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A gradient theory of finite viscoelasticity. (English) Zbl 0877.73025
Summary: We present a theory which is founded on the concept of internal fields, in conjunction with a variational principle and the dissipation inequality. The internal variables, which in local theories obey local evolution equations, have been replaced by internal fields and their gradients, which arise from physical processes that involve non-affine deformation. These fields obey “internal” field equations and appropriate boundary and initial conditions. As a result, uniform boundary tractions give rise to inhomogeneous strain fields. This phenomenon is illustrated in one dimension, where it is shown that the creep function, normally a function of time only, is a function of space as well as time, even though the material domain is phenomenologically homogeneous.

74D10 Nonlinear constitutive equations for materials with memory