Well for example the definition often used in the UK is from Elizabeth Stanko[1] and is ‘any form of behaviour by an individual that intentionally threatens to or does cause physical, sexual or psychological harm to others or themselves’. Which comes from "Counting the costs"[2]. Under that definition, threats of harm are explicitly defined as a form of violence.
The definition of a crime of violence[2] in the US also explicitly includes threats as a form of violence. "The term 'crime of violence' means—... (a) an offense that has as an element the use, attempted use, or threatened use of physical force against the person or property of another, or
(b) any other offense that is a felony and that, by its nature, involves a substantial risk that physical force against the person or property of another may be used in the course of committing the offense." (18 USC § 16 my emphasis)
The definition of a crime of violence[2] in the US also explicitly includes threats as a form of violence. "The term 'crime of violence' means—... (a) an offense that has as an element the use, attempted use, or threatened use of physical force against the person or property of another, or (b) any other offense that is a felony and that, by its nature, involves a substantial risk that physical force against the person or property of another may be used in the course of committing the offense." (18 USC § 16 my emphasis)
[1] https://www.researchgate.net/profile/E-Stanko
[2] https://www.researchgate.net/profile/E-Stanko/publication/24...
[3] https://www.law.cornell.edu/uscode/text/18/16