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On the use of the QR or upper triangular decomposition in finite elasticity

Arun Srinivasa (Texas A&M University)

SES Medal Symposium in honor of D.J. Steigmann

Tue 9:00 - 10:30

MacMillan 115

In developing constitutive equations for finite elasticity, it is traditional to use the Cauchy Green Stretch tensor C (and the related tensor U) and develop constitutive equations based on suitably chose algebraic invariants of C. Recently, the difficulties of such an approach with regard to parameter identification have been highlighted. In this work, I will show that that rather than using the polar decomposition, it is more convenient to we use the QR or upper triangular decomposition of the deformation gradient and show how constitutive equations for elastic materials can be developed in a relatively simple way. The physical meaning of the upper triangular decomposition will also be discussed so that its appealing simplicity in terms of shear and stretch becomes evident. I will demonstrate that the components of the rotated Cauchy stress in this formulation can be related to individual derivatives of the strain energy function. This approach also does not suffer from the covariance problems associated with experimental parameter identification.