Heiko Topol

Hyperelastic modeling of the combined effects of tissue swelling and deformation-related collagen renewal in fibrous soft tissue

A continuum mechanics constitutive model is presented for the interaction between swelling and collagen remodeling in biological soft tissue. The model is inherently two-way: swelling stretches the collagen fibers which affects their rate of degradation—the remodeled fibrous microarchitecture provides selective directional stiffening that causes the swollen tissue to expand more in the unreinforced directions. The constitutive model specifically treats stretch-stabilization wherein the rate of enzymatic-induced degradation of collagen is a decreasing function of fiber stretch. New collagen replacement takes place in a generally swollen environment, and this synthesis is tracked as a function of time by means of a time integration scheme that accounts for the historical sequence of collagen recreation. The model allows for the specification of the collagen pre-stretch at the time of first synthesis, thus allowing for the consideration of either initially limp replacement fiber or initially pre-tensioned replacement fiber. Loading and swelling that occurs on time scales that are commensurate with the natural time scales for fiber degradation and replacement lead to the consideration of time-integral constitutive equations. Loading and swelling that take place on time scales that are very different from that of the remodeling time scales provide a simplified treatment in which there are definite notions of a short-time instantaneous response and also a large-time approach to a steady-state condition of homeostasis.

Nonlinear Elastic Waves in a 1D Layered Composite Material: Some Numerical Results

We study propagation of strain waves in nonlinear hyperelastic media with microstructure. As an illustrative example, a 1D model of a layered composite material is considered. Numerical results are presented and practical relevancy of the above mentioned effects is discussed.

Periodical Solutions of Certain Strongly Nonlinear Wave Equations

We consider a strongly nonlinear wave equation involving power nonlinearity which allows separation of variables. The exponent of power nonlinearity is chosen as a parameter of asymptotic integration. It is shown that it is possible to construct analytic periodic solutions.

Nonlinear dynamic properties of layered composite materials

We present an application of the asymptotic homogenization method to study wave propagation in a one‐dimensional composite material consisting of a matrix material and coated inclusions. Physical nonlinearity is taken into account by considering the composite’s components as a Murnaghan material, structural nonlinearity is caused by the bonding condition between the components.

Approximate Approach for Nonlinear Deformation and Failure of Fibre Composites

The load‐transfer from a periodical system of fibres to a physically nonlinear layer is herein investigated. We consider a set of cylindrical fibres weakly bonded to a matrix layer and use a composite cylinder assemblage model. The matrix is coated by a thin elastic layer rigidly bonded to the boundaries of the matrix. We treat this coating as an inextensible membrane ideally bonded to the matrix. We propose an asymptotic model consisting of a multilayered interface with thin components. The obtained results are used for the investigation of the fracture of composite materials.

Shear Waves Dispersion in Viscoelastic Composite with Elastic Parallelpiped Inclusions

We present an application of the Floquet‐Bloch approach to the study of wave dispersion in periodic viscoelastic composite materials. Solution is obtained by expanding spatially varying properties of a composite medium in Fourier series and representing unknown displacement fields by infinite plane‐wave expansions. The dispersion curves are obtained, the pass and stop frequency bands are identified.