Hyper-elastic Materialsmi@se.ed.cn
Hyper-elastic Materials
Outline·Introduction（引言）·Mechanical behavior of rubbers（橡胶性能）·Mechanical behaviorofpolymericfoams（泡沫性能）·Strainmeasure（应变度量）·Stress measure（应力度量）·Generalized constitutive law（一般本构关系）·Incompressibility（不可压缩性）·Polynomialmodels for rubbers（橡胶多项式本构）·More sophisticated rubber models（复杂本构）·Foam constitutive models（泡沫本构）·Calibrating nonlinearelastic models（模型校准）2
Outline • Introduction（引言） • Mechanical behavior of rubbers（橡胶性能） • Mechanical behavior of polymeric foams（泡沫性能） • Strain measure（应变度量） • Stress measure（应力度量） • Generalized constitutive law（一般本构关系） • Incompressibility（不可压缩性） • Polynomial models for rubbers（橡胶多项式本构） • More sophisticated rubber models（复杂本构） • Foam constitutive models（泡沫本构） • Calibrating nonlinear elastic models（模型校准） 2
Introduction: Main applications of the theory are (1) to model therubbery behavior of a polymeric material and (2) to modelpolymeric foams that can be subjected to large reversibleshape changes (e.g., a sponge). In general, the response of a typical polymer is stronglydependent on temperature, strain history, and loading rateShear modulus (N/m?2)ViscoelasticGlassy109RubberyMelt105Glass transitiontemperatureTTemperature3
Introduction 3 Shear modulus (N/m2 ) • Main applications of the theory are (1) to model the rubbery behavior of a polymeric material and (2) to model polymeric foams that can be subjected to large reversible shape changes (e.g., a sponge). • In general, the response of a typical polymer is strongly dependent on temperature, strain history, and loading rate
Introduction. Rubbery behavior: the response is elastic, the stress does not dependstrongly on strain rate or strain history, and the modulus increaseswithtemperature. Heavily cross-linked polymers (elastomers) are the most likely toshow ideal rubbery behavior.Hyperelastic constitutive laws are intended to approximate thisrubbery behavior.Shearmodulus (N/m?)ViscoelasticGlassy109RubberyMelt105Glass transitiontemperatureTTemperature4
Introduction 4 Shear modulus (N/m2 ) • Rubbery behavior: the response is elastic, the stress does not depend strongly on strain rate or strain history, and the modulus increases with temperature. • Heavily cross-linked polymers (elastomers) are the most likely to show ideal rubbery behavior. • Hyperelastic constitutive laws are intended to approximate this rubbery behavior
Mechanical Behavior of Rubbers. Features of the behavior of a solid rubber:> The material is close to ideally elastic> The material strongly resists volume changes. The bulk modulus iscomparable with that of metals> The material is very compliant in shear: shear modulus is of theorder of 10-5 times that of most metals> The material is isotropic.> The shear modulus is temperature dependent: the material becomesstiffer as it is heated, in sharp contrast to metals5
• Features of the behavior of a solid rubber: Mechanical Behavior of Rubbers 5 The material is close to ideally elastic. The material strongly resists volume changes. The bulk modulus is comparable with that of metals. The material is very compliant in shear: shear modulus is of the order of 10−5 times that of most metals. The material is isotropic. The shear modulus is temperature dependent: the material becomes stiffer as it is heated, in sharp contrast to metals