Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects

• Published in: Computer methods in applied mechanics and engineering Vol. 399; p. 115456
• Main Authors: Weeger, Oliver, Schillinger, Dominik, Müller, Ralf
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2022; Elsevier BV
• Subjects: Algorithms; B spline functions; Beamforming; Collocation methods; Constitutive models; Deformation effects; Discretization; Elasto-visco-plasticity; Formability; Geometrically exact 3D beams; Inelastic materials; Isogeometric collocation; Kinematics; Mathematical models; Metamaterials; Mixed methods; Mullin’s effect; Nonlinear differential equations; Resultants; Softening; Viscoplastic materials; Viscoplasticity; Inelastic materials; Isogeometric collocation; Geometrically exact 3D beams; Elasto-visco-plasticity; Mixed methods; Mullin’s effect
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2022.115456

A geometrically nonlinear, shear-deformable 3D beam formulation with inelastic material behavior and its numerical discretization by a mixed isogeometric collocation method are presented. In particular, the constitutive model captures elasto-visco-plasticity with damage/softening from Mullin’s effect, which applies to the modeling of metallic and polymeric materials, e.g., in additive manufacturing applications and metamaterials. The inelastic material behavior is formulated in terms of thermodynamically consistent internal variables for viscoelastic and plastic strains and isotropic and kinematic hardening variables, as well as accompanying evolution equations. A mixed isogeometric collocation method is applied for the discretization of the strong form of the quasi-static nonlinear differential equations. Thus, the displacements of the centerline curve, the cross-section orientations, and the stress resultants (forces and moments) are discretized as B-spline or NURBS curves. The internal variables are defined only locally at the collocation points, and an implicit return-mapping algorithm is employed for their time discretization. The method is verified in comparison to 1D examples as well as reference results for 3D beams. Furthermore, its applicability to the simulation of beam lattice structures subject to large deformations and instabilities is demonstrated. [Display omitted] •Geometrically exact, shear-deformable 3D beam model with inelastic material behavior.•Thermodynamically consistent inelastic material model using internal variables.•Discretization by a mixed isogeometric collocation method using spline curves.•Mixed collocation cures locking and avoids higher derivatives of internal variables.•Applicability to beams and structures subject to large deformations and instabilities.