deformations is first studied in the microscopic perspective. The result is then used to examine to what extent different, effective mechanical stresses and forces can be derived from a given, effective functional of the mechanical free energy.Comment: 37 pages, 3 figures, minor change