Physics of Soft Bodies

Handouts

• Motion and Deformation
• Finite Element Approximation
• Computing Static Deformation
• Computing Dynamic Deformation
• Deformation Models
• Inelastic Deformation
• Isotropy and Invariants

Sample Program List

• One-dimensional Soft Body Model
• Two-dimensional Soft Body Model
• Three-dimensional Soft Body Model
• Static Deformation (2D)
• Static Deformation (3D)
• Dynamic Deformation (2D)
• Inelastic Deformation (2D)

Sample Programs: One-dimensional Soft Body Model

• dynamic deformation of a 1D soft body model
• dynamic equation under constraint
• dynamic equation of free motion
• pushing force
• reaction force from floor
• searching a specified value in ascending ordered column vector

Sample Programs: Two-dimensional Soft Body Model

• class NodalPoint
• class Triangle
• class Contour
• class Body

• calculating Lamé's constants
• nodal points and triangles of a rectangular body
• searching a specified value in ascending ordered column vector

• class SubRegion
• class Rectangle

Sample Programs: Three-dimensional Soft Body Model

• class NodalPoint
• class Tetrahedron
• class Surface
• class Body

• calculating Lamé's constants
• nodal points and tetrahedra of a cuboidal body
• searching a specified value in ascending ordered column vector

Sample Programs: Static Deformation (2D)

• Let's get started

• Deformation of rectangle body

• Expansion of membrane by pressure
• area of a polygon (directory two_dim_fea)
• gradient of area of a polygon (directory two_dim_fea)

• Deformation of layered bodies

• Cauchy and Green strains (deformed by external force)
• Cauchy and Green strains (rectangle elements, deformed by external force)
• Cauchy and Green strains (deformed by gravity)

Cauchy strain	Green strain	Cauchy strain	Green strain

• Deformation of layered body by inner pressure

• Elastic ring deformed by spring actuators
• nodal points and triangles of a ring body (directory two_dim_fea)

natural	under gravity	A1
A2	A2, A6	A2, A6, A7

• Elastic ring deforming on floor

A1, A5	on floor

Sample Programs: Static Deformation (3D)

• twisting a beam (Cauchy strain)
• twisting a beam (Green strain)

natural	Cauchy strain	Green strain

• membrane expansion by pressure
• nodal forces equivalent to pressure application

natural	40 kPa	80 kPa

Sample Programs: Dynamic Deformation (2D)

• deforming 2D soft robot model (4×4)
• deforming 2D soft robot model (10×10)

• jumping 2D soft robot model (4×4)
• jumping 2D soft robot model (10×10)

• dynamic expansion of a membrane by pressure

• beam bending (Cauchy strain)
• beam bending (Green strain)
• calculating Green strain based forces (directory two_dim_fea)

• jumping 2D soft robot model (4×4) rectangular elements
• jumping 2D soft robot model (10×10) rectangular elements

• rolling of elastic ring

Cauchy strain	Green strain

damping 2	damping 200	damping 20000

• rolling of elastic ring driven by spring actuators

Sample Programs: Inelastic Deformation (2D)

• class Triangle_ThreeElementModel
• class Body_ThreeElementModel
• class SubRegion_ThreeElementModel

• deforming 2D rheological model (three-element model) (4×4)
• deforming 2D rheological model (three-element model) (10×10)

• deforming layered rheological model (three-element model) (4×4)
• deforming layered rheological model (three-element model) (10×10)