Relaxed incremental variational formulation for damage at large strains with application to fiber-reinforced materials and materials with truss-like microstructures

• Published in: International journal for numerical methods in engineering Vol. 92; no. 6; pp. 551 - 570
• Main Authors: Balzani, Daniel, Ortiz, Michael
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 09.11.2012; Wiley; Wiley Subscription Services, Inc
• Subjects: Biological and medical sciences; Blood vessels and receptors; damage; Exact sciences and technology; fiber-reinforced materials; finite strains; Fracture mechanics (crack, fatigue, damage...); Fundamental and applied biological sciences. Psychology; Fundamental areas of phenomenology (including applications); homogenization; incremental variational formulation; multiscale; Physics; relaxation; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Vertebrates: cardiovascular system; Performance evaluation; damage; High strain; Energy function; Fiber reinforced material; incremental variational formulation; Modeling; Composite material; Cantilever beam; Hyperelasticity; finite strains; Relaxation; Reinforced beam; Variational calculus; Continuous medium; Convexity; Vascular wall; Damaging; Strain softening; Strain energy; Homogenization; Reinforced structure; Truss structure; Multiscale method; Microstructure; Effective medium model; fiber-reinforced materials; multiscale; Non convex analysis
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4351

SUMMARY In this paper, an incremental variational formulation for damage at finite strains is presented. The classical continuum damage mechanics serves as a basis where a stress‐softening term depending on a scalar‐valued damage function is prepended an effective hyperelastic strain energy function, which describes the virtually undamaged material. Because loss of convexity is obtained at some critical deformations, a relaxed incremental stress potential is constructed, which convexifies the original nonconvex problem. The resulting model can be interpreted as the homogenization of a microheterogeneous material bifurcated into a strongly and weakly damaged phase at the microscale. A one‐dimensional relaxed formulation is derived, and a model for fiber‐reinforced materials based thereon is given. Finally, numerical examples illustrate the performance of the model by showing mesh independency of the model in an extended truss, analyzing a numerically homogenized microtruss material and investigating a fiber‐reinforced cantilever beam subject to bending and an overstretched arterial wall. Copyright © 2012 John Wiley & Sons, Ltd.