A consistent algorithm for finite-strain visco-hyperelasticity and visco-plasticity of amorphous polymers

Shared rheology elements of soft tissues and additive-manufactured amorphous thermoplastics benefit from a common visco-hyperelastic and visco-plastic constitutive framework. For finite-strain and general visco/elastic/plastic constitutive laws, allowing full anisotropy, we use the Kroner-Lee decomposition of the deformation gradient combined with Mandel stress-based yield function. Relatively weak conditions are necessary for specific laws to be incorporated in this framework. For example, stress-like variables present in visco-elasticity are removed from the list of constitutive unknowns. Constitutive iteration is performed for the elastic Cauchy-Green tensor C(e )and the plastic multiplier increment increment delta lambda. The source is here the right Cauchy-Green tensor provided by any discretization. For the integration of the flow law we adopt a scaled/squared series approximation of the matrix exponential. The exact Jacobian of the second Piola-Kirchhoff stress is determined with respect to this source, consistent with the integrator. The resulting system is produced by symbolic source-code generation for each yield function and hyperelastic strain-energy density function with each of the viscous terms added. The constitutive system is solved by a damped Newton-Raphson algorithm with the corresponding stress error being extensively assessed with stress error maps. A cellular beam structure is analyzed and results compared with experiments from our group. Some of the symbolic calculations and closed-form solutions are beyond what is manually achievable and therefore the symbolic sources for this work are made available in a source code repository. (C) 2022 Elsevier B.V. All rights reserved.