The biomechanical modeling of growing tissues has recently become an area of intense interest. In particular, the interplay between growth patterns and mechanical stress is of great importance, with possible applications to arterial mechanics, embryo morphogenesis, tumor development, and bone remodeling. This review aims to give an overview of the theories that have been used to model these phenomena, categorized according to whether the tissue is considered as a continuum object or a collection of cells. Among the continuum models discussed is the deformation gradient decomposition method, which allows a residual stress field to develop from an incompatible growth field. The cell-based models are further subdivided into cellular automata, center-dynamics, and vertex-dynamics models. Of these the second two are considered in more detail, especially with regard to their treatment of cell-cell interactions and cell division. The review concludes by assessing the prospects for reconciliation between these two fundamentally different approaches to tissue growth, and by identifying possible avenues for further research.

We develop a model of the buckling (both planar and axial) of capillaries in cancer tumours, using nonlinear solid mechanics. The compressive stress in the tumour interstitium is modelled as a consequence of the rapid proliferation of the tumour cells, using a multiplicative decomposition of the deformation gradient. In turn, the tumour cell proliferation is determined by the oxygen concentration (which is governed by the diffusion equation) and the solid stress. We apply a linear stability analysis to determine the onset of mechanical instability, and the Liapunov-Schmidt reduction to determine the postbuckling behaviour. We find that planar modes usually go unstable before axial modes, so that our model can explain the buckling of capillaries, but not as easily their tortuosity. We also find that the inclusion of anisotropic growth in our model can substantially affect the onset of buckling. Anisotropic growth also results in a feedback effect that substantially affects the magnitude of the buckle.

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One of the enticing features common to most of the two-dimensional (2D) electronic systems that, in the wake of (and in parallel with) graphene, are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in the system. Since the electronic properties are ultimately determined by the details of atomic orbital overlap, such mechanical manipulations translate into modified (or, at least, perturbed) electronic properties. Here, we present a general-purpose optimization framework for tailoring physical properties of 2D electronic systems by manipulating the state of local strain, allowing a one-step route from their design to experimental implementation. A definite example, chosen for its relevance in light of current experiments in graphene nanostructures, is the optimization of the experimental parameters that generate a prescribed spatial profile of pseudomagnetic fields (PMFs) in graphene. But the method is general enough to accommodate a multitude of possible experimental parameters and conditions whereby deformations can be imparted to the graphene lattice, and complies, by design, with grapheneʼs elastic equilibrium and elastic compatibility constraints. As a result, it efficiently answers the inverse problem of determining the optimal values of a set of external or control parameters (such as substrate topography, sample shape, load distribution, etc) that result in a graphene deformation whose associated PMF profile best matches a prescribed Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.target. The ability to address this inverse problem in an expedited way is one key step for practical implementations of the concept of 2D systems with electronic properties strain-engineered to order. The general-purpose nature of this calculation strategy means that it can be easily applied to the optimization of other relevant physical quantities which directly depend on the local strain field, not just in graphene but in other 2D electronic membranes.2 New J. Phys. 16 (2014) 093044 G W Jones and V M Pereira

Cartilage tissue repair procedures currently under development aim to create a construct in which patient-derived cells are seeded and expanded ex vivo before implantation back into the body. The key challenge is producing physiologically realistic constructs that mimic real tissue structure and function. One option with vast potential is to print strands of material in a 3D structure called a scaffold that imitates the real tissue structure; the strands are composed of gel seeded with cells and so provide a template for cartilaginous tissue growth. The scaffold is placed in the construct and pumped with nutrient-rich culture medium to supply nutrients to the cells and remove waste products, thus promoting tissue growth.In this paper we use asymptotic homogenization to determine the effective flow and transport properties of such a printed scaffold system. These properties are used to predict the distribution of nutrient/waste products through the construct, and to specify design criteria for the scaffold that will optimise the growth of functional tissue. Keywords