scholarly journals Finite element modelling of elastic wave scattering within a polycrystalline material in two and three dimensions

2015 ◽  
Vol 138 (4) ◽  
pp. 2326-2336 ◽  
Author(s):  
Anton Van Pamel ◽  
Colin R. Brett ◽  
Peter Huthwaite ◽  
Michael J. S. Lowe
Keyword(s):  
Finite Element ◽  
Elastic Wave ◽  
Wave Scattering ◽  
Finite Element Modelling ◽  
Polycrystalline Material ◽  
Three Dimensions ◽  
Element Modelling ◽  
Elastic Wave Scattering

scholarly journals Volumetric finite-element modelling of biological growth

Open Biology ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 190057 ◽  
Author(s):  
Richard Kennaway ◽  
Enrico Coen
Keyword(s):  
Finite Element ◽  
Finite Element Modelling ◽  
Shape Change ◽  
Growth Patterns ◽  
Three Dimensions ◽  
Volumetric Growth ◽  
Differential Growth ◽  
Element Modelling ◽  
Wide Range ◽  
Polarity Field

Differential growth is the driver of tissue morphogenesis in plants, and also plays a fundamental role in animal development. Although the contributions of growth to shape change have been captured through modelling tissue sheets or isotropic volumes, a framework for modelling both isotropic and anisotropic volumetric growth in three dimensions over large changes in size and shape has been lacking. Here, we describe an approach based on finite-element modelling of continuous volumetric structures, and apply it to a range of forms and growth patterns, providing mathematical validation for examples that admit analytic solution. We show that a major difference between sheet and bulk tissues is that the growth of bulk tissue is more constrained, reducing the possibility of tissue conflict resolution through deformations such as buckling. Tissue sheets or cylinders may be generated from bulk shapes through anisotropic specified growth, oriented by a polarity field. A second polarity field, orthogonal to the first, allows sheets with varying lengths and widths to be generated, as illustrated by the wide range of leaf shapes observed in nature. The framework we describe thus provides a key tool for developing hypotheses for plant morphogenesis and is also applicable to other tissues that deform through differential growth or contraction.

Sign in / Sign up

Export Citation Format

Share Document